[1] Water distribution system (WDS) design naturally involves a trade-off between the cost and reliability or robustness of a design. Traditionally, WDS reliability quantification schemes have employed graph theoretic techniques or probabilistic schemes such as Monte Carlo simulation. In recent decades there has been increased interest in the application of so-called reliability surrogate measures, such as flow entropy, the resilience index, and network resilience, because of their ease of use and dramatically reduced computational burden. In this paper, these surrogate measures (as well as a mixed reliability surrogate) are employed in the multiobjective evolutionary design of a set of WDS benchmarks from the literature. The resulting Pareto-optimal sets in cost-reliability space for each surrogate measure are analyzed in terms of their ability to handle demand uncertainty and pipe failure, and a regression analysis is conducted in order to determine whether the surrogate measures are correlated to stochastic reliability and failure reliability as expressed by demand satisfaction measures. It is found that the resilience index demonstrates the best performance under pure stochastic demand variation. However, it lags when compared to the network resilience and mixed reliability measures in terms of reliability under pipe failure conditions. These are recommended as the most practical reliability surrogate measures for use in general WDS design, since they also produce designs that minimize size discontinuities between adjacent pipes. Flow entropy performs relatively poorly in terms of correlation to both stochastic reliability and failure reliability.

The design of an urban water distribution system (WDS) is a challenging problem involving multiple objectives. The goal of robust multi-objective optimization for WDS design is to find the set of solutions which embodies an acceptable trade-off between system cost and reliability, so that the ideal solution may be selected for a given budget. In addition to satisfying consumer needs, a system must be built to accommodate multiple demand loading conditions, withstand component failures and allow surplus capacity for growth. In a developmental setting, WDS robustness becomes even more crucial, owing to the limited availability of resources, especially for maintenance. Recent optimization studies have achieved success using multi-objective evolutionary algorithms, such as the Non-dominated Sorting Genetic Algorithm II (NSGA-II). However, the multi-objective design of a large WDS within a reasonable timeframe remains a formidable problem, owing to the extremely high computational complexity of the problem. In this paper, a meta-algorithm called AMALGAM is applied for the first time to WDS design. AMALGAM uses multiple metaheuristics simultaneously in an attempt to improve optimization performance. Additionally, a Jumping-gene Genetic Algorithm (NSGA-II-JG) is also applied for the first time to WDS design. These two algorithms were tested against some other metaheuristics (including NSGA-II and a new greedy algorithm) with respect to a number of benchmark systems documented in the literature, and AMALGAM demonstrated the best performance overall, while NSGA-II-JG fared worse than the ordinary NSGA-II. Large cost savings and reliability improvements are demonstrated for a real WDS developmental case study in South Africa.

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The topic of multi-objective water distribution systems (WDS) design optimisation using metaheuristics is investigated, comparing numerous modern metaheuristics, including several multi-objective evolutionary algorithms, an estimation of distribution algorithm and a recent hyperheuristic named AMALGAM (an evolutionary framework for the simultaneous incorporation of multiple metaheuristics), in order to determine which approach is most capable with respect to WDS design optimisation. Novel metaheuristics and variants of existing algorithms are developed, for a total of twenty-three algorithms examined. Testing with respect to eight small-to-large-sized WDS benchmarks from the literature reveal that the four top-performing algorithms are mutually non-dominated with respect to the various performance metrics used. These algorithms are NSGA-II, TAMALGAMJ ndu , TAMALGAM ndu and AMALGAMS ndp (the last three being novel variants of AMALGAM). However, when these four algorithms are applied to the design of a very large real-world benchmark, the AMALGAM paradigm outperforms NSGA-II convincingly, with AMALGAMS ndp exhibiting the best performance overall.

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