Pareto Evolutionary Algorithm Hybridized with Local Search for Biobjective TSP

Traveling Salesperson Problem (TSP) is among the most-studied and hard combinatorial optimization problems and has been investigated by numerous researchers of both theoretical and practical interests. Biobjective version of the problem is harder because it requires obtaining a set of diverse and equivalent (nondominated) solutions forming a Paretofront, rather a single solution. Multiobjective Evolutionary Algorithms (MOEA), which have been successfully used to solve many complex real-world applications, have been unable to explore the TSP solution space and obtain the diverse and close-to-optimal Pareto-front. Therefore, there have been attempts by many researchers to effectively solve the problem, using hybrid methods, namely, heuristic and stochastic algorithms, simulated annealing and neural networks, Pareto local and Tabu search, memetic and evolutionary algorithms. In this chapter, first, we review the major work done and highlight the issues and challenges in solving single and multiobjective TSP instances, in general. Then, we present a Pareto-rank-based evolutionary algorithm hybridized with local search heuristics. Since the problem is hard and Pareto-front is unknown, the main issue in such problem instances is how to assess convergence. Therefore, in this work, we use a simple selection process to maintain diversity and rank-histograms to assess convergence. We generate initial individuals randomly subject to a steepest local search in each objective separately, and use a range of local exchange operators to further locally explore the feasible solution space. We evaluate the approach on TSP instances taken from TSPLIB datasets, and compare the obtained results with other hybrid approaches used in the past for the biobjective TSP. We quantify the obtained solution fronts for extent, diversity, and convergence.