MatrixOptim.jl

MILP, Robust Optim. and Stochastic Optim., Decomposition Algorithms, and more in Matrix.

MatrixOptim.jl is a package to model and solve optimization in uncertain context. The templates for robust optimization and stochastic optimization formulated in matrix are very coherent comprehensive, and the algorithms in matrix are very explicit.

This is a package I developed in 2019. Don't know too much about tests and documentation that time. I am trying to keep it up-to-date these days.

Introduction

The MILP can always be formulated in the following matrixes:

min  vec_c' * vec_x + vec_f' * vec_y
s.t. mat_A * vec_x + mat_B * vec_y <= vec_b
     vec_x in R
     vec_y in Z

Installation and Test

(v1.1) pkg> add MatrixOptim

(v1.1) pkg> test MatrixOptim

How to Use

For mixed integer linear programming:

model = getModel(vec_c, mat_aa, vec_b)
solveModel!(model)

For mixed integer linear programming with Benders decomposition:

model = getModelBenders(n_x, n_y, vec_min_y, vec_max_y, vec_c, vec_f, vec_b, mat_aa, mat_bb)
solveModelBenders!(model)

Right now, the supported solver is GLPK. Will add the feature to select other solvers, like Gurobi and CPLEX later.

Features

Models

• Linear Programming
• Mixed Integer Linear Programming
• Robust Optimization
• Stochastic Optimization
• Markov Decision Process
• Dynamic Optimization

Algorithms

• Simplex Method
• Branch and Cut for MILP
• Benders Decomposition for MILP
• L-Shaped Benders Decomp for Stochastic Optim
• Dantzig-Wolfe Decomposition Family

More Info

• Cookbook for theories and algorithms in MatrixOptim: MatrixOptim-Cookbook .
• 矩阵优化：通过矩阵表示混合整数线性规划，鲁棒（抗差）优化，随机优化和分解算法。