Improving the Efficiency of Cellular Automata for Sewer Network Design Optimization Problems Using Adaptive Refinement

Abstract

This paper introduces an adaptive procedure to improve the efficiency of a two phase simulation-optimization cellular automata algorithm recently proposed by the authors for the optimal design of household sewer networks. In the proposed method, the continuous decision variables are discretized to turn the original mixed-integer problem to a discrete problem which is then solved by a two-phase CA method. It is obvious that coarse discretization requires low computational effort but may lead to sub-optimal solution while fine discretization may produce better solutions at the expense of higher computational cost. An adaptive refinement approach is, therefore, proposed to reduce the computational cost of the CA method with no adverse effect on the quality of the final solution. The optimization process starts with coarse discrete values of pipes nodal elevations and the problem is solved for optimal solution. A finer discretization of the pipe nodal elevations is then constructed in the neighborhood of optimal pipes nodal elevations obtained from the first run and the same process is used to find the new solution. This process is continued until no change in the solution is possible. The proposed method is applied to solve two benchmark problems of literature. The result explicitly shows that the proposed adaptive refinement approach leads to quality solution with much reduced computational effort.