Reviewing and Benchmarking Parameter Control Methods in Differential Evolution

Many differential evolution (DE) algorithms with various parameter control methods (PCMs) have been proposed. However, previous studies usually considered PCMs to be an integral component of a complex DE algorithm. Thus, the characteristics and performance of each method are poorly understood. We present an in-depth review of 24 PCMs for the scale factor and crossover rate in DE and a large-scale benchmarking study. We carefully extract the 24 PCMs from their original, complex algorithms and describe them according to a systematic manner. Our review facilitates the understanding of similarities and differences between existing, representative PCMs. The performance of DEs with the 24 PCMs and 16 variation operators is investigated on 24 black-box benchmark functions. Our benchmarking results reveal which methods exhibit high performance when embedded in a standardized framework under 16 different conditions, independent from their original, complex algorithms. We also investigate how much room there is for further improvement of PCMs by comparing the 24 methods with an oracle-based model, which can be considered to be a conservative lower bound on the performance of an optimal method.