A topology-based single-pool decomposition framework for large-scale global optimization

Abstract

Identification of variable interaction plays a crucial role in applying a divide-and-conquer algorithm for large-scale black-box optimization. However, most of the existing decomposition methods are less efficient in decomposing the overlapping problems. This drawback diminishes the practicality of the existing methods. In this paper, we propose an efficient single-pool decomposition framework (SPDF). The interactions of decision variables are identified in an ordinal fashion. The unbalanced grouping efficiency of the existing decomposition methods can be significantly alleviated. Furthermore, we find that the grouping efficiency can be further improved by integrating the topological information into the decomposition process. In many real-world problems, this information can be 1-, 2- or 3-dimensional coordinates, which represent the geometric structure of the large-scale systems. Based on this, we propose a topology-based decomposition method, which we call Topology-based Single-Pool Differential Grouping (TSPDG). The efficacy of our proposed methods is demonstrated on the CEC’2010 and the CEC’2013 large-scale benchmark suites, as well as a practical case study in production optimization.