Keywords: genetic algorithms, water distribution systems, automatic design, multiobjective evolutionary algorithms.

The use of optimization in the design of water distribution systems is quite common both in technical literature and in practical problems [1]. Many optimization techniques are available from the literature, however, for these kinds of problems, genetic algorithms (GA) seem to be among the most suitable. GAs are suitable for the solution of complex optimization problems in many different applications, both single and multiobjective (e.g. cost vs. benefit).

A comparison among three different multiobjective GA-based optimization approaches, namely OPTIMOGA [2], NSGA-II [3] and PESA-II [4] has been investigated. These algorithms have been tested on a benchmark problem represented by a medium-size water distribution system. The comparison showed that different implementations of GAs can find different solutions in terms of objective functions. OPTIMOGA seems to outperform the other two algorithms, in terms of economical costs of the networks and run time, while it moderately differs in terms of pressure deficits, even if almost always showing lowest deficits. NSGA-II and PESA-II performed very similarly: just in terms of run time NSGA-II proved to be slower than PESA-II. Anyway, these two approaches are quite diffused for use with different problems and are assumed in literature to be state-of-the-art GAs. OPTIMOGA is more recent than the other two algorithms and it was developed trying to overcome some problems which were posed by other GAs or more in general by other evolutionary algorithms. The results returned by OPTIMOGA are quite encouraging, in particular for applications of civil engineering.

1

D.A. Savic, G.A. Walters, "Genetic Algorithms for the Least-cost Design of Water Distribution Networks", J. Water Resour. Plan. and Manage., 123(2), 67-77, 1997. doi:10.1061/(ASCE)0733-9496(1997)123:2(67)

2

O. Giustolisi, A. Doglioni, D.A. Savic, D. Laucelli, "A proposal for an effective multi-objective non-dominated genetic algorithm: the OPTimised Multi-Objective Genetic Algorithm - OPTIMOGA", Research Report No. 2004/07, School of Engineering, Computer Science and Mathematics, Centre for Water Systems, University of Exeter, UK, 2004.

3

K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, "A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II", in M.S. et al., (Ed.), Parallel Problem Solving from Nature - PPSN VI, Springer, Berlin, 849-858, 2000.

4

D.W. Corne, N.R. Jerram, J.D. Knowles, M.J. Oates, "PESA-II: Region-based selection in evolutionary multiobjective optimization", in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), Morgan Kaufmann Publishers, San Mateo, CA, 283-290, 2001.

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