A computational study of off-the-shelf MINLP solvers on a benchmark set of congested capacitated facility location problems

TL;DR

This study evaluates five popular off-the-shelf solvers on congested capacitated facility location problems formulated as MICPs, revealing Mosek and Gurobi as the most effective for different instance sizes and complexities.

Contribution

It provides a comparative analysis of solver performance on MICPs for facility location, offering practical insights for selecting suitable solvers based on problem characteristics.

Findings

Mosek and Gurobi outperform others in efficiency and accuracy.

Xpress solves about half of the instances to optimality within time limits.

Cplex and Scip are less competitive in this problem class.

Abstract

This paper analyzes the performance of five well-known off-the-shelf optimization solvers on a set of congested capacitated facility location problems formulated as mixed-integer conic programs (MICPs). We aim to compare the computational efficiency of the solvers and examine the solution strategies they adopt when solving instances with different sizes and complexity. The solvers we compare are Gurobi, Cplex, Mosek, Xpress, and Scip. We run extensive numerical tests on a testbed of 30 instances from the literature. Our results show that Mosek and Gurobi are the most competitive solvers, as they achieve better time and gap performance, solving most instances within the time limit. Mosek outperforms Gurobi in large-size problems and provides more accurate solutions in terms of feasibility. Xpress solves to optimality about half of the instances tested within the time limit, and in this half, it achieves performance similar to that of Gurobi and Mosek. Cplex and Scip emerge as the least competitive solvers. The results provide guidelines on how each solver behaves on this class of problems and highlight the importance of choosing a solver suited to the problem type.