Influence of the Binomial Crossover on Performance of Evolutionary Algorithms
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In differential Evolution (DE) algorithms, a crossover operation filtering variables to be mutated is employed to search the feasible region flexibly, which leads to its successful applications in a variety of complicated optimization problems. To investigate whether the crossover operator of DE is helpful to performance improvement of evolutionary algorithms (EAs), this paper implements a theoretical analysis for the (1+1)EA_C and the (1+1)EA_CM, two variants of the (1+1)EA that incorporate the binomial crossover operator. Generally, the binomial crossover results in the enhancement of exploration and the dominance of transition matrices under some conditions. As a result, both the (1+1)EA_C and the (1+1)EA_CM outperform the (1+1)EA on the unimodal OneMax problem, but do not always dominate it on the Deceptive problem. Finally, we perform an exploration analysis by investigating probabilities to transfer from non-optimal statuses to the optimal status of the Deceptive problem, and propose adaptive parameter settings to strengthen the promising function of binomial crossover. It suggests that incorporation of the binomial crossover could be a feasible strategy to improve the performances of EAs.
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