Bicriterion Coevolution for the Multi-objective Travelling Salesperson Problem

Abstract

The travelling salesperson problem is an NP-hard combinatorial optimization problem. In this paper, we consider the multi-objective travelling salesperson problem (MTSP), both static and dynamic, with conflicting objectives. NSGA-II and MOEA/D, two popular evolutionary multi-objective optimization algorithms suffer from loss of diversity and poor convergence when applied separately on MTSP. However, both these techniques have their individual strengths. NSGA-II maintains di-versity through non-dominated sorting and crowding distance selection. MOEA/D is good at exploring extreme points on the Pareto front with faster convergence. In this paper, we adopt the bicriterion framework that exploits the strengths of Pareto-Criterion (PC) and Non-Pareto Criterion (NPC) evolutionary populations. In this research, NSGA-II (PC) and MOEA/D (NPC) coevolve to compensate the diversity of each other. We further improve the convergence using local search and a hybrid of order crossover and inver-over operators. To our knowledge, this is the first work that combines NSGA-II and MOEA/D in a bicriterion framework for solving MTSP, both static and dynamic. We perform various experiments on different MTSP bench-mark datasets with and without traffic factors to study static and dynamic MTSP. Our proposed algorithm is compared against standard algorithms such as NSGA-II & III, MOEA/D, and a baseline divide and conquer coevolution technique using performance metrics such as inverted generational distance, hypervolume, and the spacing metric to concurrently quantify the convergence and diversity of our proposed algorithm. We also compare our results to datasets used in the literature and show that our proposed algorithm performs empirically better than compared algorithms.