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

2025-03-23

AI Summary

Large-scale global optimization problems with complex variable overlap suffer from severe inter-subproblem coupling, limiting the performance of existing cooperative coevolutionary (CC) algorithms. To address this, we propose a two-stage cooperative evolutionary framework: in Stage I, overlapping subspaces are analytically decomposed using intrinsic mathematical properties—specifically, Hessian sparsity and functional separability; in Stage II, an adaptive subgroup collaboration mechanism dynamically coordinates overlapping regions. We further introduce the first customizable overlapping benchmark suite and release its open-source Python implementation. Experimental results demonstrate that our method significantly outperforms state-of-the-art CC algorithms on both standard and newly constructed overlapping test suites. Moreover, we provide the first systematic analysis revealing how structural characteristics of overlap—such as overlap density and topological dimension—critically influence algorithm selection, thereby establishing theoretical foundations and practical tools for overlapping optimization.

Technology Category

• Search and Optimization: Evolutionary Computation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Addresses large-scale optimization with complex overlapping variables
• Proposes decomposition method based on mathematical properties
• Introduces customizable benchmark for overlapping problems

Innovation

• Two-phase cooperative co-evolution framework
• Mathematical-based overlapping problem decomposition
• Customizable benchmark for overlapping problems