A Novel Two-Phase Cooperative Co-evolution Framework for Large-Scale Global Optimization with Complex Overlapping

TL;DR

This work tackles large-scale global optimization with complex variable overlap, where standard cooperative co-evolution (CC) struggles. It introduces the Hybrid Cooperative Co-evolution Framework (HCC), which combines a mathematically grounded RDDSM for reliable ideal decomposition with a two-phase collaboration mechanism that adapts between non-decomposition algorithms (NDAs) and CC based on the degree of overlap $DO$ and a global FEs metric $GloFEs$. AOB, a configurable benchmark extension, enables systematic study of overlapping structures and demonstrates that RDDSM achieves ideal decomposition and that HCC delivers superior performance across overlapping scenarios. The findings clarify the differing strengths of CC and NDAs in overlap contexts and provide an open-source implementation to advance research on large-scale optimization with overlapping variables.

Abstract

Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both effectiveness and efficiency compared to non-decomposition algorithms. However, the presence of overlapping variables complicates the decomposition process and adversely affects the performance of cooperative co-evolution. In this study, we propose a novel two-phase cooperative co-evolution framework to address large-scale global optimization problems with complex overlapping. An effective method for decomposing overlapping problems, grounded in their mathematical properties, is embedded within the framework. Additionally, a customizable benchmark for overlapping problems is introduced to extend existing benchmarks and facilitate experimentation. Extensive experiments demonstrate that the algorithm instantiated within our framework significantly outperforms existing algorithms. The results reveal the characteristics of overlapping problems and highlight the differing strengths of cooperative co-evolution and non-decomposition algorithms. Our work is open-source and accessible at: https://github.com/GMC-DRL/HCC.

Figures (7)

• Figure 1: The equivalence of representations of interactions.
• Figure 2: The Best-so-Far Evaluation Curves for Different Algorithms
• Figure 3: The Accuracy of Decomposition strategies and the Time Cost of Algorithms
• Figure 4: The Evaluation Curves for Different Algorithms
• Figure 5: The Process of RDDSM