An analysis of the operation of differential evolution at high and low crossover rates

Abstract

A key parameter affecting the operation of differential evolution (DE) is the crossover rate Cr ∊ [0, 1]. While very low values are recommended for and used with separable problems, on non-separable problems, which include most real-world problems, Cr = 0.9 has become the de facto standard, working well across a large range of problem domains. Recent work on separable and non-separable problems has shown that lower-dimensional searches can play an important role in the performance of search techniques in higher-dimensional search spaces. However, the standard value of Cr = 0.9 implies a very high-dimensional search, which is not effective for other search techniques. An analysis of Cr across its range [0, 1] provides insight into how its value affects the performance of DE and suggests how low values may be used to improve the performance of DE. This new understanding of the operation of DE at high and low crossover rates is useful for analysing how adaptive parameters affect DE performance and leads to new suggestions for how adaptive DE techniques might be developed.