Rising electricity demand, volatile fossil-fuel prices and the need to cut greenhouse-gas emissions are pushing power systems away from large centralised plants and towards distributed generation close to the load. A single renewable source cannot supply such loads reliably, because solar irradiance, wind speed and biomass availability vary with the hour and the season. This paper presents an optimal design methodology for an integrated renewable energy system (IRES) that combines solar photovoltaic (PV) arrays, wind turbines, a biogas generator, a hydrogen fuel cell and a lithium-ion battery bank, connected to the utility distribution grid through a bidirectional converter. The design problem is formulated as a constrained, mixed-integer optimization that minimises the Net Present Cost (NPC) and the Levelised Cost of Energy (LCOE) subject to limits on the loss of power supply probability (LPSP), the renewable fraction (RF) and component operating bounds. Hourly resource, load and economic data feed a time-series simulation, and the component sizes are searched with an adaptive-inertia particle swarm optimizer (APSO) with a penalty-based constraint handler. A case study of a rural community with an average load of 4,860 kWh/day and a peak of 612 kW gave an optimal configuration of 600 kW PV, 400 kW wind (4 turbines), 150 kW biogas, 25 kW fuel cell, 1,200 kWh battery and 450 kW converter. This configuration reached an NPC of US$ 2.95 million, an LCOE of 0.105 US$/kWh, a renewable fraction of 96.5% and an LPSP of 0.20%, while cutting annual CO₂ emissions by 96.5% relative to grid-only supply. The proposed optimizer converged in 48 iterations, against 61 to 128 for GWO, PSO and GA. Sensitivity analysis on load, component cost, wind speed and discount rate confirmed that the design is robust within ±20% parameter variation.