An Adaptive Cauchy Differential Evolution Algorithm with Population Size Reduction and Modified Multiple Mutation Strategies

Abstract

Adapting control parameters is an important task in the literature of the differential evolution (DE) algorithm. A balance between Exploration and Exploitation plays a large role in the performance of DE. A dynamic population sizing method can help maintaining the balance. In this paper, we improved an adaptive differential evolution (ACDE) algorithm by attaching the modified population size reduction (4MPSR) method. 4MPSR method reduces the population size gradually and uses four mutation strategies with different ranges of the scaling factor. In short, 4MPSR method has better Exploration during the early stage and Exploitation during the late stage. ACDE algorithm performs well in solving various benchmark problems. However, ACDE algorithm adapts two control parameters, the scaling factor and the crossover rate but uses a fixed population size. By attaching 4MPSR method to ACDE algorithm, all of the control parameters can be adapted and, hence, the performance can be improved. We compared the proposed algorithm with some state-of-the-art DE algorithms in various benchmark problems. The performance evaluation results showed that the proposed algorithm is significantly improved for solving both the unimodal problems and the multimodal problems. And the proposed algorithm obtained the better final solutions than the state-of-the-art DE algorithms.