An efficient hybrid approach for multiobjective optimization of water distribution systems

Abstract

An efficient hybrid approach for the design of water distribution systems (WDSs) with multiple objectives is described in this paper. The objectives are the minimization of the network cost and maximization of the network resilience. A self-adaptive multiobjective differential evolution (SAMODE) algorithm has been developed, in which control parameters are automatically adapted by means of evolution instead of the presetting of fine-tuned parameter values. In the proposed method, a graph algorithm is first used to decompose a looped WDS into a shortest-distance tree (T) or forest, and chords (X). The original two-objective optimization problem is then approximated by a series of single-objective optimization problems of the T to be solved by nonlinear programming (NLP), thereby providing an approximate Pareto optimal front for the original whole network. Finally, the solutions at the approximate front are used to seed the SAMODE algorithm to find an improved front for the original entire network. The proposed approach is compared with two other conventional full-search optimization methods (the SAMODE algorithm and the NSGA-II) that seed the initial population with purely random solutions based on three case studies: a benchmark network and two realworld networks with multiple demand loading cases. Results show that (i) the proposed NLP-SAMODE method consistently generates better-quality Pareto fronts than the full-search methods with significantly improved efficiency; and (ii) the proposed SAMODE algorithm (no parameter tuning) exhibits better performance than the NSGA-II with calibrated parameter values in efficiently offering optimal fronts.

GALAXY: A new hybrid MOEA for the optimal design of Water Distribution Systems

“…Recently, several hybrid algorithms have been proposed in order to improve the effectiveness and efficiency of EAs or MOEAs by combining different algorithms and/or strategies into a unified framework. The ideas of hybridization for the WDS design problems can be generally divided into three categories: (i) those using different techniques to provide a good initial population (rather than randomly generated), such as the heuristic‐based, local representative cellular automata approach [ Keedwell and Khu , ] and the graph decomposition based approach [ Zheng et al ., ]; (ii) those combining various EAs, MOEAs or local search methods during the evolutionary process; such as the Borg MOEA [ Wang et al ., ] and the hybrid Pareto archived dynamically dimensioned search method [ Asadzadeh and Tolson , ] (iii) those implementing the search space simplification (or reduction) before optimization, such as the dual‐stage multiobjective optimization method [ Zheng and Zecchin , ].…”

Review of the Quantitative Resilience Methods in Water Distribution Networks

“…A surrogate measure can also be combined into single-object or multi-object optimization. The multi-object optimization schemes of Zheng et al [116], Wang et al [117], Bi et al [98], and Suribabu [118] maximize the resilience while minimizing the cost. Other researchers (Alvisi and Franchini [119], Di Nardo and Natale [120] and Campbell et al [121]) combined surrogate measures with graph theory for water-loss detection and pressure management in district metered areas (DMAs).…”

Non-Dominated Sorting Harmony Search Differential Evolution (NS-HS-DE): A Hybrid Algorithm for Multi-Objective Design of Water Distribution Networks

“…The application of DE in single-objective designs of WDN has been reported in several studies [17,32,33]. More recently, Zheng et al [9] developed a DE for multi-objective WDN problems by hybridizing it with NLP to estimate the Pareto front in three WDN case studies.…”

“…For instance, some studies developed cross entropy MOEA methods and compared their performances with NSGA2 [8]. Zheng et al [9] developed the graph decomposition approach to solve the design problem of WDN in the multi-objective optimization framework. This approach was applied for the optimization of each sub-network and it achieved the Pareto optimal solutions for each one.…”

“…AMALGAM showed the best results. Zheng et al [9] developed SAMODE which is a hybrid of Non-Linear Programming (NLP) and Multi-Objective Differential Evolution. SAMODE outperformed NSGA2 on three benchmark WDN case studies.…”