Multi-objective optimization of stepped spillway and stilling basin dimensions

In the present paper, an optimization procedure is proposed for stepped spillway design dimensions, which leads to maximum energy dissipation rate and minimum construction cost, considering independently the chute cost and stilling basin cost. Three independent objective functions are thus simultaneously satisfied. The procedure involves four main tools: the multi-objective particle swarm optimization method (MOPSO) to find Pareto solutions in one run, the K-means clustering algorithm to reduce the size of the obtained non-dominated solutions, the pseudo-weight vector approach (PWV) to facilitate the decision making and to select some adequate solutions, and finally, CFD simulations to analyze the retained optimal solutions. The suitability of the proposed procedure is tested through an example of application. As results, a set of 20 solutions with different satisfaction levels is found and compared to existing solutions. A multi-objective optimization problem may have many different solutions; the originality of the present work lies in the proposed procedure, which explores several possible solutions and reduces their number to give help to the decision making. Furthermore, an approximate expression of spillway total cost is also derived as a function of flow energy dissipation rate.