A Recursive Decomposition Method for Large Scale Continuous Optimization

Abstract

Cooperative Co-evolution (CC) is an evolutionary computation framework that can be used to solve high dimensional optimization problems via a 'divide-and-conquer' mechanism. However, the main challenge when using this framework lies in problem decomposition. That is, deciding how to allocate decision variables to a particular sub-problem, especially interacting decision variables. Existing decomposition methods are typically computationally expensive. In this paper, we propose a new decomposition method, which we call Recursive Differential Grouping (RDG), by considering the interaction between decision variables based on non-linearity detection. RDG recursively examines the interaction between a selected decision variable and the remaining variables, placing all interacting decision variables into the same sub-problem. We use analytical methods to show that RDG can be used to efficiently decompose a problem, without explicitly examining all pairwise variable interactions. We evaluated the efficacy of the RDG method using large scale benchmark optimization problems. Numerical simulation experiments showed that RDG greatly improved the efficiency of problem decomposition in terms of time complexity. Significantly, when RDG was embedded in a CC framework, the optimization results were better than results from seven other decomposition methods.

A Parallel Divide-and-Conquer-Based Evolutionary Algorithm for Large-Scale Optimization

“…If so, such pair of decision variables were deemed to be interdependent and grouped together. More works [17], [22], [34] improved the grouping accuracy by referencing a tighter interdependency among decision variables, i.e., the additively separability [35].…”

Adaptive threshold parameter estimation with recursive differential grouping for problem decomposition

“…In the second method, intelligent decomposition, the structure of the components is determined by the identiied variable interactions [3,12,14,20]. Take a 6-dimensional problem as an example, where x 3 interacts with x 2 and x 4 , and x 5 interacts with x 6 .…”

“…The main challenge of using the CC framework lies in problem decomposition which is the process of identifying and grouping interacting decision variables into respective components [2,9,12]. A good decomposition should relect the underlying interaction structure of decision variables [12,14,20].…”

“…The recently proposed recursive diferential grouping (RDG) [20] method achieves great computational eiciency by recursively examining the interaction between two subsets of decision variables (instead of two variables commonly used in most decomposition algorithms). The number of function evaluations (FEs) used by RDG to decompose an n-dimensional problem has been shown to be less than 6n log(n).…”

Limited evaluation cooperative co-evolutionary differential evolution for large-scale neuroevolution

“…If the problem is separable, then the problem can be decomposed into its separable subcomponents. If there is no/uncertain knowledge of the problem domain, then automated methods can be used to identify the interactions of the subcomponents [23,33].…”