Tabu Search Solution of Water Distribution Network Optimization

The optimization of water distribution networks are complex, multi-modal and discretevariable problems that cannot be easily solved with conventional optimization algorithms. Hence, evolutionary techniques such as genetic algorithms and simulated annealing have been extensively employed during the last decade. This study adopts a Tabu search (TS), which is an evolutionary method based on explicit memory systems and several searching strategies designed to avoid the entrapments by local solutions, to obtain the least-cost designs of looped water distribution networks. Two well known benchmark water distribution network optimization problems (Hanoi and New York networks) as well as a much more complicated design (Taichung network) are used as case studies. A comparison of the results of this study with relevant literature data suggests that TS is an attractive technique for optimizing water distribution network designs, as it can achieve optimal solutions with a high rate of success. *Corresponding author Email: [email protected] INTRODUCTION Since the water distribution network is a vital component of urban infrastructure and requires significant investment, optimization of water distribution network designs has received considerable attention over the past three decades. Such optimization problems consider various aspects including capital, operation and maintenance costs, layout design, hydraulics, reliability, material availability and demand pattern, and the least cost design problem has been frequently studied in the literature. However, the real design aspects of layout selection and choosing suitable pipe diameters are very cumbersome. Because joint consideration of network layout and pipe selection is extremely complex and since layout is largely restricted by the location of the roads, many studies have been proposed and tested for pipe-selection problems only. Various classical optimization techniques such as linear programming gradient [1-5], dynamic programming [6], and nonlinear programming [7-8] have been evolved primarily for solving minimal-cost problems. However, most of these models are either linearized or simplified to make their applications possible. Furthermore, the selection of commercially available discrete-valued pipe diameters to constitute a least capital cost water supply network has been proven an NP-hard problem that is generally impossible to be solved by classical optimization techniques [9-10]. Recently, the heuristic algorithms have been given more consideration and used as alternatives to optimize engineering problems. These algorithms (such as simulated annealing (SA), genetic algorithms (GA), and tabu search (TS), etc.) are initially developed for combinatorial optimization problems. They are also applied to the optimization of multi-modal problems. However, compared with SA [10] and GA [11-12], the application of in water distribution network designs is very limited and therefore there is a need to explore this method further. This paper employs the TS technique as a solution tool to optimize several design problems of water distribution networks, and the results are compared with those solved by other optimization methods to evaluate their performance with respect to optimization capability. OPTIMIZATION MODEL FORMULATION The water distribution network optimization model proposed in this paper is formulated as a leastcost problem to identify the pipe sizes that give the minimum cost for a given layout. The pipe layout, nodal demands, minimum head requirements and ve178 J. Environ. Eng. Manage., 17(3), 177-187 (2007) locity requirements are all assumed known. There are no pumps considered in the networks and the reservoirs are all taken as water source nodes with fixed heads. The objective function expressing the network cost is formulated as a function of the pipe diameters. The optimal design problem for a general water distribution network can be shown as the following mathematical statement [10,12-15]: