genetic_algorithm.log

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2023-12-18 20:50:34,763 - INFO - Number List: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]
2023-12-18 20:50:34,763 - INFO - Bucket Size: 1000
2023-12-18 20:50:34,769 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Optimize and research innovative methods to enhance an algorithm\'s performance. Develop new mathematical approaches for superior efficiency.\n\n        Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Develop a Python function named \'optimized_bucket_filler\'. This function should take two parameters: a list of numbers (\'numbers\') and a bucket size limit (\'bucket_limit\'). \n        2. The function\'s task is to optimize and arrange the numbers into buckets, each adhering to the bucket size limit. Each bucket should contain numbers that sum up to less than or equal to the \'bucket_limit\'.\n        3. Ensure that the function handles edge cases and operates safely with list manipulations to avoid errors like \'IndexError\'.\n        4. Create pseudocode for the \'optimized_bucket_filler\' function. The pseudocode should clearly describe the logic and steps involved in the function, including handling of edge cases.\n        5. The final output should consist solely of the function definition and the corresponding pseudocode. Do not include function calls or print statements in the output.\n        6. If no specific pip dependencies are required for the function, default the \'pip_command\' to \'None\'.\n        7. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        8. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition",\n            "pseudocode": "Pseudocode describing the logic of \'optimized_bucket_filler\'",\n            "equation": "Mathematical Logic in LaTeX representing the Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
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2023-12-18 20:51:07,105 - INFO - ----- Master Program Details -----
2023-12-18 20:51:07,106 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    # First, sort the numbers list to optimize bucket allocations.
    numbers.sort(reverse=True)

    # Initialize empty buckets and an index to keep track of bucket placement
    buckets = []
    bucket_index = -1

    # Iterate through each number in the list
    for number in numbers:
        # Handle edge case: If a single number is larger than the bucket limit, it can't be placed.
        if number > bucket_limit:
            continue

        # Attempt to place the number in an existing bucket
        placed = False
        for i, bucket in enumerate(buckets):
            if sum(bucket) + number <= bucket_limit:
                bucket.append(number)
                placed = True
                break

        # If the number was not placed, create a new bucket
        if not placed:
            buckets.append([number])

    return buckets
2023-12-18 20:51:07,106 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item For each element $l$ in $L$:
    \begin{itemize}
        \item If $l > B$, continue to next iteration.
        \item Iterate over buckets $k$:
        \item If $\sum k + l \leq B$:
            \begin{itemize}
                \item Append $l$ to $k$.
                \item Break the loop.
            \end{itemize}
        \item If $l$ was not placed in any bucket, create a new bucket with $l$.
    \end{itemize}
    \item Return collection of buckets.
\end{itemize}
2023-12-18 20:51:07,106 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list
    SET bucket_index to -1

    FOR each number in numbers
        IF number is larger than bucket_limit
            CONTINUE to next iteration
        SET placed as False

        FOR each bucket in buckets
            IF sum of bucket and number is less than or equal to bucket_limit
                APPEND number to bucket
                SET placed as True
                BREAK the loop

        IF not placed
            CREATE a new bucket with number

    RETURN buckets
2023-12-18 20:51:07,107 - INFO - ----- Master Results Evaluation -----
2023-12-18 20:51:07,113 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
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2023-12-18 20:51:33,725 - ERROR - An error occurred during parent generation: No module named 'sortedcontainers'. Retrying...
2023-12-18 20:51:33,730 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Contextual Note: In the process of optimizing the algorithm, it\'s crucial to avoid replicating any previously generated algorithms that are already recorded as parents in the GeneticAlgorithmConfig. Each iteration must be unique in terms of its approach, methodology, and results.\n\n        Previous Attempt Details:\n        - Program Code: \n        No module named \'sortedcontainers\'\n\n        - Error Message: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # Improve initial sorting to group close values together for more efficient packing\n    numbers.sort()\n\n    # Use a binary search tree to store and efficiently find the best-fit bucket for each number\n    from sortedcontainers import SortedList\n    buckets = SortedList(key=lambda x: bucket_limit - sum(x))\n\n    for number in numbers:\n        # Skip number if it exceeds the bucket limit\n        if number > bucket_limit: continue\n\n        # Find the least-full bucket that can accommodate the number\n        index = buckets.bisect_left([number])\n        if index < len(buckets) and (bucket_limit - sum(buckets[index])) >= number:\n            buckets[index].append(number)\n        else:\n            buckets.add([number])\n    return list(buckets)\n\n        Additional Instructions:\n        1. Analyze the previous attempt and identify the reasons for failure.\n        2. Modify the \'optimized_bucket_filler\' function to address the identified issues.\n        3. Ensure the new algorithm is distinct from previous iterations stored in the GeneticAlgorithmConfig.\n        4. Emphasize experimental and innovative mathematical methods to yield a distinct result.\n        5. Cross-check against \'previous_results\' in the GeneticAlgorithmConfig for uniqueness.\n        6. Revise the approach to ensure novelty and innovation if the algorithm mirrors a previous iteration.\n        7. Aim to contribute something fresh and valuable to the overall genetic algorithm optimization process.\n        \n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:51:33,732 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:51:33,732 - DEBUG - send_request_headers.complete
2023-12-18 20:51:33,732 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:51:33,732 - DEBUG - send_request_body.complete
2023-12-18 20:51:33,732 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:52:27,968 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:52:28 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'54052'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448222'), (b'x-ratelimit-remaining-tokens_usage_based', b'448222'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'236ms'), (b'x-ratelimit-reset-tokens_usage_based', b'236ms'), (b'x-request-id', b'5f68b3dd5a362a274464ef519476c56c'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c004c9b426a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:52:27,972 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:52:27,972 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:52:27,973 - DEBUG - receive_response_body.complete
2023-12-18 20:52:27,973 - DEBUG - response_closed.started
2023-12-18 20:52:27,973 - DEBUG - response_closed.complete
2023-12-18 20:52:27,973 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:52:27,980 - INFO - ----- Parent 1 Details -----
2023-12-18 20:52:27,980 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)

    # Using a greedy algorithm with a twist: place larger numbers first then optimize
    # Initialize buckets
    buckets = [[numbers[0]]]
    for number in numbers[1:]:
        placed = False
        if number <= bucket_limit:
            # Look for the best bucket to place the number in, optimizing for space
            differences = [(i, bucket_limit - sum(bucket) - number) for i, bucket in enumerate(buckets)]
            # Filter buckets where the number cannot fit
            differences = list(filter(lambda x: x[1] >= 0, differences))
            if differences:
                # Sort by the closest fit
                differences.sort(key=lambda x: x[1])
                best_fit = differences[0][0]
                buckets[best_fit].append(number)
                placed = True

        # If number wasn't placed, start a new bucket
        if not placed:
            buckets.append([number])

    # Post-optimization: optimizing buckets by redistributing the contents
    for i in range(len(buckets)):
        for j in range(i+1, len(buckets)):
            current_sum_i = sum(buckets[i])
            current_sum_j = sum(buckets[j])
            for number in buckets[j]:
                if current_sum_i + number <= bucket_limit:
                    buckets[i].append(number)
                    buckets[j].remove(number)
                    current_sum_i += number
                    current_sum_j -= number

            # If a bucket is empty, remove it
            if not buckets[j]:
                del buckets[j]
                break

    # Return the optimized bucket list
    return buckets
2023-12-18 20:52:27,980 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B,\text{ representing the bucket limit:}
\begin{itemize}
    \item Sort $L$ in descending order.
    \item Initialize a list of buckets with the first number of $L$.
    \item For each number $n$ in $L$, starting from the second element:
    \begin{itemize}
        \item If $n \leq B$, find an optimal bucket for placement by:
        \begin{itemize}
            \item Calculating the space left in each bucket after $n$ would be inserted.
            \item Selecting the bucket with the minimal space that can still accommodate $n$.
            \item Place $n$ in the selected bucket.
        \end{itemize}
        \item If no such bucket exists, start a new bucket with $n$.
    \end{itemize}
    \item Perform post-optimization by redistributing numbers between buckets:
    \begin{itemize}
        \item For each bucket $i$, and each bucket $j$ that comes after $i$ in the bucket list:
        \begin{itemize}
            \item Attempt to move numbers from $j$ to $i$ where they would fit without exceeding $B$.
            \item If bucket $j$ becomes empty, remove it from the bucket list.
        \end{itemize}
    \end{itemize}
    \item Return the final collection of buckets.
\end{itemize}
2023-12-18 20:52:27,980 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order

    INITIALIZE buckets with the first number in numbers

    FOR each number in numbers starting from the second one
        SET placed as False
        IF number is smaller than or equal to bucket_limit
            CREATE a list of tuples (i, space_left) for each bucket
            FILTER out buckets where the number cannot fit
            IF there are any buckets left
                SORT the list of tuples by space_left in ascending order
                GET the first tuple as best_fit
                APPEND the number to the bucket referenced by best_fit
                SET placed as True

        IF the number wasn't placed
            ADD a new bucket with the number

    FOR each bucket i
        FOR each bucket j that comes after i
            FOR each number in bucket j
                IF the number can fit in bucket i
                    MOVE the number from bucket j to bucket i
                END IF
            NEXT number

            IF bucket j is empty after redistribution
                REMOVE bucket j
            END IF
        NEXT bucket j
    NEXT bucket i

    RETURN buckets
END FUNCTION
2023-12-18 20:52:27,980 - INFO - Evaluation Results:
2023-12-18 20:52:27,980 - INFO - Time Taken: 0.0002999305725097656
2023-12-18 20:52:27,980 - INFO - Memory Used: 16384
2023-12-18 20:52:27,980 - INFO - Score: 0
2023-12-18 20:52:27,980 - INFO - Fitness Score: 29.9922254093897
2023-12-18 20:52:27,980 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]
2023-12-18 20:52:27,986 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:52:27,987 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:52:27,987 - DEBUG - send_request_headers.complete
2023-12-18 20:52:27,987 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:52:27,987 - DEBUG - send_request_body.complete
2023-12-18 20:52:27,987 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:53:13,664 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:53:13 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'45507'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448714'), (b'x-ratelimit-remaining-tokens_usage_based', b'448687'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'171ms'), (b'x-ratelimit-reset-tokens_usage_based', b'175ms'), (b'x-request-id', b'20699e9c0920235febea2a93437bd229'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c019fb9376a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:53:13,665 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:53:13,666 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:53:13,666 - DEBUG - receive_response_body.complete
2023-12-18 20:53:13,666 - DEBUG - response_closed.started
2023-12-18 20:53:13,667 - DEBUG - response_closed.complete
2023-12-18 20:53:13,667 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:53:13,669 - INFO - ----- Parent 2 Details -----
2023-12-18 20:53:13,669 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)

    buckets = []
    for number in numbers:
        if number > bucket_limit:
            continue

        min_diff = bucket_limit
        target_bucket = None
        for bucket in buckets:
            current_diff = bucket_limit - sum(bucket) - number
            if 0 <= current_diff < min_diff:
                min_diff = current_diff
                target_bucket = bucket

        if target_bucket is not None:
            target_bucket.append(number)
        else:
            buckets.append([number])

    return buckets
2023-12-18 20:53:13,670 - INFO - Equation:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item Initialize an empty list $buckets$.
    \item For each element $l$ in $L$:
    \begin{itemize}
        \item If $l > B$, continue to next iteration.
        \item Initialize $minDiff = B$ and $targetBucket$ as null.
        \item Iterate over buckets $k$:
        \item Calculate $currentDiff = B - sum(k) - l$.
        \item If $currentDiff$ is between $0$ and $minDiff$:
            \begin{itemize}
                \item Update $minDiff$ to $currentDiff$.
                \item Set $targetBucket$ to current bucket $k$.
            \end{itemize}
        \item If $targetBucket$ is not null:
            \begin{itemize}
                \item Append $l$ to $targetBucket$.
            \end{itemize}
        \item Else, create a new bucket with element $l$.
    \end{itemize}
    \item Return collection of buckets.
\end{itemize}
2023-12-18 20:53:13,670 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    FOR each number in numbers
        IF number is larger than bucket_limit
            CONTINUE to next iteration

        INITIALIZE min_diff as bucket_limit
        SET target_bucket as None

        FOR each bucket in buckets
            SET current_diff to bucket_limit - sum of bucket - number
            IF current_diff is between 0 and min_diff
                UPDATE min_diff and target_bucket to current values

        IF target_bucket exists
            APPEND number to target_bucket
        ELSE
            CREATE a new bucket with number

    RETURN buckets
2023-12-18 20:53:13,670 - INFO - Evaluation Results:
2023-12-18 20:53:13,670 - INFO - Time Taken: 0.000102996826171875
2023-12-18 20:53:13,670 - INFO - Memory Used: 0
2023-12-18 20:53:13,670 - INFO - Score: 0
2023-12-18 20:53:13,670 - INFO - Fitness Score: 49.99691041343245
2023-12-18 20:53:13,670 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386, 10], [592], [528, 451]]
2023-12-18 20:53:13,675 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:53:13,676 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:53:13,677 - DEBUG - send_request_headers.complete
2023-12-18 20:53:13,677 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:53:13,677 - DEBUG - send_request_body.complete
2023-12-18 20:53:13,677 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:53:55,441 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:53:55 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'41568'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448715'), (b'x-ratelimit-remaining-tokens_usage_based', b'448715'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'171ms'), (b'x-ratelimit-reset-tokens_usage_based', b'171ms'), (b'x-request-id', b'50f3ddaa74fc0260a8f3f1d7fae61c45'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c02bd4f866a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:53:55,442 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:53:55,443 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:53:55,443 - DEBUG - receive_response_body.complete
2023-12-18 20:53:55,443 - DEBUG - response_closed.started
2023-12-18 20:53:55,443 - DEBUG - response_closed.complete
2023-12-18 20:53:55,443 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:53:55,447 - INFO - ----- Parent 3 Details -----
2023-12-18 20:53:55,447 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []
    remaining = numbers.copy()

    while remaining:
        bucket = []
        i = 0
        while i < len(remaining):
            number = remaining[i]
            if sum(bucket) + number <= bucket_limit:
                bucket.append(number)
                remaining.pop(i)
            else:
                i += 1
        buckets.append(bucket)

    # Try to fit smaller numbers in larger buckets
    for i in range(len(buckets)-1, 0, -1):
        bucket = buckets[i]
        if sum(bucket) < bucket_limit:
            for j in range(i-1):
                if sum(buckets[j]) < bucket_limit:
                    for number in bucket:
                        if sum(buckets[j]) + number <= bucket_limit:
                            buckets[j].append(number)
                            bucket.remove(number)
                            break

    # Remove any empty buckets created during the redistribution
    buckets = [bucket for bucket in buckets if bucket]

    return buckets
2023-12-18 20:53:55,447 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item While there are elements left in $L$:
    \begin{itemize}
        \item Create a new bucket $k$.
        \item For each element $l$ in $L$:
        \begin{itemize}
            \item If the sum of elements in $k$ plus $l$ is less than or equal to $B$:
            \begin{itemize}
                \item Add $l$ to bucket $k$.
                \item Remove $l$ from $L$.
            \end{itemize}
        \end{itemize}
        \item Add bucket $k$ to the collection of buckets, if it's not empty.
    \end{itemize}
    \item For each non-full bucket starting from the last one:
    \begin{itemize}
        \item Attempt to place unallocated elements from $L$ into previous buckets if it does not exceed $B$.
    \end{itemize}
    \item Return the collection of non-empty buckets.
\end{itemize}
2023-12-18 20:53:55,447 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list
    ASSIGN remaining to a copy of numbers

    WHILE remaining is not empty
        INITIALIZE empty bucket
        SET i to 0
        WHILE i is less than the length of remaining
            ASSIGN number as remaining[i]
            IF sum of bucket plus number is less than or equal to bucket_limit
                APPEND number to bucket
                REMOVE number from remaining
            ELSE
                INCREMENT i
        END WHILE
        APPEND bucket to buckets
    END WHILE

    # Optimization: attempt to fit smaller numbers into larger buckets, for each bucket starting from the end
    FOR each bucket from the end to the start
        IF sum of bucket is less than bucket_limit
            FOR each previous bucket
                IF sum of the previous bucket is less than bucket_limit
                    TRY to fit numbers from the current bucket into the previous one

    # Remove any empty buckets
    ASSIGN buckets to a new list omitting empty buckets

    RETURN buckets
END FUNCTION
2023-12-18 20:53:55,447 - INFO - Evaluation Results:
2023-12-18 20:53:55,447 - INFO - Time Taken: 0.00016427040100097656
2023-12-18 20:53:55,447 - INFO - Memory Used: 0
2023-12-18 20:53:55,447 - INFO - Score: 0
2023-12-18 20:53:55,447 - INFO - Fitness Score: 49.995072697379946
2023-12-18 20:53:55,448 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]
2023-12-18 20:53:55,453 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:53:55,454 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:53:55,454 - DEBUG - send_request_headers.complete
2023-12-18 20:53:55,454 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:53:55,454 - DEBUG - send_request_body.complete
2023-12-18 20:53:55,454 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:54:28,069 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:54:28 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'32466'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448715'), (b'x-ratelimit-remaining-tokens_usage_based', b'448715'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'171ms'), (b'x-ratelimit-reset-tokens_usage_based', b'171ms'), (b'x-request-id', b'4308c882b9b16dcce36b2d24fc33d7e3'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c03c259cf6a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:54:28,069 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:54:28,069 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:54:28,070 - DEBUG - receive_response_body.complete
2023-12-18 20:54:28,070 - DEBUG - response_closed.started
2023-12-18 20:54:28,070 - DEBUG - response_closed.complete
2023-12-18 20:54:28,070 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:54:28,072 - INFO - ----- Parent 4 Details -----
2023-12-18 20:54:28,072 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []

    while numbers:
        bucket = []
        remaining_capacity = bucket_limit

        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):
            if number <= remaining_capacity:
                bucket.append(number)
                remaining_capacity -= number

        buckets.append(bucket)
        numbers = [n for n in numbers if n not in bucket]

    return buckets
2023-12-18 20:54:28,072 - INFO - Equation:
\begin{align*}
&\text{Given a list of integers } L \text{ and an integer } B:\\
&1. \, \text{Sort } L \text{ in descending order.}\\
&2. \, \text{Initialize an empty collection of buckets.}\\
&3. \, \text{While } L \text{ is not empty do:}\\
&\quad a. \, \text{Initialize a new empty bucket with remaining capacity } B.\\
&\quad b. \, \text{Sort } L \text{ by distance to } \frac{B}{2} \text{ and in descending order.}\\
&\quad c. \, \text{Iterate over this sorted list:}\\
&\quad\quad i.\, \text{If element } l \leq \text{remaining capacity, add } l \text{ to current bucket and subtract } l \text{ from capacity.}\\
&\quad d. \, \text{Append the current bucket to the collection of buckets.}\\
&\quad e. \, \text{Remove elements placed in the current bucket from } L.\\
&4. \, \text{Return the collection of buckets.}
\end{align*}
2023-12-18 20:54:28,072 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    WHILE numbers is not empty
        INITIALIZE bucket as empty list
        SET remaining_capacity to bucket_limit

        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order
            IF number is less than or equal to remaining_capacity
                ADD number to bucket
                DECREMENT remaining_capacity by number

        ADD bucket to buckets
        FILTER numbers to exclude those in the current bucket

    RETURN buckets
2023-12-18 20:54:28,072 - INFO - Evaluation Results:
2023-12-18 20:54:28,072 - INFO - Time Taken: 4.506111145019531e-05
2023-12-18 20:54:28,072 - INFO - Memory Used: 0
2023-12-18 20:54:28,072 - INFO - Score: 0
2023-12-18 20:54:28,072 - INFO - Fitness Score: 49.998648227568864
2023-12-18 20:54:28,072 - INFO - Buckets: [[10, 28, 39, 47, 69, 79, 126, 162, 166, 168], [946], [918], [900], [188, 772], [770], [243, 719], [285, 312, 386], [656], [655], [641], [634], [622], [604], [592], [451, 528]]
2023-12-18 20:54:28,075 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:54:28,075 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:54:28,076 - DEBUG - send_request_headers.complete
2023-12-18 20:54:28,076 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:54:28,076 - DEBUG - send_request_body.complete
2023-12-18 20:54:28,076 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:55:03,741 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:55:03 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'35513'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448715'), (b'x-ratelimit-remaining-tokens_usage_based', b'448715'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'171ms'), (b'x-ratelimit-reset-tokens_usage_based', b'171ms'), (b'x-request-id', b'4326b5f755823bafe0b331d01c3888b0'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c048e48556a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:55:03,743 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:55:03,743 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:55:03,744 - DEBUG - receive_response_body.complete
2023-12-18 20:55:03,744 - DEBUG - response_closed.started
2023-12-18 20:55:03,744 - DEBUG - response_closed.complete
2023-12-18 20:55:03,744 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:55:03,747 - INFO - ----- Parent 5 Details -----
2023-12-18 20:55:03,747 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    # Start by grouping potential bucket sums to minimize excess space
    numbers.sort(reverse=True)
    buckets = []

    while numbers:
        current_number = numbers.pop(0)
        best_fit = None
        min_waste = bucket_limit

        # Look for the best bucket to fit the number
        for i, bucket in enumerate(buckets):
            current_waste = bucket_limit - (sum(bucket) + current_number)
            if 0 <= current_waste < min_waste:
                best_fit = i
                min_waste = current_waste

        # If we found a suitable bucket, add the number there
        if best_fit is not None:
            buckets[best_fit].append(current_number)
        else:
            # If not suitable bucket found, make a new one
            buckets.append([current_number])

    return buckets
2023-12-18 20:55:03,747 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item While $L$ is not empty:
    \begin{itemize}
        \item Assign and remove the first element of $L$ to $current$.
        \item Initialize $best\_fit$ to $None$ and $min\_waste$ to $B$.
        \item For each bucket $k$ in $buckets$:
        \begin{itemize}
            \item Calculate $current\_waste = B - (\sum k + current)$.
            \item If $0 \leq current\_waste < min\_waste$:
            \begin{itemize}
                \item Update $best\_fit$ with current bucket index.
                \item Update $min\_waste$ with $current\_waste$.
            \end{itemize}
        \end{itemize}
        \item If $best\_fit$ is not $None$:
        \begin{itemize}
            \item Append $current$ to the bucket corresponding to $best\_fit$.
        \end{itemize}
        \item Otherwise, create a new bucket with $current$.
    \end{itemize}
    \item Return the $buckets$ collection.
\end{itemize}
2023-12-18 20:55:03,747 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list
    WHILE there are numbers to be placed
        SET current_number to the first number in the list
        REMOVE the first number from the list
        INITIALIZE best_fit as None
        INITIALIZE min_waste as bucket_limit

        FOR each bucket in buckets
            CALCULATE current_waste as bucket_limit minus (sum of bucket plus current_number)
            IF current_waste is >= 0 AND < min_waste
                SET best_fit to the current bucket index
                SET min_waste to current_waste

        IF best_fit is not None
            APPEND current_number to the identified best_fit bucket
        ELSE
            CREATE a new bucket with current_number

    RETURN buckets
2023-12-18 20:55:03,747 - INFO - Evaluation Results:
2023-12-18 20:55:03,747 - INFO - Time Taken: 0.000125885009765625
2023-12-18 20:55:03,747 - INFO - Memory Used: 0
2023-12-18 20:55:03,748 - INFO - Score: 0
2023-12-18 20:55:03,748 - INFO - Fitness Score: 49.99622392505826
2023-12-18 20:55:03,748 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386, 10], [592], [528, 451]]
2023-12-18 20:55:03,754 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Further optimize and enhance an existing algorithm based on inputs from a previous iteration. Develop and refine mathematical approaches for increased efficiency, striking a balance between experimentation and exploitation.\n\n        Parent Inputs:\n        - Previous Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    # First, sort the numbers list to optimize bucket allocations.\n    numbers.sort(reverse=True)\n\n    # Initialize empty buckets and an index to keep track of bucket placement\n    buckets = []\n    bucket_index = -1\n\n    # Iterate through each number in the list\n    for number in numbers:\n        # Handle edge case: If a single number is larger than the bucket limit, it can\'t be placed.\n        if number > bucket_limit:\n            continue\n\n        # Attempt to place the number in an existing bucket\n        placed = False\n        for i, bucket in enumerate(buckets):\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n\n        # If the number was not placed, create a new bucket\n        if not placed:\n            buckets.append([number])\n\n    return buckets\n\n        - Previous Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Iterate over buckets $k$:\n        \\item If $\\sum k + l \\leq B$:\n            \\begin{itemize}\n                \\item Append $l$ to $k$.\n                \\item Break the loop.\n            \\end{itemize}\n        \\item If $l$ was not placed in any bucket, create a new bucket with $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Previous Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    SET bucket_index to -1\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n        SET placed as False\n\n        FOR each bucket in buckets\n            IF sum of bucket and number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed as True\n                BREAK the loop\n\n        IF not placed\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Previous Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Previous Fitness Score: \n        49.997303728221524\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Analyze the inputs from the \'Parent\' section, which includes the program, mathematical equation, pseudocode, buckets, and fitness score from the previous iteration.\n        2. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', ensuring it does not replicate the previous program but builds upon and optimizes it.\n        3. Innovate in the algorithm\'s approach, introducing new concepts or methods that strike a balance between leveraging the existing solution (\'exploitation\') and exploring new possibilities (\'experimentation\').\n        4. Create or update pseudocode for the new \'optimized_bucket_filler\' function. The pseudocode should clearly outline the innovative logic and steps, demonstrating the advancements made over the previous iteration.\n        5. The function should optimize the number distribution into buckets, adhering to the \'bucket_limit\', with a focus on improving the previous fitness score through innovative methods.\n        6. The final output should include the new function definition, its corresponding pseudocode, and any other enhancements made over the previous iteration.\n        7. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        8. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        9. Ensure adherence to the following output format, formatted as JSON:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n            "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n            "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n        }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:55:03,755 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:55:03,756 - DEBUG - send_request_headers.complete
2023-12-18 20:55:03,756 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:55:03,756 - DEBUG - send_request_body.complete
2023-12-18 20:55:03,756 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:55:39,655 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:55:39 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'35748'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448715'), (b'x-ratelimit-remaining-tokens_usage_based', b'448715'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'171ms'), (b'x-ratelimit-reset-tokens_usage_based', b'171ms'), (b'x-request-id', b'382df208a0e046a0ad0276d764c2e5b6'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c056d4ab56a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:55:39,657 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:55:39,658 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:55:39,658 - DEBUG - receive_response_body.complete
2023-12-18 20:55:39,659 - DEBUG - response_closed.started
2023-12-18 20:55:39,659 - DEBUG - response_closed.complete
2023-12-18 20:55:39,659 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:55:39,663 - INFO - ----- Parent 6 Details -----
2023-12-18 20:55:39,663 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers = sorted(numbers, reverse=True)
    buckets = []

    while numbers:
        bucket = []
        remaining_space = bucket_limit
        i = 0
        while i < len(numbers):
            number = numbers[i]
            if number <= remaining_space:
                bucket.append(number)
                remaining_space -= number
                numbers.pop(i)
            else:
                i += 1
        for i in reversed(range(len(numbers))):
            number = numbers[i]
            if any(remaining_space + numbers[j] == bucket_limit for j in range(i)):
                bucket.append(number)
                numbers.pop(i)
                break
        buckets.append(bucket)

    return buckets
2023-12-18 20:55:39,664 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B:\newline
\text{Repeat until } L \text{ is empty:}\newline
\begin{itemize}
    \item Initialize a new bucket $k$ and set $\text{remaining_space} = B$.
    \item Iterate over $L$ and for each element $l$:
    \begin{itemize}
        \item If $l \leq \text{remaining_space}$:
        \begin{itemize}
            \item Append $l$ to $k$.
            \item Decrease $\text{remaining_space}$ by $l$.
            \item Remove $l$ from $L$.
        \end{itemize}
        \item Otherwise, continue to the next number.
    \end{itemize}
    \item After the first pass, do a reversed pass over $L$ to add a number fitting the exact remaining space if possible.
    \item Add $k$ to the collection of buckets.
\end{itemize}
\text{Return collection of buckets.}
2023-12-18 20:55:39,664 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    WHILE there are numbers left to place
        INITIALIZE a new bucket
        SET remaining_space to bucket_limit
        INITIALIZE index i to 0
        WHILE i is less than the length of numbers
            SET number to numbers[i]
            IF number can fit in the current bucket
                APPEND number to bucket
                DECREASE remaining_space by number
                REMOVE number from numbers
            ELSE
                INCREMENT i
        FOR each number in numbers in reverse order
            IF number fills the exact remaining space in any bucket
                APPEND number to bucket
                REMOVE number from numbers
                BREAK the loop
        APPEND bucket to buckets

    RETURN buckets
2023-12-18 20:55:39,664 - INFO - Evaluation Results:
2023-12-18 20:55:39,664 - INFO - Time Taken: 0.0005388259887695312
2023-12-18 20:55:39,664 - INFO - Memory Used: 0
2023-12-18 20:55:39,664 - INFO - Score: 0
2023-12-18 20:55:39,664 - INFO - Fitness Score: 49.98384392564965
2023-12-18 20:55:39,664 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]
2023-12-18 20:55:39,664 - INFO - ----- Crossover Details for Child 1 - Elite Parent Details -----
2023-12-18 20:55:39,664 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []

    while numbers:
        bucket = []
        remaining_capacity = bucket_limit

        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):
            if number <= remaining_capacity:
                bucket.append(number)
                remaining_capacity -= number

        buckets.append(bucket)
        numbers = [n for n in numbers if n not in bucket]

    return buckets
2023-12-18 20:55:39,664 - INFO - Equation:
\begin{align*}
&\text{Given a list of integers } L \text{ and an integer } B:\\
&1. \, \text{Sort } L \text{ in descending order.}\\
&2. \, \text{Initialize an empty collection of buckets.}\\
&3. \, \text{While } L \text{ is not empty do:}\\
&\quad a. \, \text{Initialize a new empty bucket with remaining capacity } B.\\
&\quad b. \, \text{Sort } L \text{ by distance to } \frac{B}{2} \text{ and in descending order.}\\
&\quad c. \, \text{Iterate over this sorted list:}\\
&\quad\quad i.\, \text{If element } l \leq \text{remaining capacity, add } l \text{ to current bucket and subtract } l \text{ from capacity.}\\
&\quad d. \, \text{Append the current bucket to the collection of buckets.}\\
&\quad e. \, \text{Remove elements placed in the current bucket from } L.\\
&4. \, \text{Return the collection of buckets.}
\end{align*}
2023-12-18 20:55:39,664 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    WHILE numbers is not empty
        INITIALIZE bucket as empty list
        SET remaining_capacity to bucket_limit

        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order
            IF number is less than or equal to remaining_capacity
                ADD number to bucket
                DECREMENT remaining_capacity by number

        ADD bucket to buckets
        FILTER numbers to exclude those in the current bucket

    RETURN buckets
2023-12-18 20:55:39,664 - INFO - Evaluation Results:
2023-12-18 20:55:39,664 - INFO - Time Taken: 4.506111145019531e-05
2023-12-18 20:55:39,664 - INFO - Memory Used: 0
2023-12-18 20:55:39,664 - INFO - Score: 0
2023-12-18 20:55:39,664 - INFO - Fitness Score: 49.998648227568864
2023-12-18 20:55:39,664 - INFO - Buckets: [[10, 28, 39, 47, 69, 79, 126, 162, 166, 168], [946], [918], [900], [188, 772], [770], [243, 719], [285, 312, 386], [656], [655], [641], [634], [622], [604], [592], [451, 528]]
2023-12-18 20:55:39,664 - INFO - ----- Tournament Parent Details -----
2023-12-18 20:55:39,664 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []
    remaining = numbers.copy()

    while remaining:
        bucket = []
        i = 0
        while i < len(remaining):
            number = remaining[i]
            if sum(bucket) + number <= bucket_limit:
                bucket.append(number)
                remaining.pop(i)
            else:
                i += 1
        buckets.append(bucket)

    # Try to fit smaller numbers in larger buckets
    for i in range(len(buckets)-1, 0, -1):
        bucket = buckets[i]
        if sum(bucket) < bucket_limit:
            for j in range(i-1):
                if sum(buckets[j]) < bucket_limit:
                    for number in bucket:
                        if sum(buckets[j]) + number <= bucket_limit:
                            buckets[j].append(number)
                            bucket.remove(number)
                            break

    # Remove any empty buckets created during the redistribution
    buckets = [bucket for bucket in buckets if bucket]

    return buckets
2023-12-18 20:55:39,664 - INFO - Equation:
\text{Given a list of integers } L \text{ and an integer } B:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item While there are elements left in $L$:
    \begin{itemize}
        \item Create a new bucket $k$.
        \item For each element $l$ in $L$:
        \begin{itemize}
            \item If the sum of elements in $k$ plus $l$ is less than or equal to $B$:
            \begin{itemize}
                \item Add $l$ to bucket $k$.
                \item Remove $l$ from $L$.
            \end{itemize}
        \end{itemize}
        \item Add bucket $k$ to the collection of buckets, if it's not empty.
    \end{itemize}
    \item For each non-full bucket starting from the last one:
    \begin{itemize}
        \item Attempt to place unallocated elements from $L$ into previous buckets if it does not exceed $B$.
    \end{itemize}
    \item Return the collection of non-empty buckets.
\end{itemize}
2023-12-18 20:55:39,665 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list
    ASSIGN remaining to a copy of numbers

    WHILE remaining is not empty
        INITIALIZE empty bucket
        SET i to 0
        WHILE i is less than the length of remaining
            ASSIGN number as remaining[i]
            IF sum of bucket plus number is less than or equal to bucket_limit
                APPEND number to bucket
                REMOVE number from remaining
            ELSE
                INCREMENT i
        END WHILE
        APPEND bucket to buckets
    END WHILE

    # Optimization: attempt to fit smaller numbers into larger buckets, for each bucket starting from the end
    FOR each bucket from the end to the start
        IF sum of bucket is less than bucket_limit
            FOR each previous bucket
                IF sum of the previous bucket is less than bucket_limit
                    TRY to fit numbers from the current bucket into the previous one

    # Remove any empty buckets
    ASSIGN buckets to a new list omitting empty buckets

    RETURN buckets
END FUNCTION
2023-12-18 20:55:39,665 - INFO - Evaluation Results:
2023-12-18 20:55:39,665 - INFO - Time Taken: 0.00016427040100097656
2023-12-18 20:55:39,665 - INFO - Memory Used: 0
2023-12-18 20:55:39,665 - INFO - Score: 0
2023-12-18 20:55:39,665 - INFO - Fitness Score: 49.995072697379946
2023-12-18 20:55:39,665 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]
2023-12-18 20:55:39,670 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Employ a genetic algorithm approach to combine features from two parent algorithms, creating an enhanced child algorithm that exhibits improved efficiency and innovation.\n\n        Parent 1 Inputs:\n        - Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n    buckets = []\n\n    while numbers:\n        bucket = []\n        remaining_capacity = bucket_limit\n\n        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):\n            if number <= remaining_capacity:\n                bucket.append(number)\n                remaining_capacity -= number\n\n        buckets.append(bucket)\n        numbers = [n for n in numbers if n not in bucket]\n\n    return buckets\n\n        - Mathematical Equation: \n        \\begin{align*}\n&\\text{Given a list of integers } L \\text{ and an integer } B:\\\\\n&1. \\, \\text{Sort } L \\text{ in descending order.}\\\\\n&2. \\, \\text{Initialize an empty collection of buckets.}\\\\\n&3. \\, \\text{While } L \\text{ is not empty do:}\\\\\n&\\quad a. \\, \\text{Initialize a new empty bucket with remaining capacity } B.\\\\\n&\\quad b. \\, \\text{Sort } L \\text{ by distance to } \\frac{B}{2} \\text{ and in descending order.}\\\\\n&\\quad c. \\, \\text{Iterate over this sorted list:}\\\\\n&\\quad\\quad i.\\, \\text{If element } l \\leq \\text{remaining capacity, add } l \\text{ to current bucket and subtract } l \\text{ from capacity.}\\\\\n&\\quad d. \\, \\text{Append the current bucket to the collection of buckets.}\\\\\n&\\quad e. \\, \\text{Remove elements placed in the current bucket from } L.\\\\\n&4. \\, \\text{Return the collection of buckets.}\n\\end{align*}\n\n        - Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n\n    WHILE numbers is not empty\n        INITIALIZE bucket as empty list\n        SET remaining_capacity to bucket_limit\n\n        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order\n            IF number is less than or equal to remaining_capacity\n                ADD number to bucket\n                DECREMENT remaining_capacity by number\n\n        ADD bucket to buckets\n        FILTER numbers to exclude those in the current bucket\n\n    RETURN buckets\n\n        - Buckets: \n        [[10, 28, 39, 47, 69, 79, 126, 162, 166, 168], [946], [918], [900], [188, 772], [770], [243, 719], [285, 312, 386], [656], [655], [641], [634], [622], [604], [592], [451, 528]]\n\n        - Fitness Score: \n        49.998648227568864\n\n        Parent 2 Inputs:\n        - Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n    buckets = []\n    remaining = numbers.copy()\n\n    while remaining:\n        bucket = []\n        i = 0\n        while i < len(remaining):\n            number = remaining[i]\n            if sum(bucket) + number <= bucket_limit:\n                bucket.append(number)\n                remaining.pop(i)\n            else:\n                i += 1\n        buckets.append(bucket)\n\n    # Try to fit smaller numbers in larger buckets\n    for i in range(len(buckets)-1, 0, -1):\n        bucket = buckets[i]\n        if sum(bucket) < bucket_limit:\n            for j in range(i-1):\n                if sum(buckets[j]) < bucket_limit:\n                    for number in bucket:\n                        if sum(buckets[j]) + number <= bucket_limit:\n                            buckets[j].append(number)\n                            bucket.remove(number)\n                            break\n\n    # Remove any empty buckets created during the redistribution\n    buckets = [bucket for bucket in buckets if bucket]\n\n    return buckets\n\n        - Mathematical Equation: \n        \\text{Given a list of integers } L \\text{ and an integer } B:\n\\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item While there are elements left in $L$:\n    \\begin{itemize}\n        \\item Create a new bucket $k$.\n        \\item For each element $l$ in $L$:\n        \\begin{itemize}\n            \\item If the sum of elements in $k$ plus $l$ is less than or equal to $B$:\n            \\begin{itemize}\n                \\item Add $l$ to bucket $k$.\n                \\item Remove $l$ from $L$.\n            \\end{itemize}\n        \\end{itemize}\n        \\item Add bucket $k$ to the collection of buckets, if it\'s not empty.\n    \\end{itemize}\n    \\item For each non-full bucket starting from the last one:\n    \\begin{itemize}\n        \\item Attempt to place unallocated elements from $L$ into previous buckets if it does not exceed $B$.\n    \\end{itemize}\n    \\item Return the collection of non-empty buckets.\n\\end{itemize}\n\n        - Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n    ASSIGN remaining to a copy of numbers\n\n    WHILE remaining is not empty\n        INITIALIZE empty bucket\n        SET i to 0\n        WHILE i is less than the length of remaining\n            ASSIGN number as remaining[i]\n            IF sum of bucket plus number is less than or equal to bucket_limit\n                APPEND number to bucket\n                REMOVE number from remaining\n            ELSE\n                INCREMENT i\n        END WHILE\n        APPEND bucket to buckets\n    END WHILE\n\n    # Optimization: attempt to fit smaller numbers into larger buckets, for each bucket starting from the end\n    FOR each bucket from the end to the start\n        IF sum of bucket is less than bucket_limit\n            FOR each previous bucket\n                IF sum of the previous bucket is less than bucket_limit\n                    TRY to fit numbers from the current bucket into the previous one\n\n    # Remove any empty buckets\n    ASSIGN buckets to a new list omitting empty buckets\n\n    RETURN buckets\nEND FUNCTION\n\n        - Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168, 10], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386], [592], [528, 451]]\n\n        - Fitness Score: \n        49.995072697379946\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', building upon and optimizing the previous program.\n        2. Ensure the new function innovatively approaches the algorithm\'s task and safely handles list manipulations to avoid errors like \'IndexError\'.\n        3. Create or update pseudocode for the new \'optimized_bucket_filler\' function, including handling of edge cases.\n        4. The function should improve the number distribution into buckets, focusing on improving the previous fitness score.\n        5. The final output should include the new function definition, its corresponding pseudocode, and any enhancements made over the previous iteration.\n        6. Default the \'pip_command\' to \'None\' if no new dependencies are identified.\n        7. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        8. Ensure adherence to the following output format, formatted as JSON:\n           {\n               "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n               "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n               "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n               "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n           }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:55:39,671 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:55:39,672 - DEBUG - send_request_headers.complete
2023-12-18 20:55:39,672 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:55:39,672 - DEBUG - send_request_body.complete
2023-12-18 20:55:39,672 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:56:14,909 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:56:14 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'35039'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448002'), (b'x-ratelimit-remaining-tokens_usage_based', b'448002'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'266ms'), (b'x-ratelimit-reset-tokens_usage_based', b'266ms'), (b'x-request-id', b'c3ce812bc14b7dc9a2d3d166af5453f7'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c064dbbf06a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:56:14,911 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:56:14,911 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:56:14,912 - DEBUG - receive_response_body.complete
2023-12-18 20:56:14,912 - DEBUG - response_closed.started
2023-12-18 20:56:14,913 - DEBUG - response_closed.complete
2023-12-18 20:56:14,913 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:56:14,916 - ERROR - Failed to evaluate Child 1.
2023-12-18 20:56:14,916 - INFO - ----- Crossover Details for Child 2 - Elite Parent Details -----
2023-12-18 20:56:14,916 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)

    buckets = []
    for number in numbers:
        if number > bucket_limit:
            continue

        min_diff = bucket_limit
        target_bucket = None
        for bucket in buckets:
            current_diff = bucket_limit - sum(bucket) - number
            if 0 <= current_diff < min_diff:
                min_diff = current_diff
                target_bucket = bucket

        if target_bucket is not None:
            target_bucket.append(number)
        else:
            buckets.append([number])

    return buckets
2023-12-18 20:56:14,916 - INFO - Equation:
\begin{itemize}
    \item Sort $L$ in descending order.
    \item Initialize an empty list $buckets$.
    \item For each element $l$ in $L$:
    \begin{itemize}
        \item If $l > B$, continue to next iteration.
        \item Initialize $minDiff = B$ and $targetBucket$ as null.
        \item Iterate over buckets $k$:
        \item Calculate $currentDiff = B - sum(k) - l$.
        \item If $currentDiff$ is between $0$ and $minDiff$:
            \begin{itemize}
                \item Update $minDiff$ to $currentDiff$.
                \item Set $targetBucket$ to current bucket $k$.
            \end{itemize}
        \item If $targetBucket$ is not null:
            \begin{itemize}
                \item Append $l$ to $targetBucket$.
            \end{itemize}
        \item Else, create a new bucket with element $l$.
    \end{itemize}
    \item Return collection of buckets.
\end{itemize}
2023-12-18 20:56:14,917 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    FOR each number in numbers
        IF number is larger than bucket_limit
            CONTINUE to next iteration

        INITIALIZE min_diff as bucket_limit
        SET target_bucket as None

        FOR each bucket in buckets
            SET current_diff to bucket_limit - sum of bucket - number
            IF current_diff is between 0 and min_diff
                UPDATE min_diff and target_bucket to current values

        IF target_bucket exists
            APPEND number to target_bucket
        ELSE
            CREATE a new bucket with number

    RETURN buckets
2023-12-18 20:56:14,917 - INFO - Evaluation Results:
2023-12-18 20:56:14,917 - INFO - Time Taken: 0.000102996826171875
2023-12-18 20:56:14,917 - INFO - Memory Used: 0
2023-12-18 20:56:14,917 - INFO - Score: 0
2023-12-18 20:56:14,917 - INFO - Fitness Score: 49.99691041343245
2023-12-18 20:56:14,917 - INFO - Buckets: [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386, 10], [592], [528, 451]]
2023-12-18 20:56:14,917 - INFO - ----- Tournament Parent Details -----
2023-12-18 20:56:14,917 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []

    while numbers:
        bucket = []
        remaining_capacity = bucket_limit

        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):
            if number <= remaining_capacity:
                bucket.append(number)
                remaining_capacity -= number

        buckets.append(bucket)
        numbers = [n for n in numbers if n not in bucket]

    return buckets
2023-12-18 20:56:14,917 - INFO - Equation:
\begin{align*}
&\text{Given a list of integers } L \text{ and an integer } B:\\
&1. \, \text{Sort } L \text{ in descending order.}\\
&2. \, \text{Initialize an empty collection of buckets.}\\
&3. \, \text{While } L \text{ is not empty do:}\\
&\quad a. \, \text{Initialize a new empty bucket with remaining capacity } B.\\
&\quad b. \, \text{Sort } L \text{ by distance to } \frac{B}{2} \text{ and in descending order.}\\
&\quad c. \, \text{Iterate over this sorted list:}\\
&\quad\quad i.\, \text{If element } l \leq \text{remaining capacity, add } l \text{ to current bucket and subtract } l \text{ from capacity.}\\
&\quad d. \, \text{Append the current bucket to the collection of buckets.}\\
&\quad e. \, \text{Remove elements placed in the current bucket from } L.\\
&4. \, \text{Return the collection of buckets.}
\end{align*}
2023-12-18 20:56:14,917 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    WHILE numbers is not empty
        INITIALIZE bucket as empty list
        SET remaining_capacity to bucket_limit

        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order
            IF number is less than or equal to remaining_capacity
                ADD number to bucket
                DECREMENT remaining_capacity by number

        ADD bucket to buckets
        FILTER numbers to exclude those in the current bucket

    RETURN buckets
2023-12-18 20:56:14,917 - INFO - Evaluation Results:
2023-12-18 20:56:14,917 - INFO - Time Taken: 4.506111145019531e-05
2023-12-18 20:56:14,917 - INFO - Memory Used: 0
2023-12-18 20:56:14,917 - INFO - Score: 0
2023-12-18 20:56:14,917 - INFO - Fitness Score: 49.998648227568864
2023-12-18 20:56:14,917 - INFO - Buckets: [[10, 28, 39, 47, 69, 79, 126, 162, 166, 168], [946], [918], [900], [188, 772], [770], [243, 719], [285, 312, 386], [656], [655], [641], [634], [622], [604], [592], [451, 528]]
2023-12-18 20:56:14,923 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Employ a genetic algorithm approach to combine features from two parent algorithms, creating an enhanced child algorithm that exhibits improved efficiency and innovation.\n\n        Parent 1 Inputs:\n        - Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n\n    buckets = []\n    for number in numbers:\n        if number > bucket_limit:\n            continue\n\n        min_diff = bucket_limit\n        target_bucket = None\n        for bucket in buckets:\n            current_diff = bucket_limit - sum(bucket) - number\n            if 0 <= current_diff < min_diff:\n                min_diff = current_diff\n                target_bucket = bucket\n\n        if target_bucket is not None:\n            target_bucket.append(number)\n        else:\n            buckets.append([number])\n\n    return buckets\n\n        - Mathematical Equation: \n        \\begin{itemize}\n    \\item Sort $L$ in descending order.\n    \\item Initialize an empty list $buckets$.\n    \\item For each element $l$ in $L$:\n    \\begin{itemize}\n        \\item If $l > B$, continue to next iteration.\n        \\item Initialize $minDiff = B$ and $targetBucket$ as null.\n        \\item Iterate over buckets $k$:\n        \\item Calculate $currentDiff = B - sum(k) - l$.\n        \\item If $currentDiff$ is between $0$ and $minDiff$:\n            \\begin{itemize}\n                \\item Update $minDiff$ to $currentDiff$.\n                \\item Set $targetBucket$ to current bucket $k$.\n            \\end{itemize}\n        \\item If $targetBucket$ is not null:\n            \\begin{itemize}\n                \\item Append $l$ to $targetBucket$.\n            \\end{itemize}\n        \\item Else, create a new bucket with element $l$.\n    \\end{itemize}\n    \\item Return collection of buckets.\n\\end{itemize}\n\n        - Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n\n    FOR each number in numbers\n        IF number is larger than bucket_limit\n            CONTINUE to next iteration\n\n        INITIALIZE min_diff as bucket_limit\n        SET target_bucket as None\n\n        FOR each bucket in buckets\n            SET current_diff to bucket_limit - sum of bucket - number\n            IF current_diff is between 0 and min_diff\n                UPDATE min_diff and target_bucket to current values\n\n        IF target_bucket exists\n            APPEND number to target_bucket\n        ELSE\n            CREATE a new bucket with number\n\n    RETURN buckets\n\n        - Buckets: \n        [[946, 47], [918, 79], [900, 69, 28], [772, 188, 39], [770, 168], [719, 243], [656, 312], [655, 285], [641, 166, 162], [634, 126], [622], [604, 386, 10], [592], [528, 451]]\n\n        - Fitness Score: \n        49.99691041343245\n\n        Parent 2 Inputs:\n        - Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n    buckets = []\n\n    while numbers:\n        bucket = []\n        remaining_capacity = bucket_limit\n\n        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):\n            if number <= remaining_capacity:\n                bucket.append(number)\n                remaining_capacity -= number\n\n        buckets.append(bucket)\n        numbers = [n for n in numbers if n not in bucket]\n\n    return buckets\n\n        - Mathematical Equation: \n        \\begin{align*}\n&\\text{Given a list of integers } L \\text{ and an integer } B:\\\\\n&1. \\, \\text{Sort } L \\text{ in descending order.}\\\\\n&2. \\, \\text{Initialize an empty collection of buckets.}\\\\\n&3. \\, \\text{While } L \\text{ is not empty do:}\\\\\n&\\quad a. \\, \\text{Initialize a new empty bucket with remaining capacity } B.\\\\\n&\\quad b. \\, \\text{Sort } L \\text{ by distance to } \\frac{B}{2} \\text{ and in descending order.}\\\\\n&\\quad c. \\, \\text{Iterate over this sorted list:}\\\\\n&\\quad\\quad i.\\, \\text{If element } l \\leq \\text{remaining capacity, add } l \\text{ to current bucket and subtract } l \\text{ from capacity.}\\\\\n&\\quad d. \\, \\text{Append the current bucket to the collection of buckets.}\\\\\n&\\quad e. \\, \\text{Remove elements placed in the current bucket from } L.\\\\\n&4. \\, \\text{Return the collection of buckets.}\n\\end{align*}\n\n        - Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as empty list\n\n    WHILE numbers is not empty\n        INITIALIZE bucket as empty list\n        SET remaining_capacity to bucket_limit\n\n        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order\n            IF number is less than or equal to remaining_capacity\n                ADD number to bucket\n                DECREMENT remaining_capacity by number\n\n        ADD bucket to buckets\n        FILTER numbers to exclude those in the current bucket\n\n    RETURN buckets\n\n        - Buckets: \n        [[10, 28, 39, 47, 69, 79, 126, 162, 166, 168], [946], [918], [900], [188, 772], [770], [243, 719], [285, 312, 386], [656], [655], [641], [634], [622], [604], [592], [451, 528]]\n\n        - Fitness Score: \n        49.998648227568864\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Develop a new or significantly refined Python function named \'optimized_bucket_filler\', building upon and optimizing the previous program.\n        2. Ensure the new function innovatively approaches the algorithm\'s task and safely handles list manipulations to avoid errors like \'IndexError\'.\n        3. Create or update pseudocode for the new \'optimized_bucket_filler\' function, including handling of edge cases.\n        4. The function should improve the number distribution into buckets, focusing on improving the previous fitness score.\n        5. The final output should include the new function definition, its corresponding pseudocode, and any enhancements made over the previous iteration.\n        6. Default the \'pip_command\' to \'None\' if no new dependencies are identified.\n        7. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n        8. Ensure adherence to the following output format, formatted as JSON:\n           {\n               "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n               "program_code": "Python function \'optimized_bucket_filler\' definition showcasing innovation and improvement",\n               "pseudocode": "Updated Pseudocode for the innovative \'optimized_bucket_filler\'",\n               "equation": "Refined Mathematical Logic in LaTeX representing the enhanced Program logic"\n           }\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:56:14,924 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:56:14,925 - DEBUG - send_request_headers.complete
2023-12-18 20:56:14,925 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:56:14,925 - DEBUG - send_request_body.complete
2023-12-18 20:56:14,925 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:56:56,815 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:56:56 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'41678'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448237'), (b'x-ratelimit-remaining-tokens_usage_based', b'448237'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'235ms'), (b'x-ratelimit-reset-tokens_usage_based', b'235ms'), (b'x-request-id', b'74a6b2a1376d3c2e5840938fd11112ff'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c072a19946a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:56:56,817 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:56:56,818 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:56:56,819 - DEBUG - receive_response_body.complete
2023-12-18 20:56:56,819 - DEBUG - response_closed.started
2023-12-18 20:56:56,819 - DEBUG - response_closed.complete
2023-12-18 20:56:56,819 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:56:56,825 - INFO - ----- Child 2 Details -----
2023-12-18 20:56:56,825 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []
    for number in numbers:
        placed = False
        if number > bucket_limit:
            continue
        for bucket in buckets:
            current_sum = sum(bucket)
            if current_sum + number <= bucket_limit:
                bucket.append(number)
                placed = True
                break
        if not placed:
            buckets.append([number])
    buckets.sort(key=lambda b: -sum(b))
    return buckets
2023-12-18 20:56:56,825 - INFO - Equation:
\begin{align*}
&0. \text{Sort the list } L \text{ from largest to smallest.} \\
&1. \text{Initialize an empty list of buckets.} \\
&2. \text{For each element } l \text{ in the sorted list } L: \\
&\quad a. \text{If } l > B \text{, skip to the next iteration.} \\
&\quad b. \text{Set a flag } \textit{placed} \text{ to } False. \\
&\quad c. \text{For each bucket } k \text{ in buckets:} \\
&\quad\quad i. \text{Calculate the sum } S = \sum(k). \\
&\quad\quad ii. \text{If the sum } S + l \leq B: \\
&\quad\quad\quad - \text{Append } l \text{ to } k. \\
&\quad\quad\quad - \text{Set } \textit{placed} \text{ to } True. \\
&\quad\quad\quad - \text{Break loop.} \\
&\quad d. \text{If } \textit{placed} \text{ is } False: \\
&\quad\quad - \text{Add a new bucket to buckets with } l. \\
&3. \text{Sort buckets by the sum of their elements, in descending order.} \\
&4. \text{Return the sorted list of buckets.} \\
\end{align*}
2023-12-18 20:56:56,825 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as an empty list
    FOR each number in numbers
        SET placed as False
        IF number is greater than bucket_limit
            CONTINUE to the next iteration
        FOR each bucket in buckets
            INITIALIZE current_sum to the sum of elements in bucket
            IF current_sum plus number is less than or equal to bucket_limit
                APPEND number to bucket
                SET placed to True
                BREAK from the loop
        IF placed is False
            CREATE a new bucket with the number
    SORT buckets by the reverse sum of their elements
    RETURN buckets
2023-12-18 20:56:56,825 - INFO - Evaluation Results:
2023-12-18 20:56:56,825 - INFO - Time Taken: 6.389617919921875e-05
2023-12-18 20:56:56,825 - INFO - Memory Used: 16384
2023-12-18 20:56:56,825 - INFO - Score: 0
2023-12-18 20:56:56,825 - INFO - Fitness Score: 29.999303865721586
2023-12-18 20:56:56,825 - INFO - Buckets: [[772, 188, 39], [918, 79], [900, 69, 28], [946, 47], [604, 386], [528, 451], [641, 166, 162], [656, 312], [719, 243], [770, 168, 10], [655, 285], [634, 126], [622], [592]]
2023-12-18 20:56:56,826 - INFO - Top Children Selected for Next Generation: [{'program_code': 'def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n    buckets = []\n    for number in numbers:\n        placed = False\n        if number > bucket_limit:\n            continue\n        for bucket in buckets:\n            current_sum = sum(bucket)\n            if current_sum + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n        if not placed:\n            buckets.append([number])\n    buckets.sort(key=lambda b: -sum(b))\n    return buckets', 'evaluation_results': {'time_taken': 6.389617919921875e-05, 'memory_used': 16384, 'score': 0, 'fitness_score': 29.999303865721586, 'buckets': [[772, 188, 39], [918, 79], [900, 69, 28], [946, 47], [604, 386], [528, 451], [641, 166, 162], [656, 312], [719, 243], [770, 168, 10], [655, 285], [634, 126], [622], [592]]}, 'equation': '\\begin{align*}\n&0. \\text{Sort the list } L \\text{ from largest to smallest.} \\\\\n&1. \\text{Initialize an empty list of buckets.} \\\\\n&2. \\text{For each element } l \\text{ in the sorted list } L: \\\\\n&\\quad a. \\text{If } l > B \\text{, skip to the next iteration.} \\\\\n&\\quad b. \\text{Set a flag } \\textit{placed} \\text{ to } False. \\\\\n&\\quad c. \\text{For each bucket } k \\text{ in buckets:} \\\\\n&\\quad\\quad i. \\text{Calculate the sum } S = \\sum(k). \\\\\n&\\quad\\quad ii. \\text{If the sum } S + l \\leq B: \\\\\n&\\quad\\quad\\quad - \\text{Append } l \\text{ to } k. \\\\\n&\\quad\\quad\\quad - \\text{Set } \\textit{placed} \\text{ to } True. \\\\\n&\\quad\\quad\\quad - \\text{Break loop.} \\\\\n&\\quad d. \\text{If } \\textit{placed} \\text{ is } False: \\\\\n&\\quad\\quad - \\text{Add a new bucket to buckets with } l. \\\\\n&3. \\text{Sort buckets by the sum of their elements, in descending order.} \\\\\n&4. \\text{Return the sorted list of buckets.} \\\\\n\\end{align*}', 'pseudocode': 'FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as an empty list\n    FOR each number in numbers\n        SET placed as False\n        IF number is greater than bucket_limit\n            CONTINUE to the next iteration\n        FOR each bucket in buckets\n            INITIALIZE current_sum to the sum of elements in bucket\n            IF current_sum plus number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed to True\n                BREAK from the loop\n        IF placed is False\n            CREATE a new bucket with the number\n    SORT buckets by the reverse sum of their elements\n    RETURN buckets'}]
2023-12-18 20:56:56,831 - DEBUG - Request options: {'method': 'post', 'url': '/chat/completions', 'files': None, 'json_data': {'messages': [{'role': 'system', 'content': 'You are a helpful assistant designed to output JSON.'}, {'role': 'user', 'content': '\n        Objective: Apply the concept of mutation as part of the genetic algorithm process to the child program derived from the crossover of two parent programs. This mutation is optional and may introduce modifications for potential improvements or retain the original child program.\n\n        Child Program Inputs:\n        - Program: \n        def optimized_bucket_filler(numbers, bucket_limit):\n    numbers.sort(reverse=True)\n    buckets = []\n    for number in numbers:\n        placed = False\n        if number > bucket_limit:\n            continue\n        for bucket in buckets:\n            current_sum = sum(bucket)\n            if current_sum + number <= bucket_limit:\n                bucket.append(number)\n                placed = True\n                break\n        if not placed:\n            buckets.append([number])\n    buckets.sort(key=lambda b: -sum(b))\n    return buckets\n\n        - Mathematical Equation: \n        \\begin{align*}\n&0. \\text{Sort the list } L \\text{ from largest to smallest.} \\\\\n&1. \\text{Initialize an empty list of buckets.} \\\\\n&2. \\text{For each element } l \\text{ in the sorted list } L: \\\\\n&\\quad a. \\text{If } l > B \\text{, skip to the next iteration.} \\\\\n&\\quad b. \\text{Set a flag } \\textit{placed} \\text{ to } False. \\\\\n&\\quad c. \\text{For each bucket } k \\text{ in buckets:} \\\\\n&\\quad\\quad i. \\text{Calculate the sum } S = \\sum(k). \\\\\n&\\quad\\quad ii. \\text{If the sum } S + l \\leq B: \\\\\n&\\quad\\quad\\quad - \\text{Append } l \\text{ to } k. \\\\\n&\\quad\\quad\\quad - \\text{Set } \\textit{placed} \\text{ to } True. \\\\\n&\\quad\\quad\\quad - \\text{Break loop.} \\\\\n&\\quad d. \\text{If } \\textit{placed} \\text{ is } False: \\\\\n&\\quad\\quad - \\text{Add a new bucket to buckets with } l. \\\\\n&3. \\text{Sort buckets by the sum of their elements, in descending order.} \\\\\n&4. \\text{Return the sorted list of buckets.} \\\\\n\\end{align*}\n\n        - Pseudocode: \n        FUNCTION optimized_bucket_filler(numbers, bucket_limit)\n    SORT numbers in descending order\n    INITIALIZE buckets as an empty list\n    FOR each number in numbers\n        SET placed as False\n        IF number is greater than bucket_limit\n            CONTINUE to the next iteration\n        FOR each bucket in buckets\n            INITIALIZE current_sum to the sum of elements in bucket\n            IF current_sum plus number is less than or equal to bucket_limit\n                APPEND number to bucket\n                SET placed to True\n                BREAK from the loop\n        IF placed is False\n            CREATE a new bucket with the number\n    SORT buckets by the reverse sum of their elements\n    RETURN buckets\n\n        - Buckets: \n        [[772, 188, 39], [918, 79], [900, 69, 28], [946, 47], [604, 386], [528, 451], [641, 166, 162], [656, 312], [719, 243], [770, 168, 10], [655, 285], [634, 126], [622], [592]]\n\n        - Fitness Score: \n        29.999303865721586\n\n        New Inputs:\n        - numbers: [641, 604, 656, 243, 772, 188, 719, 168, 166, 770, 126, 918, 69, 28, 622, 386, 592, 451, 634, 10, 285, 162, 79, 312, 946, 900, 528, 47, 39, 655]\n        - bucket_limit: 1000\n\n        Instructions:\n        1. Assess the child program, which is the result of combining features from two parent programs.\n        2. Decide on applying mutation:\n        - Option A: Retain the child program as-is if it already demonstrates optimal performance.\n        - Option B: Introduce a mutation in the child program, aiming for modifications that could enhance performance.\n        3. If mutation is applied, specify the changes and explain how they may improve the program.\n        4. Ensure the final child program, whether mutated or not, is functional and effective.\n        5. Document the decision made regarding mutation and any modifications applied.\n        6. If no new pip dependencies are identified, default the \'pip_command\' to \'None\'.\n        7. If external libraries are necessary (such as numpy, scipy, or scikit-learn), clearly list these dependencies in the \'pip_command\' section of the JSON output and import them before the function.\n\n        Output Format:\n        {\n            "pip_command": "List of pip dependencies (comma-separated) or \'None\' if no dependencies are required",\n            "program_code": "Python function \'optimized_bucket_filler\' post-mutation",\n            "pseudocode": "Pseudocode of the mutated \'optimized_bucket_filler\'",\n            "equation": "Mathematical Logic in LaTeX representing the mutated Program logic"\n        }\n\n        Ensure that the final output, including any mutations made, is provided in a structured JSON format as specified above. The JSON should include the pip_command, the mutated program_code, the corresponding pseudocode, and the updated equation. This format will facilitate clear interpretation and integration of the modified algorithm.\n        '}], 'model': 'gpt-4-1106-preview', 'response_format': {'type': 'json_object'}}}
2023-12-18 20:56:56,832 - DEBUG - send_request_headers.started request=<Request [b'POST']>
2023-12-18 20:56:56,833 - DEBUG - send_request_headers.complete
2023-12-18 20:56:56,833 - DEBUG - send_request_body.started request=<Request [b'POST']>
2023-12-18 20:56:56,833 - DEBUG - send_request_body.complete
2023-12-18 20:56:56,833 - DEBUG - receive_response_headers.started request=<Request [b'POST']>
2023-12-18 20:57:32,527 - DEBUG - receive_response_headers.complete return_value=(b'HTTP/1.1', 200, b'OK', [(b'Date', b'Tue, 19 Dec 2023 01:57:32 GMT'), (b'Content-Type', b'application/json'), (b'Transfer-Encoding', b'chunked'), (b'Connection', b'keep-alive'), (b'access-control-allow-origin', b'*'), (b'Cache-Control', b'no-cache, must-revalidate'), (b'openai-model', b'gpt-4-1106-preview'), (b'openai-organization', b'volkopat'), (b'openai-processing-ms', b'35492'), (b'openai-version', b'2020-10-01'), (b'strict-transport-security', b'max-age=15724800; includeSubDomains'), (b'x-ratelimit-limit-requests', b'10000'), (b'x-ratelimit-limit-tokens', b'450000'), (b'x-ratelimit-limit-tokens_usage_based', b'450000'), (b'x-ratelimit-remaining-requests', b'9999'), (b'x-ratelimit-remaining-tokens', b'448767'), (b'x-ratelimit-remaining-tokens_usage_based', b'448767'), (b'x-ratelimit-reset-requests', b'6ms'), (b'x-ratelimit-reset-tokens', b'164ms'), (b'x-ratelimit-reset-tokens_usage_based', b'164ms'), (b'x-request-id', b'a0432124c4b48e9aacede30f130f3653'), (b'CF-Cache-Status', b'DYNAMIC'), (b'Server', b'cloudflare'), (b'CF-RAY', b'837c08300a2e6a57-EWR'), (b'Content-Encoding', b'gzip'), (b'alt-svc', b'h3=":443"; ma=86400')])
2023-12-18 20:57:32,530 - INFO - HTTP Request: POST https://api.openai.com/v1/chat/completions "HTTP/1.1 200 OK"
2023-12-18 20:57:32,530 - DEBUG - receive_response_body.started request=<Request [b'POST']>
2023-12-18 20:57:32,531 - DEBUG - receive_response_body.complete
2023-12-18 20:57:32,531 - DEBUG - response_closed.started
2023-12-18 20:57:32,531 - DEBUG - response_closed.complete
2023-12-18 20:57:32,531 - DEBUG - HTTP Request: POST https://api.openai.com/v1/chat/completions "200 OK"
2023-12-18 20:57:32,535 - INFO - Best Performing Algorithm:
2023-12-18 20:57:32,535 - INFO - Program Code:
def optimized_bucket_filler(numbers, bucket_limit):
    numbers.sort(reverse=True)
    buckets = []

    while numbers:
        bucket = []
        remaining_capacity = bucket_limit

        for number in sorted(numbers, key=lambda n: -abs(bucket_limit / 2 - n)):
            if number <= remaining_capacity:
                bucket.append(number)
                remaining_capacity -= number

        buckets.append(bucket)
        numbers = [n for n in numbers if n not in bucket]

    return buckets
2023-12-18 20:57:32,535 - INFO - Equation:
\begin{align*}
&\text{Given a list of integers } L \text{ and an integer } B:\\
&1. \, \text{Sort } L \text{ in descending order.}\\
&2. \, \text{Initialize an empty collection of buckets.}\\
&3. \, \text{While } L \text{ is not empty do:}\\
&\quad a. \, \text{Initialize a new empty bucket with remaining capacity } B.\\
&\quad b. \, \text{Sort } L \text{ by distance to } \frac{B}{2} \text{ and in descending order.}\\
&\quad c. \, \text{Iterate over this sorted list:}\\
&\quad\quad i.\, \text{If element } l \leq \text{remaining capacity, add } l \text{ to current bucket and subtract } l \text{ from capacity.}\\
&\quad d. \, \text{Append the current bucket to the collection of buckets.}\\
&\quad e. \, \text{Remove elements placed in the current bucket from } L.\\
&4. \, \text{Return the collection of buckets.}
\end{align*}
2023-12-18 20:57:32,535 - INFO - Pseudocode:
FUNCTION optimized_bucket_filler(numbers, bucket_limit)
    SORT numbers in descending order
    INITIALIZE buckets as empty list

    WHILE numbers is not empty
        INITIALIZE bucket as empty list
        SET remaining_capacity to bucket_limit

        FOR number in numbers sorted by closest distance to bucket_limit / 2 in descending order
            IF number is less than or equal to remaining_capacity
                ADD number to bucket
                DECREMENT remaining_capacity by number

        ADD bucket to buckets
        FILTER numbers to exclude those in the current bucket

    RETURN buckets
2023-12-18 20:57:32,535 - INFO - Fitness Score: 49.998648227568864