ACO-Based Neighborhoods for Fixed-charge Capacitated Multi-commodity Network Design Problem

The fixed-charge Capacitated Multi-commodity Network Design (CMND) is a well-known problem of both practical and theoretical significance. Network design models represent a wide variety of planning and operation management issues in transportation telecommunication, logistics, production and distribution. In this paper, Ant Colony Optimization (ACO) based neighborhoods are proposed for CMND problem. In the proposed neighborhoods, first, an open arc based on the incumbent solution is closed; then, by using an ant colony optimization algorithm called Ant Colony System (ACS), a new solution is generated by constructing new paths for the demands delivered on the closed arc. An algorithm is presented to construct new paths by using ACS algorithm for demands with continuous volume. A sub mixed integer programming (MIP) model is then created by joining the ACS and incumbent solutions. The generated sub-MIP is solved by using an MIP solver and its solution is considered as a neighborhood. In order to evaluate the proposed neighborhoods, an algorithm is developed. The algorithm parameters are tuned by using design of experiments. To assess the algorithm, several benchmark problems with different sizes are used. The statistical analysis shows the efficiency and effectiveness of the proposed algorithm compared to the best approaches found in the literature.