Effective Relaxations and Partitioning Schemes for Solving Water Distribution Network Design Problems to Global Optimality

Introduction The design of water distribution systems has consistently received a great deal of attention because of its importance to society. Even so, many of the existing pipe networks in older urbanized areas function at severely reduced levels of efficiency and in some cases, are inadequate with respect to meeting the required pressure and flow demands. The investments associated with the installation, expansion and maintenance of water distribution systems are very high, and account for the largest proportion in municipal maintenance budgets. An important component in this process of designing a cost effective water distribution system or extending a preexisting network is to design the sizes of the various pipes that are capable of satisfying the flow demand, in addition to satisfying the minimum pressure head and hydraulic redundancy requirements. However, this least cost pipe design problem is a hard nonconvex optimization problem having a number of local optima, and has hence proven difficult to solve. A number of research efforts over the last two decades have focused on solving this problem, most of them generating improved local optimum solutions for several standard test problems from the literature, with no adequate lower bounds to evaluate the prescribed solutions. Three notable exceptions discussed below that are capable of providing solutions within a proven tolerance of a global optimum are the methods due to are Eiger et al. (1994), Sherali and