Chaos-Directed Genetic Algorithms for Water Distribution Network Design: An Enhanced Search Method

Abstract The design of a water distribution network (WDN) is an ever-challenging problem. Development and application of optimization techniques for WDN design have been an important area of research. Recently, the introduction of chaos theory-based evolutionary algorithms (EAs) in addition to traditional random-based ones has elevated the scope for further improving the performance of EAs. The present study proposes a chaos-directed genetic algorithm (CDGA) by incorporating chaos ergodicity in GA mechanics for WDN optimal design. Two novel frameworks, the non-sequential approach (NSA) and sequential approach (SA) are introduced. The influence of chaotic systems with high dimensionality maps in improving the search efficacy of GA when compared to the low dimensionality maps is explored. Considering four widely studied WDN benchmark problems, the performance of the proposed GA and CDGA models is evaluated. From the results, it is observed that the CDGA models outperform GA with better search efficacy, requiring fewer function evaluations to locate the optimal solution. Also, concerning the different chaotic maps used in the present study to induce chaos ergodicity, the results highlight the usefulness of chaos-directed search in improving the computational efficiency of GA. From the computational results, the study suggests the usage of a chaotic system with other bio-inspired techniques for their improved search and computational efficiency.