Solving the Multiple Traveling Salesman Problem Using Memetic Algorithm

Abstract

The Multiple Traveling Salesman Problem (MTSP) is considered as an NP-complete problem due to the difficulty of finding the shortest tour between different cities with a set of constraints such as visiting each city once by one salesman. The solution tour represents the sum of all tours' costs performed by n salesmen. In this research, we propose a novel approach to find different solutions for various instances of MTSP based on a memetic algorithm using Genetic Algorithm (GA) and Hill-Climbing (HC) algorithm. The experimental results proved that the memetic approach achieved promising results i.e., minimum total tour compared to other existing approaches.

A Biogeography-Based Optimization with a Greedy Randomized Adaptive Search Procedure and the 2-Opt Algorithm for the Traveling Salesman Problem

“…Table 4 shows that when the number of city points is less than 100 locations Eil51 (Eil76), the best solution values of these algorithms Table 4. Execution results of three TSP test sets for original BBO algorithm, G2BBO algorithm, MA algorithm [10], DRSO algorithm [11], GA-JGHO algorithm [13], BBOEAX algorithm [9].…”

“…Several approximate algorithms have been proposed lately. There are various approximations such as edge assembly cross-over BBO (EAX-BBO) [9], memetic algorithm (MA) [10], discrete rat swarm optimization (DRSO) [11,12], a genetic algorithm with jumping gene (GA-JGHO) [13]. Despite the differences in search mechanisms, these methods strive to avoid the local minimum problem with complicated mathematics.…”