An integrated electrical and thermal residential renewable energy system consisting of solar thermal collectors, gas boiler, fuel cell combined heat and power, a photovoltaic system with battery, inverter, and thermal storage for a single-family house of Sonnenhaus standard is investigated with a model predictive controller (MPC). The main focus of this article is to define a multi-objective mathematical function, develop a coupled simulation framework for the nonlinear time-varying deterministic discrete-time problem of the energy system using TRNSYS and MATLAB. With the developed methodology, a sensitivity analysis of maximum optimization time, swarm (or population or mesh) size of a typical spring day and a typical summer day assuming a 100% accurate weather and load forecast with three different algorithms: particle swarm optimization (PSO), genetic algorithm (GA) and global pattern search (GPS) are analyzed. Finally, the obtained results are compared with a status quo controller. Results show that the PSO algorithm optimizer performs the best in this MPC for such a complex and time-consuming MPC model in both the spring day and the summer day. The obtained results show that the PSO with swarm size 50 in the selected typical spring day and the PSO with swarm size 40 in the selected summer day reduces the objective function’s fitness value from 413 to −177 within 6 h optimization time and from 1396 to 1090 in 4 h optimization time respectively.