Abstract-Cooperative co-evolution has been introduced into evolutionary algorithms with the aim of solving increasingly complex optimization problems through a divide-and-conquer paradigm. In theory, the idea of co-adapted subcomponents is desirable for solving large-scale optimization problems. However, in practice, without prior knowledge about the problem, it is not clear how the problem should be decomposed. In this paper, we propose an automatic decomposition strategy called differential grouping that can uncover the underlying interaction structure of the decision variables and form subcomponents such that the interdependence between them is kept to a minimum. We show mathematically how such a decomposition strategy can be derived from a definition of partial separability. The empirical studies show that such near-optimal decomposition can greatly improve the solution quality on large-scale global optimization problems. Finally, we show how such an automated decomposition allows for a better approximation of the contribution of various subcomponents, leading to a more efficient assignment of the computational budget to various subcomponents.

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Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

Standard Cooperative Co-evolution uses a round-robin method to select subcomponents to undergo optimization. In a non-separable (epistatic) optimization problem, dividing the computational budget equally between all of the subcomponents is not necessarily the best strategy. When dealing with non-separable problems, there is usually an imbalance between the contribution of various subcomponents to the global fitness of the individuals. Using a round-robin fashion treats all of the subcomponents equally and wastes the computational budget. In this paper, we propose a Contribution Based Cooperative Co-evolution (CBCC) that selects the subcomponents based on their contributions to the global fitness. This alleviates the imbalance issue and allows the computational resources to be used more efficiently. Experiments on several benchmark functions with the "imbalance issue" show that this new scheme is promising, especially when it is combined with a grouping algorithm that captures interacting variables in common subcomponents.

In this paper we propose three techniques to improve the performance of one of the major algorithms for large scale continuous global function optimization. Multilevel Cooperative Co-evolution (MLCC) is based on a Cooperative Co-evolutionary framework and employs a technique called random grouping in order to group interacting variables in one subcomponent. It also uses another technique called adaptive weighting for co-adaptation of subcomponents. We prove that the probability of grouping interacting variables in one subcomponent using random grouping drops significantly as the number of interacting variables increases. This calls for more frequent random grouping of variables. We show how to increase the frequency of random grouping without increasing the number of fitness evaluations. We also show that adaptive weighting is ineffective and in most cases fails to improve the quality of found solution, and hence wastes considerable amount of CPU time by extra evaluations of objective function. Finally we propose a new technique for self-adaptation of the subcomponent sizes in CC. We demonstrate how a substantial improvement can be gained by applying these three techniques.

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This is a repository copy of Decomposition for Large-scale Optimization Problems with Overlapping Components.