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1 Control and Cybernetics

1 2010

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The grouping differential evolution algorithm for multi-dimensional optimization problems

Piotrowski A. P., Napiórkowski J. J.

Control and Cybernetics

2010

Vol. 39, no 2

527-550

A variant of the Differential Evolution method is presented. The classical Differential Evolution approach is very successful for simple problems, but does not perform well enough for troublesome multi-dimensional non-convex continuous functions. To overcome some of the drawbacks, the Grouped Multi-Strategy Differential Evolution algorithm is proposed here. The main idea behind the new approach is to exploit the knowledge about the local minima already found in different parts of the search space in order to facilitate further search for the global one. In the proposed method, the population is split into four groups: three of them rarely communicate with the others, but one is allowed to gain all available knowledge from the whole population throughout the search process. The individuals simultaneously use three different crossover/mutation strategies, which makes the algorithm more flexible. The proposed approach was compared with two Differential Evolution based algorithms on a set of 10- to 100-dimensional test functions of varying difficulty. The proposed method achieved very encouraging results; its advantage was especially significant when more difficult 50- and 100-dimensional problems were considered. When dividing population into separate groups, the total number of individuals becomes a crucial restriction. Hence, the impact of the number of individuals on the performance of the algorithms was studied. It was shown that increasing the number of individuals above the number initially proposed for classic Differential Evolution method is in most cases not advantageous and sometimes may even result in deterioration of results.