Differential Evolution With Underestimation-Based Multimutation Strategy.

As we know, the performance of differential evolution (DE) highly depends on the mutation strategy. However, it is difficult to choose a suitable mutation strategy for a specific problem or different running stages. This paper proposes an underestimation-based multimutation strategy (UMS) for DE. In the UMS, a set of candidate offsprings are simultaneously generated for each target individual by utilizing multiple mutation strategies. Then a cheap abstract convex underestimation model is built based on some selected individuals to obtain the underestimation value of each candidate offspring. According to the quality of each candidate offspring measured by the underestimation value, the most promising candidate solution is chosen as the offspring. Compared to the existing probability-based multimutation techniques, no mutation strategies are lost during the search process as each mutation strategy has the same probability to generate a candidate solution. Moreover, no extra function evaluations are produced because the candidate solutions are filtered by the underestimation value. The UMS is integrated into some DE variants and compared with their original algorithms and several advanced DE approaches over the CEC 2013 and 2014 benchmark sets. Additionally, a well-known real-world problem is employed to evaluate the performance of the UMS. Experimental results show that the proposed UMS can improve the performance of the advanced DE variants.