The hybrid model of the power network infrastructure is an essential part of the sophisticated technology of the electrical network. For the traditional Optimal Power Flow (OPF) problem, thermal generators are typically employed to generate electricity. In this case, the amount of fuel required to produce power is constrained, and emissions from the network are frequently neglected. Renewable Energy Sources (RESs) have received increasing attention due to various potential characteristics such as cleanliness, diversity, and renewability. As an outcome, RESs are being integrated into the electrical grid at an increasing rate. The study in this paper proposes a techno-monetary investigation into the single-and multi-objective OPF, coordinating with RESs like wind, PhotoVoltaic (PV), and small hydropower units with hybrid PV. Moreover, the probability density functions of Weibull, Lognormal, and Gumble have been used independently to predict the required power in this paper. This paper considers an equilibrium optimizer for handling the OPF problem. The superior performance of the equilibrium optimizer is further verified with the results of both single-and multi-objective through comparative analysis with state-of-the-art counterparts, and the indications are that the proposed method can find better optimal solutions, use a lower number of generated solutions, and faster convergence with well distributed optimal Pareto front for multi-objective problems. The results are verified by employing a modified IEEE-30 bus hybrid power network, and performance comparisons are made among several well-established algorithms. Simulation findings show that the suggested strategy can achieve a reasonable compromise solution for different objectives.