Investigation of a New Hybrid Optimization Algorithm Performance in the Optimal Operation of Multi-Reservoir Benchmark Systems

Abstract

Reservoirs’ optimal operation is a critical issue in the management of surface water resources. In the present study, after combining the whale optimization algorithm (WOA) with genetic algorithm (GA), which is called hybrid whale-genetic algorithm (HWGA), the precision and convergence rate of HWGA is evaluated in the optimal operation of continuous-time four-reservoir benchmark system (FRBS) and ten-reservoir benchmark system (TRBS). This combination benefits from the GA high precision and the WOA high convergence rate. The precision and convergence rate of HWGA, GA, and WOA are compared to the absolute optimum solution, obtained using Lingo software. Results indicated that the absolute optimal solution was 308.292 in the FRBS and 1194.441 in the TRBS. The best optimal solutions using the HWGA, GA and WOA were 96.08%, 95.76%, and 85.19% of the absolute optimal in the FRBS, respectively, and 97.24%, 89.54%, and 84.42% of the absolute optimal in the TRBS, respectively. So, the precision of HWGA, GA and WOA ranked first to third, respectively. Also, the variation coefficient of HWGA solutions (0.006 in the FRBS and 0.011 in the TRBS) had the lowest value in both benchmark systems. The variation coefficients of GA and WOA solutions were 1.24 and 3.57 times the variation coefficient of HWGA in the FRBS, respectively, and 1.55 and 5.32 times the variation coefficient of HWGA in the TRBS, respectively. Therefore, it could be concluded that in the current study the HWGA solutions variation range was narrower than other algorithms’ solutions. According to four criteria of the objective function average, standard deviation, number of population, and maximum number of iterations, the performance of the algorithms in the present study is compared to the performance of some algorithms in other literatures using Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The results of TOPSIS indicated that HWGA ranked first and WOA ranked last in both benchmark systems.