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Through the use of effectively unlimited energy from the environment, contemporary heat pump installations have proven to be a highly efficient means for satisfying both heating and cooling needs. As such, they are often regarded as a key driver in the electrification process of the thermal domain. Keeping in mind the significant share of the thermal demand in building energy requirements, this aspect in particular is projected to have a great impact on the overall energy efficiency improvement of buildings and increase of demand-side flexibility. The latter point is considered crucial for improving the precarious balance against the contemporary intermittent power supply obtained from a variety of renewable sources. However, in the process of increasing their efficiency, heat pump systems are becoming significantly more complex with combinations of various different sources of energy from the ground, air and the Sun. By extension, the complexity of managing their operation has also increased and proves to be a challenge even for experienced plant operators. In order to aid in this regard, relevant literature suggests that optimization algorithms can be considered as a viable tool. This paper explores the limited extent of existing state-of-the-art approaches for hybrid heat pump control via metaheuristic optimization and broadens the subject matter with a comparative study that analyzes and benchmarks several metaheuristic approaches found in the literature on similar problems. A real-world multisource heat pump installation in Ferrara is utilized as the basis for the study. [Display omitted] • Novel systematization of optimization applications for heat pump operation and design. • Modeling approach suitable for novel optimization-assisted control algorithms. • Optimization as an enabler for increased operational efficiency of future HP systems. • Comparative analysis of optimization performances for a selection of metaheuristics. • Analysis of reference tracking and convergence results in GA being the best algorithm. [ABSTRACT FROM AUTHOR]