Multi-objective optimization of stepped spillways in order to reduce the design costs and maximize the energy dissipation (case study: Sarooq reservoir spillway)

Document Type : Research Article


1 MSc Graduate, Department of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran.

2 University of Sistan and Baluchestan

3 Department of Civil Engineering, Faculty of Engineering, University of Sistan and Baluchestan, Zahedan, Iran



Introduction: Considering that dams are one of the most important water storage resources in water projects, therefore, proper construction and operation management of them is one of the most important responsibilities of water resource managers. One of the important parts in the construction of any dam is the design of the dam spillway, which is responsible for discharging excess water from the reservoir to downstream in case of floods. Destruction or inefficiency of spillways causes severe damage to the dam or even causes its complete destruction, that is why the design and construction of this part of the dam is very important. Among different types of spillways, stepped spillways, in addition to passing excess water from the reservoir of dams, are also a structure that consumes flow energy. Until now, in the studies carried out in this field, the optimization of stepped spillways has been considered as a single objective, which usually aims to optimize, minimize construction costs or maximize energy consumption in these spillways, and rarely optimize the dimensions of spillways with Taking into account the two factors of cost and energy consumption has been considered simultaneously. Therefore, in this study, for the first time, a multi-objective optimization model has been developed by benefiting from the capabilities of the improved version of the dragonfly optimization algorithm for the design of stair overflows with the aim of minimizing the volume of concrete used and increasing energy consumption.
Methodology: In the design of the stepped spillway, the discharge parameters (Q) and the horizontal length of the overflow (L) are among the most important input parameters, which are determined based on the initial studies of topography and hydrology and are considered constant during the design. According to the purpose of the present research, an optimal combination of effective parameters in the design of a stepped spillway, including slope, width, height of the spillway, water pressure on the spillway, and step height, should be determined in a way that leads to the highest energy consumption and the lowest design costs with By-law restrictions should be taken into account. In the current research, the objective function, which consists of decision variables, should simultaneously provide the maximum amount of energy consumption and the minimum volume of consumed concrete, while satisfying the constraints and hydraulic conditions of the design problem. For this purpose, the dragonfly optimization algorithm, which is one of the powerful algorithms of collective intelligence methods, and was first proposed by Mirjalili.
This algorithm is inspired by the group and social behavior of dragonflies in nature. Dragonflies usually live alone in the wild and only act in groups for hunting and migration. The basis of the dragonfly optimization algorithm to find the optimal answer is their two crowding behaviors. In this way, based on the static behavior, the members of the algorithm population are divided into smaller groups and search the problem space, then based on their dynamic behavior (exploitation phase), they determine the optimal answer with more members.
Results: The spillway of Sarouq Dam, located in West Azarbaijan province, was selected as a case study in this research to evaluate the developed model. In the first part, the problem of optimal design of the stepped spillway of Sarouk Dam was investigated as a single-objective problem with the aim of maximizing the amount of energy consumption. The purpose of redesigning Sarouk dam spillway was to provide an optimal design for a stepped spillway instead of the existing flat spillway with the aim of maximizing energy consumption downstream of the dam. In all the optimal models provided by IDA, the consumption of water energy has increased significantly. According to the report of Hosseini, 2019, the amount of energy consumption at the foot of the existing spillway of Sarouk Dam is equal to 23.41, which the use of the stepped spillway in the present research increases it for the flow rates of 560.2, 776.9, and 422 cubic meters per second, respectively. 71.32, 65.72 and 74.74 percent. According to the main goal of this article, in this section, the new and improved algorithm based on the dragonfly algorithm has been used to optimize the multi-objective overflow of Sarouk Dam by considering the amount of concrete pouring and the amount of energy consumption as objective functions. The results shown that, using the multi-objective optimization approach for the design of stair overflows leads to the presentation of different types of designs with different implementation costs and energy consumption rates. Therefore, using the multi-objective optimization approach has led to the production of many answers, which allows the employer to design the overflow according to the budget he has.
Conclusion: In this research, using the improvement of a new metaheuristic algorithm called the dragonfly algorithm, a single-objective model was developed with the aim of maximizing energy consumption, and another multi-objective model was developed with the objectives of minimizing the construction costs of the stair overflow. The developed models were used for the optimal design of Sarouk Dam spillway.
The use of the improved Dragonfly multi-objective optimization algorithm to minimize construction costs and increase energy consumption showed that the multi-objective optimization approach can provide a set of answers that is a great help to the employer in order to achieve an economic plan based on the budget. available


Main Subjects

Articles in Press, Accepted Manuscript
Available Online from 10 February 2024
  • Receive Date: 19 August 2023
  • Revise Date: 28 September 2023
  • Accept Date: 29 September 2023