GENETIC ALGORITHMS COMPARED TO OTHER TECHNIQUES

The genetic algorithm technique is a relatively new optimization tech- nique. In this paper we present a methodology for optimizing pipe networks using genetic algorithms. Unknown decision variables are coded as binary strings. We investigate a three-operator genetic algorithm comprising reproduction, crossover, and mutation. Results are compared with the techniques of complete enumeration and nonlinear programming. We apply the optimization techniques to a case study pipe network. The genetic algorithm technique finds the global optimum in rela- tively few evaluations compared to the size of the search space. INTRODUCTION The construction and maintenance of

pipelines for water supply costs many millions of dollars every year. As funds for the development of new infrastructure become increasingly scarce, there is an increasing desire to achieve the highest level of effectiveness for each dollar spent. Traditionally, the design of water distribution networks has been based on experience. However, there is now a significant (and growing) body of literature devoted to optimization of pipe networks. Much of the research to date has applied deterministic optimization tech- niques (including linear programming, dynamic programming, and nonlin- ear programming) to the problems of network design. A new and developing field involves the application of stochastic optimization techniques (such as genetic algorithms and simulated annealing) to large combinatorial prob- lems. This paper applies genetic algorithms to the problem of designing pipe networks and compares its performance with the techniques of com- plete enumeration and nonlinear programming. PIPE NETWORK OPTIMIZATION PROBLEM In its simplest form, the problem of pipe network design for gravity systems is usually formulated in the following way. For a given layout of pipes and specified demands at the nodes, find the combination of pipe sizes that gives the minimum cost, subject to the following constraints: 1. Continuity of flow must be maintained at all junctions or nodes in the network. ~Sr. Lect., Dept. of Civ. and Envir. Engrg., Univ. of Adelaide, Adelaide, South Australia 5005. 2Assoc. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Adelaide, Adelaide, South Australia 5005. 3Res. Ofcr., Dept. of Civ. and Envir. Engrg., Univ. of Adelaide, Adelaide, South Australia 5005. Note. Discussion open until January l, 1995. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on July 28, 1992. This paper is part of the Journal of Water Resources Planning and Man- agement, Vol. 120, No. 4, July/August, 1994. 9 ISSN 0733-9496/94/0004-0423/ $2.00 + $.25 per page. Paper No. 4480. 423 2. The head loss in each pipe is a known function of the flow in the pipe, its diameter, length, and hydraulic properties. 3. The total head loss around a loop must equal zero or the head loss along a path between two reservoirs must equal the elevation difference. 4. Minimum and maximum pressure head limitations must be satisfied at certain nodes in the network. 5. Minimum and maximum diameter...

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