Penalty-free multi-objective evolutionary optimization of water distribution systems

A major limitation of the widely used evolutionary optimization (EO) methods is their inability to handle constraints directly. To address this issue, penalty function methods have been used in most EO applications involving constrained problems such as those of the water distributions networks (WDNs). However, the disadvantage of penalty function methods is that the parameters involved require great expertise in calibration with numerous time consuming trial runs. In addition, penalty parameters are case sensitive and do not necessarily steer the EO search toward the best solutions in every situation. This paper presents a penalty-free multi-objective evolutionary approach (PFMOEA) for the optimization of water distribution networks. The basis behind this approach is to involve the pressure dependent analysis (PDA) in developing a multi-objective evolutionary search. PDA is capable of simulating both normal and pressure deficient networks and provides a quick and precise means to identify the feasible region of the solution space. The proposed PFMOEA couples the renowned NSGA II with an enhanced seamless version of EPANET 2 which is capable of PDA. The PFMOEA has been applied to several WDN benchmarks. Excellent results in terms of the initial network cost and number of hydraulic simulations required were obtained. Comprehensive discussions along with comparisons of solutions from previous studies are presented herein.