Recently, renewable energy resources (RESs) have been utilized to supply electricity to remote areas, instead of the conventional methods of electrical energy production. In this paper, the optimal design of a standalone hybrid RES comprising photovoltaic (PV), wind turbine (WT), and biomass sources as well as an energy storage system, such as a hydro-pumped storage system, is studied. The problem of the optimal sizing of the generating units in the proposed energy system is formulated as an optimization problem and the algorithms heap-based optimizer (HBO), grey wolf optimizer (GWO), and particle swarm optimization (PSO) are applied to achieve the optimal sizing of each component of the proposed grid-independent hybrid system. The optimization problem is formulated depending on the real-time meteorological data of the Ataka region on the Red Sea in Egypt. The main goal of the optimization process is to minimize the cost of energy (COE) and the loss of power supply probability (LPSP), while satisfying the constraints of system operation. The results clarify that the HBO algorithm succeeded in obtaining the best design for the selected RE system with the minimum COE of 0.2750 USD/kWh and a net present cost (NPC) of USD 8,055,051. So, the HBO algorithm has the most promising performance over the GWO algorithm in addressing this optimization problem.