Development a Two-objective Simulation - Optimization Model for Optimal Design of Geometric Dimensions and Slope of the Stepped Spillway of Upstream Siah-Bisheh Dam Using NSGA-II Algorithm

For safe pass of flood flow from upstream to downstream of dams, the spillways are used. Among the various spillways, in stepped spillways, the flow is dissipated when passing through the structure. This will reduce the cost of downstream energy-dissipaters structures such as stilling basin. In addition to energy dissipation, the volume and cost of stepped spillways can affect its design. The best design of the stepped spillway is that the remaining energy and the volume and cost of the spillway will be minimized. Therefore, the stepped spillway design is a multi-objective optimization problem. In the present study, a two-objective simulation-optimization model based on the NSGA-II algorithm was used to minimize the possible remaining energy and spillway volume. The results showed with increasing the relative height of spillway stairs, the amount of remaining energy is increased initially and after reaching a peak point, it would be reduced to a constant value. From the perspective of volume and cost of spillway, by increasing the relative height of the spillway stairs, its volume is increased linearly and by increasing the spillway angle, its volume decreased. The results of multi-objective optimization model showed that in the current plan of Siah-Bisheh Dam spillway, the remaining energy and the volume of spillway criteria were considered well. So that 83.7 percent of the flow energy is dissipated.