Development of GWO–DSO and PSO–DSO hybrid models to redesign the optimal dimensions of labyrinth spillway

In this study, considering the importance of dams spillways redesign to provide optimal dimensions, the hybrid of particle swarm optimization, gray wolf optimization (GWO) and direct search optimization meta-heuristic approach were proposed. In this methodology, the total volume of spillway body, which indicates the amount of concrete and cost, is considered as the objective function and height of spillway, the number of cycles, apex length and angle of wall are defined as decision variables. By implementing the proposed model based on the data of the Ute dam labyrinth spillway, the optimal dimensions of spillway were determined and compared with the other studies. The results indicated that the hybrid of meta-heuristic algorithms has a very good performance in generating global optimal values, except that the GWO algorithm has a higher convergence rate. In the proposed method, the optimal dimensions provided by the hybrid algorithm led to saving in concrete and reduction of costs to 64% as compared to the existing design of dam. Investigating the optimal dimension of trapezoidal labyrinth spillway also indicates that these dimensions increase the flow capacity of the spillway to \(15{,}760\,\hbox {m}^{3}{/}\hbox {s}\). Finally, comparison of the optimum dimensions obtained with two trapezoidal and triangular sections showed that the optimal form for labyrinth spillway is triangular and leads to improved spillway hydraulic performance.