The technique proposed in this paper, the self-adaptive population hybrid Rao algorithm (SAPHR), is intended to handle single- and multi-objective optimization problems. Unlike traditional methods, it does away with the necessity for metaphors and particular algorithm settings. According to improvements in the fitness value seen during the search process, the algorithm under consideration modifies the population size. The population is divided into three sub-population groups through a random process. Randomly assigned perturbation equations are provided to each sub-population, with each Equation guiding solutions to explore distinct regions within the search space. Evaluating the performance of the proposed algorithm involves using the well-known reservoir benchmark problem known as the discrete four-reservoir operation (DFRO) problem. The results of the algorithm are compared with other methods from the past study, revealing that the proposed method achieves superior outcomes.