Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes

TLDR

Many-objective evolutionary algorithms that use systematically generated weight vectors have been proposed and continue to improve, achieving strong performance on standard DTLZ and WFG test problems. This paper argues that the race to improve performance on these test problems risks overspecialization, and calls for more general test problems and flexible algorithms. The authors analyze DTLZ and WFG test problems and examine how their features interact with weight vector-based algorithms such as MOEA/D, NSGA‑III, MOEA/DD, and θ‑DEA. Computational experiments show that even slight modifications to DTLZ and WFG formulations markedly reduce the performance of these algorithms.

Abstract

Recently, a number of high performance many-objective evolutionary algorithms with systematically generated weight vectors have been proposed in the literature. Those algorithms often show surprisingly good performance on widely used DTLZ and WFG test problems. The performance of those algorithms has continued to be improved. The aim of this paper is to show our concern that such a performance improvement race may lead to the overspecialization of developed algorithms for the frequently used many-objective test problems. In this paper, we first explain the DTLZ and WFG test problems. Next, we explain many-objective evolutionary algorithms characterized by the use of systematically generated weight vectors. Then we discuss the relation between the features of the test problems and the search mechanisms of weight vector-based algorithms such as multiobjective evolutionary algorithm based on decomposition (MOEA/D), nondominated sorting genetic algorithm III (NSGA-III), MOEA/dominance and decomposition (MOEA/DD), and θ-dominance based evolutionary algorithm (θ-DEA). Through computational experiments, we demonstrate that a slight change in the problem formulations of DTLZ and WFG deteriorates the performance of those algorithms. After explaining the reason for the performance deterioration, we discuss the necessity of more general test problems and more flexible algorithms.