A Niching Regression Adaptive Memetic Algorithm for Multimodal Optimization of the Euclidean Traveling Salesman Problem

Abstract

The traveling salesman problem (TSP) has been studied for many years. In particular, the multimodal optimization of the TSP is important for practical applications, because decision-makers can select the best candidate based on current conditions and requirements. In the Euclidean Traveling Salesman Problem, there are n points in Rd space with Euclidean distance between any two points, that is, d(x,y)=||x-y||2. The goal is to find a tour of minimum length visiting each point. In this paper, we only focus on the case that d=2. Recently, in order to efficiently handle the multimodal optimization of the TSP, some methods have been developed to deal with it. Nevertheless, these methods usually perform poorly for large-scale cases. In this paper, we propose a niching regression adaptive memetic algorithm to handle the multimodal optimization of the Euclidean TSP. We use the memetic algorithm as the baseline algorithm and incorporate the neighborhood strategy to maintain the population diversity. In addition, we design a novel regression partition initialization and adaptive parameter control to enhance our algorithm, and propose the concept of the redundant individual to improve the search efficiency. To validate performance of the proposed algorithm, we comprehensively conduct experiments on the multimodal optimization of TSP benchmark and the well-known TSPLIB library. The experimental results reveal that the proposed method outperforms other methods, especially for large-scale cases.