Parametric Analysis of Differential Evolution Algorithm Applied to Water Distribution System Optimization

Differential evolution (DE),as one of the evolutionary algorithms, has recently been employed to optimize water distribution systems (WDSs). Several parameters need to be determined in the use of DE, including: population size, N; mutation weighting factor, F; and crossover rate, CR. The search behaviour of DE is governed by these three parameters. The objective of this paper is to investigate the sensitivity of the performance of DE applied to optimize WDSs on the mutation weighting factor F and crossover rate CR. The performance of the DE with different parameter values is assessed for two case studies from the literature. It is demonstrated that DE with F in the range of 0.5-0.7 and CR in the range of 0.6-0.8 exhibit good performance for the WDS optimization. In addition, the best F value for each case study is found to be independent of the CR value. This shows that these two parameters have little joint influence on DE’s search performance. Based on these observations, a parameter tuning heuristic is developed to select appropriate F and CR values for DE application to different WDS optimization problems.