Keywords: water distribution network, optimal design, differential evolution, particle swarm optimization.

In the case of the design of a pipe network the optimization problem can be stated as follows: minimize the cost of the network components subject to the satisfactory performance of the water distribution system (mainly, the satisfaction of the allowable pressures). Various algorithms ranging from artificial intelligence to the optimization domain have been applied.

Nevertheless, it must be pointed out that there is still some uncertainty as to how close any heuristic method can get to a global optimum of the task to be solved. Research should therefore continue, and the evaluation of other methods is still important.

The paper proposes a new multiphase methodology based on a combination of differential evolution (DE) and particle swarm optimization (PSO) called DEPSO, for solving the optimal design of a water distribution system. Its effectiveness is determined by applying two basic principles: a multi-step optimization procedure and the DEPSO methodology as an optimization engine. The multi-step optimization procedure means, that the optimization is accomplished in two or more phases (optimization runs) and that in each further run, the optimization problem comes with reduced search space. This reduction of the search space is based on the assumption of the significant similarity between the flows in sub-optimal solutions and the flows in a global optimal solution.

This assumption was empirically verified on the large irrigation network Balerma, to which this methodology was applied. The calculation results for the presented network demonstrate better performance of the proposed methodology when compared with the traditional, one-step application of various heuristic methods (results of various authors are summarised, for example in [1]).

The focus of this paper is the simplification of the calculation for practical use. From this point of view the most important is the ability of the algorithm to solve large networks, and find the solution as close to the global optimum as possible. No adaptation of heuristics parameters was conducted, since a typical end user cannot research the details of a particular optimization algorithm. This leads to a greater number of iterations required to obtain the final result than is usual: two optimization runs with 2000 generations and a population size equal to 250. Authors are of the opinion, that the practical usefulness of the calculation effectivity in terms of iteration counts is less important than substantial cost-saving for the network, but this aspect of the proposed methodology should be refined in future research.

1

A. Bolognesi, C. Bragalli, A. Marchi, S. Artina, "Genetic Heritage Evolution by Stochastic Transmission in the optimal design of water distribution networks", Advances in Engineering Software, 41(5), 792-801, 2009. doi:10.1016/j.advengsoft.2009.12.020

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