Optimization of Water Distribution Systems by a Tabu Search Metaheuristic

Abstract

A Tabu Search optimisation technique is proposed for designing, planning and maintaining water distribution systems. As design and maintenance of pipe networks for water supply distribution require high costs, achieving the highest level of performance of existing networks at minimum costs is mandatory. The problem involves setting a lot of variables, as location and diameters of new pipes, operations on existing pipes, and so on. The domain of variables is discrete in nature, due to the fact that pipes are available with unified dimensions. Furthermore, the objective function to be minimised, i.e., the total cost of the plant, is non linear, non differentiable, highly illconditioned, and presents a huge amount of local minima. Recently, increasing attention has been paid to heuristic optimisation techniques, such as genetic algorithms (GA), simulated annealing (SA), and tabu-search (TS) for large combinatorial optimisation problems. In particular, GA has been applied to the problem of designing and maintaining water distribution networks. Results show good performance of the GA in terms of objective function values, but high computation time. One of the most promising approaches to combinatorial optimisation problems is the TS metaheuristic, that showed flexibility and effectiveness in a lot of applications. The aim of this paper is to present a TS based algorithm to the design of water distribution systems, and to demonstrate its validity in this field. 2 INTRODUCTIONA water distribution network is a system of hydraulic elements connected together to transfer predefined flow-rates of water from sources to demand centres. It has proved particularly useful to adopt a graph structure as a topological support to the model optimisation. Nodes can represent sources and demand centres as well as control elements in the network. Arcs represent connection pipes between nodes. Besides other well-known advantages, a graph structure allows the use of highly efficient data structure in the optimisation process.In this paper we consider the optimal design problem which has been extensively investigated in many research studies in past decades (Alperovits and Shamir, 1977; Quindry et al., 1981;Kessler and Shamir, 1989;Fujiwara and Khang, 1990; Eigher et al., 1994). Many investigative methods and solution techniques have been proposed and tested for this problem, but it seems generally accepted that, with general optimisation tools, it is not possible to solve the design problem with real-size systems complexity.An adequate approach to the design and maintenance optimisation of pipe networks for the water supply distribution should consider the nonlinear relations between head-losses in each pipe, its diameter, length, and hydraulic property. The literature on optimisation procedures of pipe networks is extensive.The mathematical models describing this kind of problem are typically characterised by difficulties in handling features, such as discrete variables, large dimensions and often the absence of those mathema...

Robust multi‐objective optimization for water distribution system design using a meta‐metaheuristic

“…Heuristics may be divided into blind searches or informed searches which exploit the structure of the objective function (often called metaheuristics when they have been formalized). Genetic algorithms (Goldberg and Kuo, 1987), simulated annealing (Loganathan et al, 1995) and tabu searches (Fanni et al, 2000) are common metaheuristics. Heuristic searches typically consider only the objective function value of current solutions during an iterative search procedure.…”

“…Simulated annealing was applied by Loganathan et al (1995), and by Cunha and Sousa (1999). Tabu searches were employed by Fanni et al (2000), and by Da Conceicao Cunha and Ribeiro (2004). Simpson et al (2001) were the first to apply Ant Colony Optimization (ACO) to WDS optimization in 2001.…”

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“…The development and applications of meta-heuristic optimization methodologies for design and management problems in water distribution networks have been proposed in recent years (Murphy et al 1993;Simpson et al 1994;Dandy et al 1996;Savic and Walters 1997;Walters et al 1999;Fanni et al 2000;Babayan et al 2007).…”

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“…We implemented a so-called reactive kind of TS scheme: RTS [4]. An extended illustration of the RTS variant to WDND problems has been reported in [10]. In this variant, the RTS memory structure of the past solutions is dynamical, and its optimal value is estimated automatically from the algorithm by means of a retroactive assessment of the search history.…”