Pareto simulated annealing—a metaheuristic technique for multiple‐objective combinatorial optimization

Abstract

This paper presents a multiple-objective metaheuristic procedureÐPareto simulated annealing. The goal of the procedure is to find in a relatively short time a good approximation of the set of efficient solutions of a multipleobjective combinatorial optimization problem. The procedure uses a sample, of so-called generating solutions. Each solution explores its neighbourhood in a way similar to that of classical simulated annealing. Weights of the objectives, used for their local aggregation, are tuned in each iteration in order to assure a tendency for approaching the efficient solutions set while maintaining a uniform distribution of the generating solutions over this set. A computational experiment shows that the method is a better tool for approximating the efficient set than some previous proposals.

Design and analysis of stochastic local search for the multiobjective traveling salesman problem

“…As one representative of the SAC search model, we examine the straight-forward approach that solves several scalarizations of the objective function vector and tackles each of these problems with an underlying algorithm for the corresponding single objective version, an approach which underlies many earlier proposed algorithms [20,21,[26][27][28][29]. We follow the well-known principle of defining scalarizations of the objective function vector with respect to a weighted sum.…”

A Similarity-Based Mating Scheme for Evolutionary Multiobjective Optimization

“…This performance measure was used in Czyzak & Jaszkiewicz [2] and referred to as R D1 in Knowles & Corne [15]. The R D1 measure needs all Pareto-optimal solutions of each test problem.…”

A Two-Phase Local Search for the Biobjective Traveling Salesman Problem

“…In order to guarantee that a dispersed set of efficient solutions is obtained, several techniques have been proposed; these can be classified into one of two main groups: Methods that aggregate the objective functions and dynamically modify the search direction during the search process or within several runs [3,6,7,9,10,19,23], and methods that are based on a Paretolike dominance relation as an acceptance criterion in the search to distinguish between candidate solutions [24,13]; this second type of methods avoid the aggregation of objectives. Recently, empirical evidence was gathered suggesting that methods belonging to the first group perform particularly well [10], the main reason being that local search algorithms can deal more easily with aggregated objective functions.…”