Robust and Reliable Design Alternatives to Water Distribution Networks: Introducing a Penalty-Free Hybrid Metaheuristic Multiobjective Algorithm with a Posterior Performance Investigation Model

The present study introduces a novel penalty-free hybrid metaheuristic, differential evolution–krill herd algorithm (DE-KHA) a multiobjective algorithm (MOA) for the reliability-based optimal design of water distribution networks (WDNs). The selection mechanism of the DE-KHA MOA is equipped with nondominated sorting and density estimation schemes to obtain a Pareto front with diverse trade-off solutions. The introduced penalty-free scheme allows the algorithm to search for hydraulically functional nondominant solutions. With this implemented framework of the DE-KHA MOA, the WDN design problem is formulated with two conflicting objectives, (1) minimizing pipe investment cost; and (2) maximizing network’s reserve through flow entropy (${\mathrm{S}}_{\mathrm{F}}$), a surrogate reliability measure. The application and computational efficiency of the proposed MOA are demonstrated by employing two well-established benchmark case studies. Parallelly a trial-based approach for conducting sensitivity analysis for MOAs is demonstrated. The computational results manifest the efficacy of the penalty-free DE-KHA MOA in resulting in the Pareto front comprising the hydraulic feasible nondominant solutions of disparate trade-off relationships. As well, the results highlight the applicability of the proposed sensitivity analysis approach in improving the convergence behavior of the MOA. Following the reliability-based design, to assess the flexibility of the solved nondominant solutions under critical scenarios above design standards, the study performed a posterior performance investigation using pressure-driven analysis. The results demonstrate the effectiveness of the proposed approach with supported subjective knowledge in selecting robust design alternatives that are mechanically and hydraulically reliable. Moreover, the proposed approach eases the effort and perplexing state of handling increased nondominant design options with larger-size WDNs.

The present study introduces a computationally efficient multiobjective algorithm for the economical and reliable design of water distribution networks. By considering the reliability measure (flow entropy) in the design framework, the study focuses on proposing design alternatives for water utilities with inherent redundancy and tolerance to failures (mechanical). Following optimal design, the study proposes a performance investigation model that is useful in assessing the network’s integrity, detailing the quantitative and qualitative performance of alternate designs in the face of uncertainties. This particular framework is notably more useful in proposing water utilities, a set of economical yet robust (flexible) design alternatives, which quickly adapt to uncertainties. As well, the proposed design approach eases the effort of designers in handling the increased design options with larger-size networks.