Enhancing the Dhouib-Matrix-4 Metaheuristic to Generate the Pareto Non-Dominated Set Solutions for Multi-objective Travelling Salesman Problem: The DM4-PMO Method

This paper focuses on the multi-objective Travelling Salesman Problem for which the aim is to find the set of efficient solutions. To obtain this Pareto set's solutions, a novel metaheuristic named DM4-PMO is proposed. The DM4-PMO is based on the first enhancement of the new Dhouib-Matrix-4 (DM4) method and composed of two steps. First, a weighted sum function with a multi variation of weights is used to find the first non-dominated pareto frontier solutions. Second, a lexicographical resolution is applied in some non-dominated solutions found in the first Pareto frontier to generate the final Pareto frontier solutions. The performance of the proposed approach is demonstrated by the experiment on two-objective problems that are taken from TSP-LIB and DIMACS datasets. The test results show that the proposed DM4-PMO is robust, fast, and simply structured, and obtain a Pareto non-dominated set solutions in short computational times using very few user-defined parameters.