Experimental Analysis of Design Elements of Scalarizing Functions-based Multiobjective Evolutionary Algorithms

TL;DR

This paper systematically investigates the influence of key design elements in scalarizing functions-based multiobjective evolutionary algorithms, revealing that parent selection mechanism significantly impacts performance, while weight vector selection is less critical with enough vectors.

Contribution

It identifies the parent selection mechanism as the primary factor affecting performance in scalarizing functions-based MOEAs, providing insights for algorithm design.

Findings

Parent selection mechanism significantly influences performance.

Weight vector selection is less critical with sufficient vectors.

Experimental validation on three multiobjective combinatorial problems.

Abstract

In this paper we systematically study the importance, i.e., the influence on performance, of the main design elements that differentiate scalarizing functions-based multiobjective evolutionary algorithms (MOEAs). This class of MOEAs includes Multiobjecitve Genetic Local Search (MOGLS) and Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) and proved to be very successful in multiple computational experiments and practical applications. The two algorithms share the same common structure and differ only in two main aspects. Using three different multiobjective combinatorial optimization problems, i.e., the multiobjective symmetric traveling salesperson problem, the traveling salesperson problem with profits, and the multiobjective set covering problem, we show that the main differentiating design element is the mechanism for parent selection, while the selection of weight vectors, either random or uniformly distributed, is practically negligible if the number of uniform weight vectors is sufficiently large.