A Trigonometric Mutation Operation to Differential Evolution

Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. However, the convergence rate of differential evolution in optimizing a computationally expensive objective function still does not meet all our requirements, and attempting to speed up DE is considered necessary. In this paper, a new local search operation, trigonometric mutation, is proposed and embedded into the differential evolution algorithm. This modification enables the algorithm to get a better trade-off between the convergence rate and the robustness. Thus it can be possible to increase the convergence velocity of the differential evolution algorithm and thereby obtain an acceptable solution with a lower number of objective function evaluations. Such an improvement can be advantageous in many real-world problems where the evaluation of a candidate solution is a computationally expensive operation and consequently finding the global optimum or a good sub-optimal solution with the original differential evolution algorithm is too time-consuming, or even impossible within the time available. In this article, the mechanism of the trigonometric mutation operation is presented and analyzed. The modified differential evolution algorithm is demonstrated in cases of two well-known test functions, and is further examined with two practical training problems of neural networks. The obtained numerical simulation results are providing empirical evidences on the efficiency and effectiveness of the proposed modified differential evolution algorithm.