Optimization of pipe networks including pumps by simulated annealing

Abstract

The objective of this work is to present an application of the simulated annealing method for the optimal design of pipe networks including pumps. Although its importance, the optimization of pumped networks did not receive great attention in the literature. The proposed search scheme explores the discrete space of the decision variables: pipe diameters and pump sizes. The behavior of the pumps is describe through the characteristic curve, generating more realistic solutions. In order to demonstrate the versatility of the approach, three different examples of optimal design problems are solved

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) …”

“…In terms of the model objectives, the pump design or capital and/or operating costs were mostly incorporated together with the costs of other network elements (e.g., pipes, tanks, valves) into one economic function (see, for example, [17,26,51,60,93,95,96,119]). 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].…”

“…These networks vary in size, complexity, and the types of network components that they contain (i.e., nodes, pipes, pumps, tanks, reservoirs/sources and/or valves). The simplest networks are small gravity WDSs with one source, a few nodes and pipes (see, for example, [14,60]), or simplified pumped WDSs including only one source, one pump, one pipe and one tank (see, for example, [71]). An example of a large network represents EXNET [82], which is a realistic WDS comprising two sources, control valves and almost 2500 pipes.…”

“…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].…”

Locating Leaks with TrustRank Algorithm Support

“…These equations are solved by the Newton-Raphson method. This method has been successfully applied in several works [13,[53][54][55], and here it is supported by a line search algorithm to optimize the step length in order to improve convergence and avoid the drawbacks of the original method. The node equations implicitly ensure the mass conservation and the energy laws, and the head losses were estimated with the Hazen-Williams Formula (2):…”