Multiobjective Robust Optimization of Water Distribution Networks

Due to its practical importance and inherent complexity, the optimization of distribution networks for supplying drinking water has been the subject of extensive study for the past 30 years. The optimization is governed by sizing the pipes in the water distribution network (WDN). The pipe diameters are to be selected from a list of available commercial diameters, making WDN optimization a pure discrete optimization problem. The size of the search space is determined by the number of available diameters, raised to the power of the number of pipes (e.g., 634, 1621). Originally being a search for the least cost solution, subject to delivering pre-defined water demands to the consumer nodes at a minimum required pressure, the optimization model has gradually changed to a multiobjective scheme including objectives for reliability under mechanical failure (e.g., pipe breakage) and hydraulic failure (e.g., increased demands). Also, robust optimization schemes have been suggested, which aim for hydraulically reliable optima by accounting for fluctuating demands at the consumer nodes. We intend to determine the added value of the multiobjective robust approach (robust), over the basic multiobjective model (raw). Raw and robust results, obtained using the same number of evaluations, are both re-evaluated to approximate their robustness using 2000 randomly generated demand samples per solution. Surprisingly, the results indicate that in terms of robustness, the raw Multiobjective Evolutionary Algorithms used (NSGA-II, SMS-EMOA) outperform their variants that explicitly include extensions for robust evaluation; the standard extensions for robust optimization, namely the Single Evaluation Model (SEM) and Multi Evaluation Model (MEM), were tested.