Abstract
Modern real-valued optimization problems are complex and high-dimensional, and they are known as “large-scale global optimization (LSGO)” problems. Classic evolutionary algorithms (EAs) perform poorly on this class of problems because of the curse of dimensionality. Cooperative Coevolution (CC) is a high-performed framework for performing the decomposition of large-scale problems into smaller and easier subproblems by grouping objective variables. The efficiency of CC strongly depends on the size of groups and the grouping approach. In this study, an improved CC (iCC) approach for solving LSGO problems has been proposed and investigated. iCC changes the number of variables in subcomponents dynamically during the optimization process. The SHADE algorithm is used as a subcomponent optimizer. We have investigated the performance of iCC-SHADE and CC-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation. The results of numerical experiments have shown that iCC-SHADE outperforms, on average, CC-SHADE with a fixed number of subcomponents. Also, we have compared iCC-SHADE with some state-of-the-art LSGO metaheuristics. The experimental results have shown that the proposed algorithm is competitive with other efficient metaheuristics.
Highlights
Evolutionary computation [1,2,3] includes a research field, where bio-inspired algorithms are used for solving global optimization problems with different levels of complexity.This family of algorithms demonstrates high performance in solving hard real-world [4,5,6,7]and benchmark [8,9] problems when the number of variables is not large
We have investigated the performance of iCCSHADE and Cooperative Coevolution (CC)-SHADE on fifteen problems from the LSGO CEC’13 benchmark set provided by the IEEE Congress of Evolutionary Computation
The variable grouping is a challenging task for several reasons: (1) metaheuristics are limited in the number of fitness evaluations (FEVs); (2) the landscape of real-world LSGO problems is complex, (3) LSGO problems are presented by a “black-box” (BB) model
Summary
Evolutionary computation [1,2,3] includes a research field, where bio-inspired algorithms are used for solving global optimization problems with different levels of complexity. This paper proposes a modification of the classic CC algorithm, which changes the number of variables in subcomponents dynamically during the optimization process for improving the performance of the search process. We have proposed a new benchmark set with high dimensional cLSGO problems, and have compared the performance ε-iCCSHADE and ε-CC-SHADE algorithms. Based on our previous study [17], this paper has been extended with a detailed analysis of the performance of iCC-SHADE by four classes of LSGO problems, namely fully-separable, partially additively separable, overlapping, and non-separable problems. We have compared the performance of CC-SHADE with a fixed number of subcomponents and iCC-SHADE on four different classes of LSGO problems, which are Fully-separable (Section 4.2.1), Partially Additively. In Section 4.2.6, we discuss a fine-tuning of the iCC-SHADE algorithm and propose some efficient values for the number of individuals in subcomponents.
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