Comparing the solvers for the mixed integer linear programming problems and the software environments that call them

The paper presents a concept for comparing the solvers for the mixed integer linear programming problems and the software environments that call them. This concept involves multiple repetition of solving mathematical programming problems with the same initial data to take into account the fact that the computer operations time can be considered as random. It is also assumed to solve the mathematical programming problem with the same structure by varying the initial data to compare the solvers. The comparison is carried out for a number of practical mathematical programming problems. For example we consider the portfolio optimization problem with the probability criterion. Solvers CPLEX, Gurobi, MATLAB, SCIP are used in testing. The features of calling solvers in various software environments are described. In particular, a modification of the source codes for calling the CPLEX solver through the Opti Toolbox add-on in Matlab environment is provided. The components of the time required to obtain a solution for various solvers and software environments are described and studied in detail. It is shown that the operating time of the solver itself can be comparable to the time of reading data from files and the time of forming constraints in a mathematical programming problem.