A Hybrid Simulated Annealing and Simplex Method for Fixed-Cost Capacitated Multicommodity Network Design

The fixed-cost Capacitated Multicommodity Network Design (CMND) problem is a well known NP-hard problem. This paper presents a matheuristic algorithm combining Simulated Annealing (SA) metaheuristic and Simplex method for CMND problem. In the proposed algorithm, a binary array is considered as solution representation and the SA algorithm manages open and closed arcs. Several strategies for opening and closing arcs are proposed and evaluated. In this matheuristic approach, for a given design vector, CMND becomes a Capacitated Multicommodity minimum Cost Flow (CMCF) problem. The exact evaluation of the CMCF problem is performed using the Simplex method. The parameter tuning for the proposed algorithm is done by means of design of experiments approach. The performance of the proposed algorithm is evaluated by solving different benchmark instances. The results of the proposed algorithm show that it is able to obtain better solutions in comparison with previous methods in the literature.