Abstract Two heuristic approaches based on particle swarm optimization (PSO), i.e., a PSO algorithm with adaptive inertia weight (PSOAIW) and a PSO algorithm with a constriction factor (PSOCF), are applied to the optimization of a hybrid system consisting of photovoltaic panels, a fuel cell, natural gas and the electrical grid to supply residential thermal and electrical loads. An economic model is developed and an economic analysis carried out for the grid-connected hybrid solar–hydrogen combined heat and power systems. The optimization seeks to achieve the minimum cost of the system with relevant constraints for residential applications. The optimization process is implemented and tested using actual data from northeastern Iran. Three other well-known meta-heuristic optimization techniques, namely the imperialist competition algorithm, genetic algorithm, and original particle swarm optimization, are applied to solve the problem and the results are compared with those obtained by the two heuristic approaches. The results show that the proposed PSOAIW and PSOCF algorithms achieve better results than other algorithms, and the hybrid solar-hydrogen system is the most cost-effective and reliable for satisfying residential energy demands in the near future.