Dynamic Search Space Reduction Methodology to Improve the Computational Efficiency of Evolutionary Algorithms for Optimal Pipe Sizing of Large Water Distribution Networks

A general optimal pipe sizing problem of a water distribution network (WDN) is a combinatorial optimization problem in which the sizes of different pipes are selected from a set of available pipe sizes. The number of combinations in a network with X number of pipes and Y number of available pipe sizes are YX. Complete enumeration to check the cost and feasibility of each combination using a network solver to search for the global optimal solution is practically not possible even for a moderate-size WDN, as the number of network analysis [called the number of functional evaluations (NFE)] will be YX. Several evolutionary algorithms (EAs) have been suggested in the last three decades, in which the search for the best in the search space (SS) is carried out by mimicking the process involved in a natural phenomenon or adopting some other strategy. Although the NFE required in EAs is substantially less as compared to that involved in complete enumeration, the computational time and efforts required to obtain the global optimal solution for large WDNs are high. Therefore, attempts have been made to reduce SS without losing the global optimal solution and to improve the efficiency and effectiveness of EAs. Various search space reduction (SSR) methodologies are described and the application of a simple dynamic search space reduction (DSSR) is shown in this chapter with two different EAs—a parameter-based Genetic Algorithm (GA) and a parameter-less Rao-II algorithm. The DSSR methodology is generic and can be applied to other EAs as well.