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The importance of water distribution network rehabilitation, replacement and expansion is discussed. The problem of choosing the best possible set of network improvements to make with a limited budget is presented as a large optimisation problem to which conventional optimisation techniques are poorly suited. A multi-objective approach is described, using capital cost and benefit as dual objectives, enabling a range of non-inferior solutions of varying cost to be derived. A Structured Messy Genetic Algorithm is developed, incorporating some of the principles of the Messy Genetic Algorithm, such as strings which increase in length during the evolution of designs. The algorithm is shown to be an effective tool for the current optimisation problem, being particularly suited both to the multi-objective approach and to problems which involve the selection of small sets of variables from large numbers of possibilities. Two examples are included which demonstrate the features of the method and show that the algorithm performs much better than a standard Genetic Algorithm for a large network.

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[1] The water distribution system (WDS) design problem is defined here as a multiobjective optimization problem under uncertainty. The two objectives are (1) minimize the total WDS design cost and (2) maximize WDS robustness. The WDS robustness is defined as the probability of simultaneously satisfying minimum pressure head constraints at all nodes in the network. Decision variables are the alternative design options for each pipe in the network. The sources of uncertainty are future water consumption and pipe roughness coefficients. Uncertain variables are modeled using probability density functions (PDFs) assigned in the problem formulation phase. The corresponding PDFs of the analyzed nodal heads are calculated using the Latin hypercube sampling technique. The optimal design problem is solved using the newly developed RNSGAII method based on the nondominated sorting genetic algorithm II (NSGAII). In RNSGAII a small number of samples are used for each fitness evaluation, leading to significant computational savings when compared to the full sampling approach. Chromosome fitness is defined here in the same way as in the NSGAII optimization methodology. The new methodology is tested on several cases, all based on the New York tunnels reinforcement problem. The results obtained demonstrate that the new methodology is capable of identifying robust Pareto optimal solutions despite significantly reduced computational effort.

Genetic algorithm (GA) optimization is well suited for optimizing the operation of water distribution systems, especially on large and complex systems. GAs have good initial convergence characteristics, but slow down considerably once the region of the optimal solution has been identified. In this study the efficiency of GA operational optimization was improved through a hybrid method which combines the GA method with a hillclimber search strategy. Hillclimber strategies complement GAs by being efficient in finding a local optimum. Two hillclimber strategies, the Hooke & Jeeves and the Fibonacci methods were investigated. The hybrid method proved to be superior to the pure GA in finding a good solution quickly, both when applied to a test problem and to a large existing water distribution system.