Improved Constructive Cooperative Coevolutionary Differential Evolution for Large-Scale Optimisation

Abstract

The Differential Evolution (DE) algorithm is widely used for real-world global optimisation problems in many different domains. To improve DE's performance on large-scale optimisation problems, it has been combined with the Cooperative Coevolution (CCDE) algorithm. CCDE adopts a divide-and-conquer strategy to optimise smaller subcomponents separately instead of tackling the large-scale problem at once. DE then evolves a separate subpopulation for each subcomponent but there is cooperation between the subpopulations to co-adapt the individuals of the subpopulations with each other. The Constructive Cooperative Coevolution (C3DE) algorithm, previously proposed by the authors, is an extended version of CCDE that has a better performance on large-scale problems, interestingly also on non-separable problems. This paper proposes a new version, called the Improved Constructive Cooperative Coevolutionary Differential Evolution (C3iDE), which removes several limitations with the previous version. A novel element of C3iDE is the advanced initialisation of the subpopulations. C3iDE initially optimises the subpopulations in a partially co-adaptive fashion. During the initial optimisation of a subpopulation, only a subset of the other subcomponents is considered for the co-adaptation. This subset increases stepwise until all subcomponents are considered. The experimental evaluation of C3iDE on 36 high-dimensional benchmark functions (up to 1000 dimensions) shows an improved solution quality on large-scale global optimisation problems compared to CCDE and DE. The greediness of the co-adaptation with C3iDE is also investigated in this paper.