Using the three-objective simulator-optimizer approach for the optimal design of the combined stepped-labyrinth spillway using the improved dragonfly optimization algorithm

The cost of implementing spillways includes a large part of the dam construction budget. Optimizing these structures can significantly reduce the cost of building dams. So far, many studies have been done on optimizing the dimensions of spillways in order to reduce the amount of materials used. Among the used optimization methods, the methods based on meta-heuristic algorithms have had stunning results. The review of the studies conducted in the field of stepped and labyrinth spillways shows that the goals of all studies in stepped spillways have been to provide an acceptable plan for energy dissipation and in labyrinth spillways to reach a the largest amount of water passing. The purpose of this study is to combine stepped spillways with labyrinth spillways and optimization in order to increase the water passage coefficient and energy consumption at the same time. For this purpose, the multi-objective optimization approach has been used.

In the present study, the redesign of the spillway of the Sarouk rockfill dam located in West Azarbaijan province has been studied. In the case of labyrinth-stepped spillway, the decision variables, constraints and objective functions of the two spillways are combined and analyzed as a multi-objective optimization problem. In this study, a dynamic coefficient is used to improve the performance of the dragonfly algorithm in the search and exploitation stage. After determining the optimal values of the regulatory parameters of the MODA, NSGA-II, MOPSO and MOIDA algorithms, four benchmark examples were solved with each of them 20 times with an initial population of 50 and a maximum number of iterations equal to 100.

After validating the improved dragonfly algorithm on benchmark functions and evaluating its performance in solving multi-objective problems, this algorithm was used to design a combined spillway on the introduced dam. In multi-objective problems, there is a set of optimal solutions rather than a single optimal solution, which appear as a Pareto front. The implementation of the improved dragonfly algorithm with 200 initial population and 500 repetitions has resulted in providing 200 optimal answers on the Pareto chart. After performing the calculations related to the fuzzy decision-making method, a design with the values of the objective functions of concreting volume: 59795.54 cubic meters, dissipated energy: 75.18%, flow rate: 1255.19 cubic meters per second was selected as the optimal answer. In addition, the design with the highest and lowest cost of concrete consumption was selected as two other answers. The flow rate passing over the spillway has increased by 120% in plans A and B, and by 25% in plan C compared to the initial design flow rate. The amount of energy dissipation of plans A and B is about 76 and 75%, respectively. In plan C, where the flow rate has not increased significantly (25%), energy dissipation has reached about 81%, which is more than the other two cases.

Among the available answers, according to the priority of the cost, the plans with the lowest (C) and the highest (A) implementation cost based on the volume of concrete were selected. Also, by using the fuzzy decision-making approach, an optimal plan (B) that has a suitable balance between the three objectives was selected. Based on the results, it was found that each of the plans A, B and C can be used based on the needs of the employer. From the economic point of view, according to the project conditions and the needs of the employer, all the proposed plans are suitable options for replacing the actual spillway and reduce the implementation costs. Also, the comparison of plan C with the stepped spillway plan presented by previous researchers showed that with almost the same volume of concrete, using a multi-objective approach in comparison with a single-objective optimization approach, in addition to increasing flow energy consumption, also led to an increase in flow through the spillway.