Solution of Multiple Travelling Salesman Problem using Particle Swarm Optimization based Algorithms

Abstract

Nowadays, the systems that are inspired by biological structures have gained importance and attracted the attention of researchers. The Multiple Travelling Salesman Problem (MTSP) is an extended version of the TSP. The aim in the MTSP is to find the tours for m salesmen, who all start and end at the depot, such that each intermediate node is visited exactly once and the total cost of visiting nodes is minimized. The Particle Swarm Optimization (PSO) algorithm which is a meta-heuristic algorithm based on the social behaviour of birds. In this article, 2 algorithms based on PSO, called APSO and HAPSO, were proposed to solve the MTSP. The APSO algorithm is based on the PSO and 2-opt algorithms, the path-relink and swap operators. While the HAPSO algorithm is based on the GRASP, PSO and 2-opt algorithms, the path-relink and swap operators. In the experiments, 5 TSP instances are used and the algorithms are compared with the GA and ACO algorithms. According to the results, the HAPSO algorithm has the better performance than the other algorithms on the most instances. Moreover the HAPSO algorithm produces more stable results than the APSO algorithm and the performance of the HAPSO algorithm is better in all the MTSP instances. Therefore, the HAPSO algorithm is more robust than the APSO algorithm.

Single Depot Multiple Travelling Salesman Problem Solved With Preference-Based Stepping Ahead Firefly Algorithm

“…Comparative experiments against particle swarm optimization (PSO) and invasive weed optimization algorithms show that IPGA outperforms in solving MTSP, as validated using TSPLIB benchmarks. Particle Swarm Optimization (PSO) based algorithms (APSO and HAPSO) were introduced by [16], demonstrating competitive results. APSO incorporates PSO, 2-opt algorithms, and path-relink and swap operators, while HAPSO combines GRASP, PSO, 2-opt algorithms, and the same path-relink and swap operators.…”

“…Variations also include the 2m depots case or the >1 and <2m depots case, as well as hybridizations of these cases [14]. The focus of this paper is on the single depot MTSP, which remains an area with room for improvement [15], [16].…”

Solving the Multiple Traveling Salesman Problem Using Memetic Algorithm

“…Gulcu and Ornek [12] proposed a swarm optimization approach to solve the MTSP. The solution utilizes two metaheuristic approaches; APSO and HAPSO whereby the former is based on a 2-opt approach while the latter utilizes the Greedy Randomized Adaptive Search Procedure (GRASP).…”

“…To show the advantage of the proposed approach over existing approaches, we compared achieved results with three recent approaches applied on five instances chosen from the TSPLIB dataset for three salesmen. These approaches used Adaptive Particle Swarm Optimization (APSO), Hybrid Particle Swarm Optimization (HPSO) [12], and Ant Colony Optimization (ACO) [17]. As can be noticed from Table 5 and Figure 3, the proposed approach achieved competitive results and small error rates (err) compared to those approaches.…”

TS and ACO in Hybrid Approach for Product Distribution Problem

“…In addition, the modifications were intended to help the DFACO algorithm find better solutions in less processing time and to avoid getting stuck in local minima. Gulcu (2019) proposed a two-hybrid approach with 2-opt algorithms hybridization. The authors found circuits for m sellers, which all started and ended at the depot so that each intermediate node was visited exactly once and the total cost of the visit nodes was minimized.…”