Cooperative coevolutionary Modified Differential Evolution with Distance-based Selection for Large-Scale Optimization Problems in noisy environments through an automatic Random Grouping

TL;DR

This paper introduces an automatic random grouping method and a modified differential evolution algorithm with distance-based selection, effectively solving large-scale noisy optimization problems by detecting variable interactions and enhancing search capabilities.

Contribution

It proposes a novel automatic grouping method and an improved differential evolution algorithm tailored for noisy large-scale optimization problems, without requiring prior landscape knowledge.

Findings

The method successfully detects variable interactions in noisy environments.

It outperforms canonical DE in exploration and exploitation abilities.

The approach is effective for high-dimensional noisy optimization problems.

Abstract

Many optimization problems suffer from noise, and nonlinearity check-based decomposition methods (e.g. Differential Grouping) will completely fail to detect the interactions between variables in multiplicative noisy environments, thus, it is difficult to decompose the large-scale optimization problems (LSOPs) in noisy environments. In this paper, we propose an automatic Random Grouping (aRG), which does not need any explicit hyperparameter specified by users. Simulation experiments and mathematical analysis show that aRG can detect the interactions between variables without the fitness landscape knowledge, and the sub-problems decomposed by aRG have smaller scales, which is easier for EAs to optimize. Based on the cooperative coevolution (CC) framework, we introduce an advanced optimizer named Modified Differential Evolution with Distance-based Selection (MDE-DS) to enhance the search ability in noisy environments. Compared with canonical DE, the parameter self-adaptation, the balance between diversification and intensification, and the distance-based probability selection endow MDE-DS with stronger ability in exploration and exploitation. To evaluate the performance of our proposal, we design $500$-D and $1000$-D problems with various separability in noisy environments based on the CEC2013 LSGO Suite. Numerical experiments show that our proposal has broad prospects to solve LSOPs in noisy environments and can be easily extended to higher-dimensional problems.