A Graph-Induced Neighborhood Search Heuristic for the Capacitated Multicommodity Network Design Problem

Abstract

In this work, an efficient graph-induced neighborhood search heuristic is proposed to address the capacitated multicommodity network design problem. This problem, which commonly arises in transportation and telecommunication, is well known for its inherent complexity and is often classified as NP-hard. Our approach commences with an arbitrary feasible solution and iteratively improves it by solving a series of small-scale auxiliary mixed-integer programming problems. These small-scale problems are closely tied to the cycles inherent in the network topology, enabling us to reroute the flow more effectively. Furthermore, we have developed a novel resource-efficient facility assignment technique that departs from standard variable neighborhood search algorithms. By solving a series of small knapsack problems, this technique not only enhances the quality of solutions further but also can serve as a primary heuristic to generate initial feasible solutions. Furthermore, we theoretically guarantee that our algorithm will always produce an integer-feasible solution within polynomial time. The experimental results highlight the superior performance of our method compared to other existing approaches. Our heuristic algorithm efficiently discovers high-quality feasible solutions, substantially reducing the computation time and number of nodes in the branch-and-bound tree.