Multi-objective optimization of water distribution system design under uncertain demand and pipe roughness

Water-distribution system design optimization is one of the most heavily researched areas in the hydraulics profession. This chapter presents a methodology for the multiobjective least-cost robust design of water distribution networks under uncertain demand. The problem is solved using genetic algorithms (GAs) after converting the original problem formulation to an equivalent, simplified, deterministic optimization problem. This way, computational efficiency of the methodology is significantly increased. The methodology is verified in a case study, where, among other things, optimal robust solutions obtained are compared to well-known deterministic solutions from the literature. The results clearly demonstrate that neglecting uncertainty in the design process may lead to serious underdesign of water distribution networks. The methodology proposed here is of a general type in terms that different uncertain parameters with different probability-distribution function (pdf) types can be considered. Its disadvantage is that the target level of the design robustness cannot be specified explicitly in the problem formulation phase, that is, it has to be specified indirectly (by specifying the target value of parameter). Therefore, the actual level of robustness can be calculated only once the optimization process has converged and the final solution is obtained.