A Global Optimization Approach to a Water Distribution Network DesignProblem

  • Authors:

  • Hanif D. Sherali;Ernest P. Smith

  • Affiliations:

  • Virginia Polytechnic Institute and State University, Department of Industrial and Systems Engineering, 302 Whittemore Hall, Blacksburg, VA 24061, U.S.A.;Air Force Institute of Technology, AFIT/ENS, Wright Patterson AFB, OH 45433, U.S.A.

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1997

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, we address a global optimization approach to a waterdistribution network design problem. Traditionally, a variety of localoptimization schemes have been developed for such problems, each new methoddiscovering improved solutions for some standard test problems, with noknown lower bound to test the quality of the solutions obtained. A notableexception is a recent paper by Eiger et al. (1994) who present a firstglobal optimization approach for a loop and path-based formulation of thisproblem, using a semi-infinite linear program to derive lower bounds. Incontrast, we employ an arc-based formulation that is linear except forcertain complicating head-loss constraints and develop a first globaloptimization scheme for this model. Our lower bounds are derived through thedesign of a suitable Reformulation-Linearization Technique (RLT) thatconstructs a tight linear programming relaxation for the given problem, andthis is embedded within a branch-and-bound algorithm. Convergence to anoptimal solution is induced by coordinating this process with an appropriatepartitioning scheme. Some preliminary computational experience is providedon two versions of a particular standard test problem for the literature forwhich an even further improved solution is discovered, but one that isverified for the first time to be an optimum, without any assumed boundson the flows. Two other variants of this problem are also solved exactly forillustrative purposes and to provide researchers with additional test caseshaving known optimal solutions. Suggestions on a more elaborate study involving several algorithmic enhancements are presented for futureresearch.