This chapter presents a series of studies we have carried out to develop more effective and efficient approaches of Cooperative Coevolutionary Algorithms (CEAs) to solve large-scale optimization problems. Early cooperative CEAs are promising alternatives to Evolutionary Algorithms (EAs) for large-scale optimization problems with high dimensionality in design variables. But they are mostly successful in solving separable problems that can be decomposed into single-variable subcomponents. The introduction section reviews existing CEAs and EAs and how high-dimensional optimization problems with interdependencies in design variables pose significant problem-solving challenges. The following sections present new mechanisms for grouping strategies to address challenges in solving nonseparable optimization problems via cooperative coevolutionary Divide-and-Conquer. A new framework in this problem-solving setting is introduced that employs random grouping. We provide theoretical motivations, a real-world algorithmic implementation, and systematic computational studies to evaluate the effectiveness and efficiency of our proposed approach to optimize nonseparable problems up to 1000 dimensions. In the following section, we address the issue associated with the lack of prior knowledge required for problem decomposition through a mechanism that performs automatic decomposition. We provide theoretical motivation for this differential grouping strategy that aims to uncover the underlying interaction structure of the decision variables and form subcomponents with minimal interdependencies. Systematic computational studies demonstrate how differential grouping is more efficient via appropriate assignment of computational budget to optimize various subcomponents through cooperative CEA. However, there are opportunities to improve this mechanism. They include a new sampling procedure that maximizes reuse of sampled points during identification of interactions between decision variables and an automatic and dynamic threshold setting of the associated parameter \(\epsilon \) that takes arithmetic roundoff errors into account. Systematic computational studies show that our second generation differential grouping strategy (DG2) improves on the original in terms of efficiency and accuracy of cooperative CEAs applied to both separable and nonseparable high-dimensional optimization problems.

Cooperative Coevolution for Large-Scale Optimization

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发表日期：

2025年

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Xin Yao,
Siang Yew Chong

摘要

This chapter presents a series of studies we have carried out to develop more effective and efficient approaches of Cooperative Coevolutionary Algorithms (CEAs) to solve large-scale optimization problems. Early cooperative CEAs are promising alternatives to Evolutionary Algorithms (EAs) for large-scale optimization problems with high dimensionality in design variables. But they are mostly successful in solving separable problems that can be decomposed into single-variable subcomponents. The introduction section reviews existing CEAs and EAs and how high-dimensional optimization problems with interdependencies in design variables pose significant problem-solving challenges. The following sections present new mechanisms for grouping strategies to address challenges in solving nonseparable optimization problems via cooperative coevolutionary Divide-and-Conquer. A new framework in this problem-solving setting is introduced that employs random grouping. We provide theoretical motivations, a real-world algorithmic implementation, and systematic computational studies to evaluate the effectiveness and efficiency of our proposed approach to optimize nonseparable problems up to 1000 dimensions. In the following section, we address the issue associated with the lack of prior knowledge required for problem decomposition through a mechanism that performs automatic decomposition. We provide theoretical motivation for this differential grouping strategy that aims to uncover the underlying interaction structure of the decision variables and form subcomponents with minimal interdependencies. Systematic computational studies demonstrate how differential grouping is more efficient via appropriate assignment of computational budget to optimize various subcomponents through cooperative CEA. However, there are opportunities to improve this mechanism. They include a new sampling procedure that maximizes reuse of sampled points during identification of interactions between decision variables and an automatic and dynamic threshold setting of the associated parameter \(\epsilon \) that takes arithmetic roundoff errors into account. Systematic computational studies show that our second generation differential grouping strategy (DG2) improves on the original in terms of efficiency and accuracy of cooperative CEAs applied to both separable and nonseparable high-dimensional optimization problems.