This study investigates the effectiveness of two recently proposed meta-heuristic methods, the Weighted Average Algorithm (WAA) and Electric Eel Foraging Optimization (EEFO), to maximize the total profit of a hybrid power system. The considered system comprises fifteen thermal generating units (TGUs) and a 100-MW solar photovoltaic farm (SPP) operating over a 20-year period. Initially, the problem is solved under conditions of fixed load demand and rated power supply from the renewable energy source while accounting for prohibited operating zone constraint and system power losses. Comparative results obtained from both algorithms demonstrate that EEFO exhibits superior performance in terms of stability and convergence speed. Specifically, EEFO demonstrates a lower fluctuation in overall electricity generation cost (OEGC) across multiple independent runs compared to WAA. Furthermore, EEFO achieves better minimum, mean, and maximum OEGC values of $0.266, $58.890, and $214.225, respectively. Subsequently, EEFO is reapplied to maximize the profit of the hybrid power system, incorporating load demand variations and real solar radiation data. This analysis includes the evaluation of initial capital expenditure (CAPEX) and operation and maintenance (O&M) costs for the SPP over the 20-year period. Current electricity and solar power prices are utilized to illustrate the cumulative profit over time. The results indicate that the hybrid system experienced the highest loss in the first year, with the minimum loss occurring after 9 years for the TGUs and 7 years for the SPP. Profitability is achieved after 10 years for the TGUs and 7 years for the SPP. The cumulative profit over 20 years amounts to $14.2 billion for the TGUs and $0.207 billion for the SPP, representing approximately 83% and 127% of their respective total costs.