An adaptive heuristic cross-entropy algorithm for optimal design of water distribution systems

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.…”

“…• An extension of the paper by [61] to a multi-objective optimisation approach, particularly by using the rank of the generated elite solutions to update the CE probabilities instead of using fitness function values.…”

“…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].…”

Coupled Binary Linear Programming–Differential Evolution Algorithm Approach for Water Distribution System Optimization

“…Afterwards, a number of other evolutionary algorithms were developed and applied to WDS design. These include simulated annealing (Cunha and Sousa 2001); harmony search (Geem et al 2002); the shuffled frog leaping algorithm (Eusuff and Lansey 2003); Ant Colony Optimization (Maier et al M a n u s c r i p t N o t C o p y e d i t e d (Suribabu and Neelakantan 2006); cross entropy (Perelman and Ostfeld, 2007); scatter search (Lin et al 2007); HD-DDS (Tolson et al 2009) and differential evolution (Suribabu 2010). These EAs have been applied to a number of WDS case studies and exhibit good performance in terms of finding optimal solutions.…”