Cross Entropy multiobjective optimization for water distribution systems design

Abstract

[1] A methodology extending the Cross Entropy combinatorial optimization method originating from an adaptive algorithm for rare events simulation estimation, to multiobjective optimization of water distribution systems design is developed and demonstrated. The single objective optimal design problem of a water distribution system is commonly to find the water distribution system component characteristics that minimize the system capital and operational costs such that the system hydraulics is maintained and constraints on quantities and pressures at the consumer nodes are fulfilled. The multiobjective design goals considered herein are the minimization of the network capital and operational costs versus the minimization of the maximum pressure deficit of the network demand nodes. The proposed methodology is demonstrated using two sample applications from the research literature and is compared to the NSGA-II multiobjective scheme. The method was found to be robust in that it produced very similar Pareto fronts in almost all runs. The suggested methodology provided improved results in all trails compared to the NSGA-II algorithm.Citation: Perelman, L., A. Ostfeld, and E. Salomons (2008), Cross Entropy multiobjective optimization for water distribution systems design, Water Resour. Res., 44, W09413,

Lost in Optimisation of Water Distribution Systems? A Literature Review of System Design

“…In the mid 1990s, after the first popular applications of a GA [20,151], there was a swing towards stochastic methods and they dominate the field since (see Figure 4). A great range of those methods has been applied to optimise design of WDSs to date, inclusive of (but not limited to) a GA [42,45,50,85,86,[152][153][154], fmGA [88], non-crossover dither creeping mutation-based GA (CMBGA) [149], adaptive locally constrained GA (ALCO-GA) [155], SA [60], shuffled frog leaping algorithm (SFLA) [103], ACO [104,156], shuffled complex evolution (SCE) [157], harmony search (HS) [105,158,159], particle swarm HS (PSHS) [160], parameter setting free HS (PSF HS) [161], combined cuckoo-HS algorithm (CSHS) [162], particle swarm optimisation (PSO) [106,153,154], improved PSO (IPSO) [163], accelerated momentum PSO (AMPSO) [164], integer discrete PSO (IDPSO) [165], newly developed swarm-based optimisation (DSO) algorithm [150], scatter search (SS) [166], CE [61,62], immune algorithm (IA) [167], heuristic-based algorithm (HBA) [168], memetic algorithm (MA) [107], genetic heritage evolution by stochastic transmission (GHEST) [169], honey bee mating optimisation (HBMO) …”

“…Although a few studies, which considered the design and operating costs as part of separate objectives (e.g., [124]), reported on their conflicting tradeoff, this relationship was not confirmed for a higher-dimensional space when required to balance numerous objectives [97]. Additionally, the pump maintenance cost (see, for example, [61,62,121]) as well as the pump replacement and refurbishment cost [71,72,77] were accounted for. More recently, GHG emission cost or GHG emissions due to the electricity that is consumed by pumps [71][72][73][74][75][76][77] were introduced as an environmental objective.…”

“…A multi-objective optimisation approach was possibly first applied in the late 1990s (Figure 1), maximising the network benefit on one hand and minimising the system cost (of network rehabilitation) on the other hand [63]. In studies of newly designed WDSs, in addition to the economic measure, the other objectives considered were the pressure deficit [30,62,[64][65][66][67] or excess [68,69] at network nodes, the penalty cost for violating the pressure constraint [70], greenhouse gas (GHG) emissions [71][72][73][74][75][76] or emission cost [77], water discolouration risk [68] and water quality [78]. A multiobjective optimisation approach is considered "very appealing for engineers as it provides a tool to investigate interesting trade-offs", for example, a marginal pressure deficit can be outweighed by a considerable cost reduction [67].…”

“…Initially, single-objective optimisation models were used to formulate WDS design problems, in which all objectives are combined into one economic (i.e., least-cost) measure (see, for example, [14,51,[60][61][62]). A multi-objective optimisation approach was possibly first applied in the late 1990s (Figure 1), maximising the network benefit on one hand and minimising the system cost (of network rehabilitation) on the other hand [63].…”

Optimal Design of Water Distribution Systems Using Many-Objective Visual Analytics

“…Multi-objective optimal design and rehabilitation of Water Distribution Systems (WDS) has attracted increasing attention over recent years (e.g., Walski and Gessler 1985;Walski et al 1990;Halhal et al 1997;Farmani et al 2003;Perelman et al 2008;Fu and Kapelan 2011). The shift from least cost design to multi-objective performance-based design advances decision makers' understanding of tradeoff relationships between conflicting design objectives (Walski 2001).…”