Classical methods have severe limitations (such as being trapped in local optima, and the curse of dimensionality) to solve optimization problems. Evolutionary or meta-heuristic algorithms are currently favored as the tools of choice for tackling such complex non-linear reservoir operations. This paper evaluates the performance of an extended multi-objective developed firefly algorithm (MODFA). The MODFA script code was developed using the MATLAB programming language and was applied in MATLAB to optimize hydropower generation by a three-reservoir system in Iran. The two objectives used in the present study are the maximization of the reliability of hydropower generation and the minimization of the vulnerability to generation deficits of the three-reservoir system. Optimal Paretos (OPs) obtained with the MODFA are compared with those obtained with the multi-objective genetic algorithm (MOGA) and the multi-objective firefly algorithm (MOFA) for different levels of performance thresholds (50%, 75%, and 100%). The case study results demonstrate that the MODFA is superior to the MOGA and MOFA for calculating proper OPs with distinct solutions and a wide distribution of solutions. This study's results show that the MODFA solves multi-objective multi-reservoir operation system with the purpose of hydropower generation that are highly nonlinear that classical methods cannot solve.

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