A novel self-adaptation and sorting selection-based differential evolutionary algorithm applied to water distribution system optimization

Abstract

The differential evolution (DE) algorithm has been demonstrated to be the most powerful evolutionary algorithm (EA) to optimally design water distribution systems (WDSs), but issues such as slow convergence speed, limited exploratory ability, and parameter adjustment remain when used for large-scale WDS optimization. This paper proposes a novel self-adaptation and sorting selection-based differential evolutionary (SA-SSDE) algorithm that can solve large-scale WDS optimization problems more efficiently while having the greater ability to explore global optimal solutions. The following two unique features enable the better performance of the proposed SA-SSDE algorithm: (1) the DE/current-to-pbest/n mutation and sorting selection operators are used to speed up the convergence and thus improve the optimization efficiency; (2) the parameter adaptation strategy in JADE (an adaptive differential evolution algorithm proposed by Zhang & Sanderson 2009) is introduced and modified to cater for WDS optimization, and it is capable of dynamically adapting the control parameters (i.e., F and CR values) to the fitness landscapes characteristic of larger-scale WDS optimization problems, allowing for greater exploratory ability. The proposed SA-SSDE algorithm found new best solutions of $7.068 million, €1.9205 million, and $30.852 million for three well-known large networks (ZJ164, Balerma454, and Rural476), having the convergence speed of 1.02, 1.92, and 5.99 times faster than the classic DE, respectively. Investigations into the searching behavior and the control parameter evolution during optimization are carried out, resulting in a better understanding of why the proposed SA-SSDE algorithm outperforms the classic DE, as well as the guidance for developing more advanced EAs.