Merge pull request #67 from kakiac/patch-4

Corrected citations in paper.md

paper/paper.md

@@ -30,7 +30,7 @@ The Vehicle Routing Problem (VRP) is amongst the most well known combinatorial o
 The vehicles start and end their routes at a common depot and each customer must be served by exactly one vehicle.
 The objective is to assign a sequence of customers to each vehicle of the fleet (a route), minimizing the total distance traveled, such that all customers are served and the total demand served by each vehicle does not exceed its capacity. Note that the VRP generalises the well-known traveling salesman problem (TSP) and is therefore computationally intractable.
 
-Mathematicians have started tackling VRPs since 1959 [@dantzig1959truck]. Ever since, algorithms and computational power have not stopped improving. State of the art techniques include column generation approaches  [@costa2019exact; bramel1997solving] on which ``vrpy`` relies; more details are given hereafter.
+Mathematicians have started tackling VRPs since 1959 [@dantzig1959truck]. Ever since, algorithms and computational power have not stopped improving. State of the art techniques include column generation approaches  [@costa2019exact; @bramel1997solving] on which ``vrpy`` relies; more details are given hereafter.
 
 ``vrpy`` is of interest to the operational research community and others (e.g., logisticians, supply chain analysts) who wish to solve vehicle routing problems, and therefore has many obvious applications in industry.
 
@@ -81,7 +81,7 @@ print(prob.best_routes)
 
 Although the VRP is a classical optimization problem, to our knowledge there is only one dedicated package in the Python ecosystem that is able to solve such a range of VRP variants: the excellent ``OR-Tools`` (Google) routing library [@ortools], released for the first time in 2014. To be precise, the core algorithms are implemented in C++, but the library provides a wrapper in Python. Popular and efficient, it is a reference for ``vrpy``, both in terms of features and performance. The current version of ``vrpy`` is able to handle the same variants as OR-Tools (mentioned in the previous section).
 
-Performance-wise, ``vrpy`` ambitions to be competitive with ``OR-Tools`` eventually, at least in terms of solution quality. For the moment, benchmarks (available in the repository) for the CVRP on the set of Augerat instances ([@augerat1995approche]) show promising results: in the performance profile in Figure 1 below, one can see that nearly the same number of instances are solved within 10 seconds with the same relative error with respect to the best known solution (42\% for ``vrpy``, 44\% for ``OR-Tools``).
+Performance-wise, ``vrpy`` ambitions to be competitive with ``OR-Tools`` eventually, at least in terms of solution quality. For the moment, benchmarks (available in the repository) for the CVRP on the set of Augerat instances [@augerat1995approche] show promising results: in the performance profile in Figure 1 below, one can see that nearly the same number of instances are solved within 10 seconds with the same relative error with respect to the best known solution (42\% for ``vrpy``, 44\% for ``OR-Tools``).
 
 | ![Performance profile](cvrp_performance_profile.png) |
 | :--------------------------------------------------: |
@@ -106,7 +106,7 @@ This column generation procedure is very generic, as for each of the featuring V
 
 Note that ``vrpy`` does not necessarily return an optimal solution. Indeed, once the pricing problems fails to find
 a route with negative marginal cost, the master problem is solved as a MIP. This *price-and-branch* strategy does not guarantee optimality. Note however that it
-can be shown ([@bramel1997solving]) that asymptotically, the relative error goes to zero as the number of customers increases. To guarantee that an optimal solution is returned, the column generation procedure should be embedded in a branch-and-bound scheme (*branch-and-price*), which is beyond the scope of the current release, but part of the future work considered.
+can be shown [@bramel1997solving] that asymptotically, the relative error goes to zero as the number of customers increases. To guarantee that an optimal solution is returned, the column generation procedure should be embedded in a branch-and-bound scheme (*branch-and-price*), which is beyond the scope of the current release, but part of the future work considered.
 
 # Advanced Features