Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study

Abstract

Abstract. In this article, we study Pareto local optimum sets for the biobjective Traveling Salesman Problem applying straightforward extensions of local search algorithms for the single objective case. The performance of the local search algorithms is illustrated by experimental results obtained for well known benchmark instances and comparisons to methods from literature. In fact, a 3-opt local search is able to compete with the best performing metaheuristics in terms of solution quality. Finally, we also present an empirical study of the features of the solutions found by 3-opt on a set of randomly generated instances. The results indicate the existence of several clusters of near-optimal solutions that are separated by only a few edges.

Combining Two Search Paradigms for Multi-objective Optimization: Two-Phase and Pareto Local Search

“…Pareto Local Search (PLS) [52] is a paradigmatic representative of dominancebased multi-objective algorithms that improve solutions one at a time by use of neighborhood search [53]. While the original motivation for proposing PLS was to study the connectedness of solutions [52], PLS turned out to be also an effective local search method for multi-objective problems.…”

“…While the original motivation for proposing PLS was to study the connectedness of solutions [52], PLS turned out to be also an effective local search method for multi-objective problems. Independently, a very similar algorithm was proposed by Angel et al [4].…”

“…As a representative of dominance-based methods we discuss Pareto Local Search (PLS) [52], and as a representative of scalarization-based methods we present Two-Phase Local Search (TPLS) [54]. We describe these two methods together with their latest associated developments and show that their hybridization provides a general framework for multi-objective combinatorial optimization that leads to high performing algorithms.…”

An Analysis of Local Search for the Bi-objective Bidimensional Knapsack Problem

“…Pareto local search (PLS) is a stochastic local search method for tackling multiobjective problems based on a natural extension of single-objective local search approaches [13]. To fully understand PLS, some background notions on multiobjective optimization are required.…”

“…Pareto local search (PLS) [13] is a straightforward but effective extension of single-objective local search to multi-objective problems. Given a set of solutions, a PLS algorithm consists of selecting one solution at a time and exploring its neighborhood, thus, generating new solutions.…”