Multimodal optimization of traveling salesman problem: a niching ant colony system

Multimodal optimization (MMO) aims at finding multiple optimal (or close to optimal) solutions, which plays a crucial role in various fields. However, most of the efforts have been devoted to the continuous MMO domain, while little attention has been paid to discrete problems like the traveling salesman problem (TSP). This paper makes a proof of principle study on multimodal TSP. Particularly, we design a test suite for multimodal TSP and then develop an ant colony algorithm to accomplish the optimization task. The traditional ant algorithms such as the ant colony system are unable to maintain multiple solutions because of the global convergence. To deal with this problem, we propose a novel niching ant colony system (NACS). The algorithm employs a niching strategy and multiple pheromone matrices to preserve population diversity and keep the trace of multiple paths. The experimental results are presented to validate the good performance of the proposed algorithm.