The Design and Rehabilitation of Water Distribution Systems Using the Hierarchical Bayesian Optimisation Algorithm

The design and rehabilitation of water distribution systems is considered here as a constrained least cost optimisation problem. In the design and rehabilitation of water distribution systems the solution space tends to be vast. This paper uses the hierarchical Bayesian Optimisation Algorithm (hBOA) to search the solution space with the aim of decreasing the number of fitness evaluations required for convergence. hBOA is a probabilistic model building genetic algorithm which uses a Bayesian network to model the set of promising solutions in each generation. This network is in turn sampled to generate the offspring to be incorporated into the next generation. hBOA has been shown to solve a number of challenging problems in sub-quadratic time, that is the number of fitness evaluations required for convergence is of order less than the square of the number of design variables. Since a fitness evaluation requires the solution of a set of hydraulic equations there are significant time benefits to be had by reducing the number of evaluations. hBOA is applied to two sample networks as deterministic, single objective problems; the New York Tunnels problem and the `Anytown' network. Initial results show hBOA to compare favourably with other evolutionary computation techniques in the literature, both in terms of the proportion of runs in which the best known solution is found and in terms of the number of fitness evaluations required.