The optimization of a water distribution network （WDN） is a highly nonlinear, multi-modal, and constrained combinatorial problem. Particle swarm opti- mization （PSO） has been shown to be a fast converging algorith...The optimization of a water distribution network （WDN） is a highly nonlinear, multi-modal, and constrained combinatorial problem. Particle swarm opti- mization （PSO） has been shown to be a fast converging algorithm for WDN optimization. An improved estimation of distribution algorithm （EDA） using historic best positions to construct a sample space is hybridized with PSO both in sequential and in parallel to improve population diversity control and avoid premature conver- gence. Two water distribution network benchmark exam- ples from the literature are adopted to evaluate the performance of the proposed hybrid algorithms. The experimental results indicate that the proposed algorithms achieved the literature record minimum （6.081 MS） for the small size Hanoi network. For the large size Balerma network, the parallel hybrid achieved a slightly lower minimum （1.921M） than the current literature reported best minimum （1.923MC）. The average number of evaluations needed to achieve the minimum is one order smaller than most existing algorithms. With a fixed, small number of evaluations, the sequential hybrid outperforms the parallel hybrid showing its capability for fast convergence. The fitness and diversity of the populations were tracked for the proposed algorithms. The track record suggests that constructing an EDA sample space with historic best positions can improve diversity control significantly. Parallel hybridization also helps to improve diversity control yet its effect is relatively less significant.展开更多
基金This work was supported by the National Science Foundation Award 0836046. The opinions expressed in this paper are solely those of the authors, and do not necessarily reflect the views of the funding agency.
文摘The optimization of a water distribution network （WDN） is a highly nonlinear, multi-modal, and constrained combinatorial problem. Particle swarm opti- mization （PSO） has been shown to be a fast converging algorithm for WDN optimization. An improved estimation of distribution algorithm （EDA） using historic best positions to construct a sample space is hybridized with PSO both in sequential and in parallel to improve population diversity control and avoid premature conver- gence. Two water distribution network benchmark exam- ples from the literature are adopted to evaluate the performance of the proposed hybrid algorithms. The experimental results indicate that the proposed algorithms achieved the literature record minimum （6.081 MS） for the small size Hanoi network. For the large size Balerma network, the parallel hybrid achieved a slightly lower minimum （1.921M） than the current literature reported best minimum （1.923MC）. The average number of evaluations needed to achieve the minimum is one order smaller than most existing algorithms. With a fixed, small number of evaluations, the sequential hybrid outperforms the parallel hybrid showing its capability for fast convergence. The fitness and diversity of the populations were tracked for the proposed algorithms. The track record suggests that constructing an EDA sample space with historic best positions can improve diversity control significantly. Parallel hybridization also helps to improve diversity control yet its effect is relatively less significant.
