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.

Cooperative co-evolution is a framework that can be used to effectively solve large scale optimization problems. This approach employs a divide and conquer strategy, which decomposes the problem into sub-components that are optimized separately. However, solution quality relies heavily on the decomposition method used. Ideally, the interacting decision variables should be assigned to the same sub-component and the interdependency between sub-components should be kept to a minimum. Differential grouping, a recently proposed method, has high decomposition accuracy across a suite of benchmark functions. However, we show that differential grouping can only identify decision variables that interact directly. Subsequently, we propose an extension of differential grouping that is able to correctly identify decision variables that also interact indirectly. Empirical studies show that our extended differential grouping method achieves perfect decomposition on all of the benchmark functions investigated. Significantly, when our decomposition method is embedded in the cooperative co-evolution framework, it achieves comparable or better solution quality than the differential grouping method.

In this paper we use a divide-and-conquer approach to tackle large-scale optimization problems with overlapping components. Decomposition for an overlapping problem is challenging as its components depend on one another. The existing decomposition methods typically assign all the linked decision variables into one group, thus cannot reduce the original problem size. To address this issue we modify the Recursive Differential Grouping (RDG) method to decompose overlapping problems, by breaking the linkage at variables shared by multiple components. To evaluate the efficacy of our method, we extend two existing overlapping benchmark problems considering various level of overlap. Experimental results show that our method can greatly improve the search ability of an optimization algorithm via divide-and-conquer, and outperforms RDG, random decomposition as well as other state-of-the-art methods. We further evaluate our method using the CEC'2013 benchmark problems and show that our method is very competitive when equipped with a component optimizer.