Probabilistic building block identification for the optimal design and rehabilitation of water distribution systems

The multi-objective design and rehabilitation of water distribution systems (WDS) is defined as the search for the set of system designs which offers the best trade-off between competing design objectives. Typically these objectives will consist of the cost of implementing a system design and a measure of the performance of that system. These measures are often in competition since improvements in the performance of a system generally come at a cost. Here three genetic algorithms which use probabilistic methods to identify building blocks—the Univariate Marginal Distribution Algorithm (UMDA) (Mühlenbein 1997), the hierarchical Bayesian Optimisation Algorithm (hBOA) (Pelikan 2002) and the Chi-Square Matrix methodology (Aporntewan & Chongstitvatana 2004)—are compared to the well-known multi-objective evolutionary algorithm NSGAII (Deb et al. 2002) for the multi-objective design and rehabilitation of water distribution systems. For single-objective problems the identification of building blocks has been seen to make evolutionary algorithms more scalable to large problems than simple genetic algorithms. In this paper these algorithms are shown to offer significantly better solutions than NSGA-II for the case of large systems. However, this improvement comes at the expense of diversity of solutions in the fronts identified.