Abstract EN:

The use of cutting planes is since severals years one of the most used methods to improve the search of an optimal solution reducing the search space in a Branch-and-Bound. The work presented here aims at studying several cutting plane methods and at proposing some strategies to integrate them in a resolution method based on Branch-and-Bound algorithm to solve mixed integer 0-1 problems. We present extensive computational experiments in ordrer to try to find efficient cutting plane generation strategies with generic mixted integer 0-1 problems and with different solvers. For this study, some solvers were used to compare their when the same cutting planes are added. Two commercial solver (Cplex and Xpress) and one free solveur (Glpk) are used to test the different strategies in a sequential Branch-and-Bound. One free solver is used to test these strategies in a parallel Branch-and-Bound. To provide an easy way to use these different solvers, a free library (Glop) that allows the user to use some solver with a same code has been created. We first present the different cutting plane methods that were integrated in the library Glop to produce computational experimentents. We then turn our interest on the different strategies we implement, the one being fixed strategies, the other being strategies that adapt to the problem resolution. We present and analyse the results of computational experiments with sequential Branch-and-Bound and in the last part, those obtained with parallel Branch-and-Bound.