68 - Improvement of Computational Efficiency of Rao-II for Water Distribution Network Design by Infusing Search Space Reduction and Self-Adaptive Penalty

The arteries that supply the potable water from the treatment plant to the consumers end are termed as Water Distribution Networks (WDNs). These are costly infrastructure and thus demands optimization. The optimal solution refers to a certain set of commercially available diameters that corresponds to the minimum cost of the network simultaneously satisfying all constraints of the problem. However, the WDN falls under the category of complex engineering problem. Evolutionary Algorithms (EAs) are used extensively for the optimal design of WDN because of various advantages associated with it. A parameter less EA, Rao-II has been successfully used earlier for the optimal design of WDNs. Computational efficiency of Rao-II is enhanced herein through two measures: (1) search space reduction model; and (2) self-adaptive penalty approach.
The sheer size of the search space (SS) indicates the enormity of the optimization of WDN. The SS encompasses all relevant decision criteria, such as pump settings, valve placements, and pipe diameters. Even in apparently small networks, the SS is huge. The SS for a small network of 8 pipes, with 14 commercially available diameters, has an incredible 148 potential possibilities to choose the best one from it. This number increases exponentially for larger networks and affects the efficiency of EAs to a greater extent. This enormous SS can be reduced by infusing the search space reduction (SSR) technique with the optimization model while ensuring that no important solution is overlooked, i.e., each crucial solution is considered. Such an exercise will direct the EAs to hunt for the optimal solution in a restricted area rather than exploring the entire SS. This in succession will increase the probability of better solutions to get picked up when the simulations are run for a fixed number of iterations.
Infeasible solutions generated during the simulations are handled by assigning the penalty which later will be added to the objective function value. In the earlier work with Rao-II algorithm, a constant penalty approach was used for handling the infeasible solutions. The constant penalty factor leads to a poor convergence and needs to be changed from problem to problem. In the present work, self-adaptive penalty function is suggested to enhance the computational efficiency of Rao-II. When compared with conventional Rao-II, the new Rao-II, hereafter read as SSRao-II, found to provide better solution with improved convergence speed for the benchmark networks. Hence, it can be stated that, SSRao-II acquired the capability to quickly and consistently locate the optimal solution in the entire SS. Data is also analysed for fixed trial runs for both conventional Rao-II and SSRao-II and enormous improvement in mean and standard deviation values are observed for SSRao-II.
Highlights:
1. Search space reduction along with self-adaptive penalty is used to improve the computational efficiency of Rao-II.
2. The methodology is applied on few networks and faster convergence is observed.
3. Entire process of optimization is parameter less.