Penalty Free Self adaptive Search Space Reduction Method for Multi objective Evolutionary Design Optimization of Water Distribution Networks
Evolutionary optimization approaches such as genetic algorithms are being used increasingly in the optimization of water distribution networks. The number of hydraulic simulations required to find good solutions can be extremely large and time consuming. It is, therefore, highly desirable to reduce the search or solution space to speed up the optimization process. The new approach herein considers the importance of every path through the network, an intrinsic property of the statistical flow entropy function. Pre processing, setting or initialization of the reduced solution space is not required a priori. Instead, the reduced solution space is determined adaptively using maximum entropy principles. The methodology comprises two main phases. In the first phase, the entire solution space is explored until a feasible solution is identified. In the second phase, exploitation is effected by means of a reference solution that is updated in every generation. The reduced set of pipe diameter options considered in each generation in the second phase is defined relative to the reference solution. The algorithm was applied to a benchmark network. The solutions obtained were generally less expensive for similar entropy values than solutions from the full solution space. The results revealed that the solution space reduction algorithm limits the search to the areas close to the feasibility boundary. Consistently good results were achieved in terms of the quality of the solutions and computational efficiency.