Proximity-Based MAENS for Capacitated Multiple Traveling Salesmen Problem

Abstract

Capacitated Multiple Traveling Salesmen Problem (CMTSP) is an extension of the traditional Multiple Traveling Salesmen Problem (MTSP). In this problem, each city has a good with a certain weight to serve, and each salesman has a maximum weight capacity to serve the goods. To solve this problem effectively, this paper proposes a proximity-based crossover strategy for an existing and widely utilized method, namely the Memetic Algorithm with Extended Neighborhood Search (MAENS), leading to a new version of MAENS, which we name as PMAENS. In particular, this paper devises a similarity measure based on the common edges to calculate the similarity between two solutions. Then, during the selection of parents for crossover in MAENS, the similarity between any two solutions is taken into consideration so that two similar solutions preserve a high probability to crossover. In this way, the algorithm could achieve a promising balance between exploration and exploitation and thus is expected to obtain promising performance. Extensive experiments on the generated CMTSP instances demonstrate that the proposed PMAENS achieves competitive or even much better performance than MAENS with respect to both the convergence speed and the solution quality. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.