Scaling Up Dynamic Optimization Problems: A Divide-and-Conquer Approach

Scalability is a crucial aspect of designing efficient algorithms. Despite their prevalence, large-scale dynamic optimization problems are not well-studied in the literature. This paper is concerned with designing benchmarks and frameworks for the study of large-scale dynamic optimization problems. We start by a formal analysis of the moving peaks benchmark and show its nonseparable nature irrespective of its number of peaks. We then propose a composite moving peaks benchmark suite with exploitable modularity covering a wide range of scalable partially separable functions suitable for the study of large-scale dynamic optimization problems. The benchmark exhibits modularity, heterogeneity, and imbalance features to resemble real-world problems. To deal with the intricacies of large-scale dynamic optimization problems, we propose a decomposition-based coevolutionary framework which breaks a large-scale dynamic optimization problem into a set of lower dimensional components. A novel aspect of the framework is its efficient bi-level resource allocation mechanism which controls the budget assignment to components and the populations responsible for tracking multiple moving optima. Based on a comprehensive empirical study on a wide range of large-scale dynamic optimization problems with up to 200 dimensions, we show the crucial role of problem decomposition and resource allocation in dealing with these problems. The experimental results clearly show the superiority of the proposed framework over three other approaches in solving large-scale dynamic optimization problems.