Nondominated Sorting Differential Evolution Algorithms for Multiobjective Optimization of Water Distribution Systems

摘要

Optimal design of reliable looped water distribution systems (WDSs) is challenging because these problems comprise nonlinear relationships between discharge and energy in the pipes and junctions, and nonconvex objective functions that relate cost and reliability to discrete choices of pipe diameters. Efficient algorithms for identifying optimal WDS designs also must be practical for realistic systems. Differential evolution (DE) algorithms, which harness the mutation operator to identify populations containing very different alternatives, have been shown to be more efficient than other heuristics for solving single objective versions of these problems, e.g.,minimizing the cost of WDSs. By examining the entire population and evaluating those members that dominate in terms of two or more objectives, nondominated sorting algorithms efficiently identify the Pareto optimal front in multiobjective problems, and one such algorithm, the improved nondominated sorting genetic algorithm (NSGA-II), has been applied successfully to evaluate the cost-reliability tradeoff for WDSs. The nondominated sorting differential evolution (NSDE) algorithm, which takes advantage of the mutation operations in DE and nondominated sorting, and its variation NSDE with ranking-based mutation (NSDE-RMO), have been demonstrated as efficient for solving multiobjective problems. In this paper, NSDE and NSDE-RMO were applied to discrete WDS optimization for the first time, and their high performance was demonstrated compared with NSGA-II and the multialgorithm, genetically adaptive multiobjective (AMALGAM) method, a widely applied hybrid metaheuristic multiobjective algorithm. For three benchmark networks, NSDE and its variation performed similarly to or better than NSGA-II and AMALGAM except at high cost levels. For hypothetical randomly generated networks ranging from 100 to 400 nodes, and 100 to 800 pipes, the Pareto optimal front of the NSDE algorithms dominated all other algorithms, exhibiting more, and more varied, Pareto optimal solutions, and they converged sooner. (C) 2016 American Society of Civil Engineers.