Proc. 3rd International Conference on Hydroinformatics, Copenhagen, August 1998. Balkema, Rotterdam 1 Application of global optimization to the design of pipe networks A.J. Abebe Arbaminch Water Technology Institute, Arbaminch, Ethiopia; currently with IHE-Delft D.P. Solomatine International Institute for Infrastructural, Hydraulic and Environmental Engineering (IHE), P.O. Box 3015, 2601 DA Delft, The Netherlands. Email: sol@ihe.nl (communication address) ABSTRACT: This paper presents an approach to the optimal design of pipe networks for water distribution. Design is important it often comprises major part of the whole investment in such a system. The problem is solved using a global optimization tool with various random search algorithms and a network simulation model that can handle both static and dynamic loading conditions. An appropriate interface between the two tools performs the decoding of the potential solutions into pipe networks for construction and calculates the corresponding network costs. Two algorithms, adaptive cluster covering and genetic algorithm, yielded promising solutions enabling a choice between accuracy and required computer time. The proposed optimiza- tion setup can handle any type of loading condition and neither makes any restriction on the type of hydraulic components in the network nor does it need analytical cost functions for the pipes. 1 INTRODUCTION A water distribution network is a system containing pipes, reservoirs, pumps, valves of different types, which are connected to each other to provide water to consumers. It is a vital component of the urban in- frastructure and requires significant investment. The problem of optimal design of water distribu- tion networks has various aspects to be considered such as hydraulics, reliability, material availability, water quality, infrastructure and demand patterns. Even though each of these factors has its own part in the planning, design and management of the system and despite their inherent dependence, it is difficult to carry out the overall analysis. Previous research indicates that the formulation of the problem on a component basis is worth doing. In the present study, the problem is posed as a multi-extremum (global) optimization. This paper deals with the determination of the op- timal diameters of pipes in a network with a prede- termined layout. This includes providing the pres- sure and quantity of water required at every demand node. An appropriate interface is created between a global optimization tool GLOBE (see the accompa- mying paper of Solomatine 1998) with various ran- dom search algorithms, and a network simulation model, EPANET (Rossman 1993), that can handle steady as well as dynamic loading conditions. 2 EXTENT OF THE PROBLEM The problem reduced to such an extent has two con- straints from hydraulic requirements. The continuity constraint states that the discharge into each node must be equal to that leaving the node, except for storage nodes (tanks and reservoirs). This secures the overall mass balance in the network. For n nodes in the network, this constraint can be written as 0 1 = ∑ = n i i Q (1) where Q i represents the discharges into or out of the node i (sign included). The second hydraulic constraint is the energy con- straint according to which the total head loss around any loop must add up to zero or is equal to the en- ergy delivered by a pump if there is any: p f E h = ∑ (2) where h f is the headloss due to friction in a pipe and E p is the energy supplied by a pump. This embeds the fact that the head loss in any pipe, which is a function of its diameter, length and hydraulic prop- erties, must be equal to the difference in the nodal heads. This constraint makes the problem highly non-linear owing to the nature of the equation that relates frictional head loss and flow. The equation can generally be written as