Single and Multi-Reservoir Operation Optimization Using the SGWO algorithm

There is an obvious quality to surface waters and that is they never stop moving, and being a being as selfish as humankind, managing and the ever-moving essence of life can be arduous. But building dams enabled humans to maintain the water and release it as they saw fit. No matter where we stand according to the environmental issues caused by massive dam construction, we cannot neglect the fact that they exist and are an important part of water systems.

Nowadays, with environmental crises happening all over the world, water scarcity turning into a pervasive matter and with the climatic changes aggravating the asymmetric spatiotemporal distribution of water, the optimum management of water reservoirs seems an imperative part of water resources management.

Water reservoirs can operate in different types of systematic structures. Sometimes we might be dealing with a single humongous reservoir that provides multiple services for the region or we can encounter a large-scale multi-reservoir system with multiple dams working together to help allocate the water and returning maximum benefits. The term “maximum benefits” can be vague as depending on our point of view the benefit can vary a lot. This situation causes the reservoir operation problems to shapeshift to complex optimization problems with multiple, mostly incompatible, objectives.

The equation governing this optimization problem is simple; the conservation of mass. But when the different objective functions concerning economic, demand management, power generation, etc. are added to the equations, solving this problem is demanding, and although classic methods have been utilized in more simplified versions of them, the required computational effort increases immensely with the size of the problem and these classic methods might not be able to provide us with an answer. Metaheuristic optimization is one of the best choices that researchers have in dealing with these problems.

In our project, the initial aim was to assess the performance of the Gray Wolf Optimizer in solving single and multi-reservoir optimization problems. With various problems encountered in this process, the Shuffled Gray Wolf Optimizer (SGWO), a hybrid of Shuffled Complex Evolution (SCE-UA) and the GWO, was developed (more details about the philosophy behind the algorithm can be found here). Before I discuss our research further, I must mention that the paper of this project is still under review and we hope that it will be published before 2022. (Hopefully!)

Three problems were analyzed and studied in our research. One, a single reservoir problem which was formulated as demand and storage management of the Dez Reservoir in Iran with 5 different approaches first two using a rule curve for two time periods of 5 and 20 years that had 36 decision variables, and the three next approaches used a time series approach for three time periods of 5, 10 and 20 years with, 60, 120 and 240 decision variables respectively. Two, a hypothetical four reservoir system with 48 decision variables, and three, and another hypothetical 10 reservoir system with 120 decision variables. These problems were solved 20 times by each of the SGWO, GWO, SCE-UA, Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA) methods. It must be noted that the single reservoir problem was a demand management problem and the objective was to minimize the deficit between the released water volume with the demand volume while the other two problems were a hydropower production management with the objective function being maximizing the net return of the system.

Fig. 1 - Computed monthly release for each reservoir in the discrete-time four reservoir operation problem

Fig. 2 - Computed monthly storage volumes for each reservoir in the discrete-time four reservoir operation problem

According to the results, the SGWO performed better compared with other algorithms in several aspects. The most improvement was observed in the number of function evaluations (NFE) required to reach the global optima. NFE is the total number of recalling the cost function. NFE is usually a considerable number and since cost function is the most time-consuming part of the computation, the lower the number of NFE the lower the computational demand of the algorithm.

Table 1 - Summary of the results of 20 consequetive runs in the discrete-time four reservoir operation problem

Table 2 - Summary of the results of 20 consequetive runs in the ten-reservoir problem

Every algorithm might be capable of reaching the global optimum but how often this would happen is important. This is the reason why the problems were solved 20 times by each algorithm. The results indicated that the SGWO algorithm reached a better global optimum point and did it often, as the standard deviations of the final results were considerably smaller than other algorithms. Of course, it must be mentioned that, specially concerning the large-scale problems with high number of decision variables, the SGWO reached to a significantly better result which shows that this algorithm performs excellent while the problem at hand possess a large number of variables.

Table 3 - Results of single reservoir operation problems