Chaotic differential evolution algorithms for optimal design of water distribution networks

ABSTRACT

Recently, coupling chaos theory with evolutionary algorithms (EAs) elevated further scope for improving EAs’ performance efficiency. In this view, the present study emphasizes investigating the influence of chaotic force on convergence properties of differential evolution (DE) algorithm in designing water distribution networks (WDNs). To this end, two novel chaos-directed DE models, Chaotic-DE and Chaotic-Fm-DE, are proposed. The Chaotic-DE model is formulated to enhance DE’s searchability and faster convergence by replacing every random phenomenon with a chaotic force. The Chaotic-Fm-DE model with a dynamic, chaotic mutation factor is developed to improve DE’s exploitation behavior. Essentially, these models differ from the previous chaos-directed EA models in how chaos ergodicity is simulated in DE mechanism. A novel scheme of non-sequential approach is used for this purpose. Further, their respective elitist models are formulated to promote the search in promising areas. Importantly, the elitism scheme developed saves the elite trial vectors to pass through the next generations. The results of proposed algorithms validated on five (new and rehabilitated) benchmark WDNs (whose dimensions vary from 8 to 454) demonstrate the enhanced search behavior of the chaotic models with solution precision and remarkable reduction in computational effort over the non-chaotic ones.

KEYWORDS:

• Design of water distribution networks
• differential evolution
• chaos theory
• chaos-directed evolutionary algorithms
• elitism operator

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The benchmark problems considered in the present study are taken from the Centre for Water Systems, benchmark problems, University of Exeter.

emps.exeter.ac.uk/engineering/research/cws/resources/benchmarks/pareto/

All the models or codes that support the findings of this study are available from the corresponding author.