Evolutionary Many-Objective Optimization Based on Adversarial Decomposition

TL;DR

This paper introduces an adversarial decomposition approach for many-objective optimization that co-evolves two populations with different scalarizing functions to better handle complex Pareto front shapes.

Contribution

It develops a novel adversarial decomposition method that enhances flexibility by co-evolving populations with different scalarizing functions and matching solutions to improve optimization performance.

Findings

Outperforms nine state-of-the-art optimizers on 130 test instances.

Effectively handles various Pareto front shapes.

Demonstrates competitive performance in many-objective problems.

Abstract

The decomposition-based method has been recognized as a major approach for multi-objective optimization. It decomposes a multi-objective optimization problem into several single-objective optimization subproblems, each of which is usually defined as a scalarizing function using a weight vector. Due to the characteristics of the contour line of a particular scalarizing function, the performance of the decomposition-based method strongly depends on the Pareto front's shape by merely using a single scalarizing function, especially when facing a large number of objectives. To improve the flexibility of the decomposition-based method, this paper develops an adversarial decomposition method that leverages the complementary characteristics of two different scalarizing functions within a single paradigm. More specifically, we maintain two co-evolving populations simultaneously by using different scalarizing functions. In order to avoid allocating redundant computational resources to the same region of the Pareto front, we stably match these two co-evolving populations into one-one solution pairs according to their working regions of the Pareto front. Then, each solution pair can at most contribute one mating parent during the mating selection process. Comparing with nine state-of-the-art many-objective optimizers, we have witnessed the competitive performance of our proposed algorithm on 130 many-objective test instances with various characteristics and Pareto front's shapes.