Metaheuristic vs. mathematical optimization: A comparison of methods for the design optimization of residential building energy systems

The energy system of residential buildings and their impact on the transition towards an emission-free energy supply has been a focus in a wide range of studies over recent years. For the design of energy systems, a variety of methods are used, most commonly heuristic, mathematical optimization and metaheuristic approaches. While the strengths and weaknesses of these methods are well known, knowledge about the discrepancy in results produced for the design of energy systems is limited. Moreover, metaheuristics have rarely been utilized in the field of household energy system planning. This leads to problems whenever findings from different studies are compared and raises the question about the optimal choice of methodology under given circumstances. To approach this question, we examine the energy system of a residential building with two different methods - a mathematical optimization and a metaheuristic optimization applied to the same MILP model. The energy system model considers a PV system, a heat pump, a heat and a battery storage system as well as a gas boiler. The layout and size of these components along with their operation are optimized. We compare the results regarding the difference in layout and size of individual components, investment costs, operational costs, CO2 emissions and computational performance of the methods. In this case study, the mathematical optimization resulted in the best Pareto front. Using the metaheuristic approaches, it is possible to compute a Pareto front in a considerably shorter time. However, the quality of the Pareto front is significantly worse.