# Optimization of Heat Pump Systems in Buildings by Minimizing Costs and CO\({}_{2}\) Emissions
[24] aimed to select an optimal energy system for a single-family building using bi-level multi-objective optimization to minimize total costs and CO2 emissions for the optimal design and operation over a long-term period. Their proposed approach combined a GA at the design level and a MILP at the operational level. They analyzed various technologies such as ground source heat pumps (GSHPs), solar thermal collectors, solar photovoltaic (PV) panels, gas boilers, electric heaters (EHs), and thermal energy storage. A multi-objective genetic algorithm (MOGA) with similar objectives was also applied in research by [PERSON] et al. [25]. They used MOGA within the HPS eOD design framework (a simulation-based optimization approach) to optimize annualized costs and emissions of HP systems considering operational behavior already during the design phase. This method was coupled with the TEASER software [26] for automatic generation of the building, thus allowing for use in various types of buildings located globally. The optimization variables in the framework correspond to components of HP systems such as compressor type, heat exchanger size, number of fans, and operational parameters. [PERSON] et al. [27] conducted an analysis to find the most cost-effective renovation solutions for large-panel apartment buildings located in cold climates over a 30-year life cycle period. In this study, various main heating systems were analyzed, and the cost-optimal solutions were determined from over 220 million renovation combinations by utilizing a simulation-based multi-objective optimization approach using the Pareto-Archive NSGA-II algorithm. The main objective of this research was to determine the cost-effective renovation concepts that provide both energy efficiency and reduction in total CO2 emissions. The study by [PERSON] et al. [28] investigated the potential of integrating short-term flexibility into long-term capacity planning for microgrids with a high proportion of renewable energy. To achieve this, they used a multi-objective optimization model to minimize the loss of power supply probability index and total life cycle costs, evaluating the most cost-effective approach for microgrid planning. The researchers employed the multi-objective particle swarm optimization algorithm, implemented in MATLAB R software, to solve the optimization problems. Additionally, nonlinear models have also been utilized in some studies to solve more complex optimization problems. One such model is the mixed-integer nonlinear programming (MINLP) model, which was analyzed in research by [PERSON] et al. [29]. The MINLP model in this study considers various factors such as the quantity and quality of heat sources, heat sink requirements, feasible integration technologies, and economic performance to optimally design low-grade heat utilization systems and HP-integrated low-grade heat utilization systems. The objective of the MINLP model is to minimize total annual cost while ensuring that other parameters such as heat sources, heat sink requirements, and integration technologies are met. To solve this optimization problem, the MINLP model was solved using the BARON solver in the General Algebraic Modeling System (GAMS) software. [PERSON] and [PERSON] [30] analyzed the MINLP model for optimal equipment selection to design and schedule a multi-energy microgrid, with the goal of minimizing the total annualized cost of the system. The equipment considered in their study included wind turbine farms, solar panels, batteries, and combined heat and power plants. [PERSON] et al. [31] used a combination of nonlinear programming and multi-objective optimization techniques to investigate the potential of a multi-module hybrid renewable energy system to reduce costs and GHG emissions over an annual period. The system consisted of a ground-air heat exchanger, photovoltaic thermal panels, and an air-to-water HP. The authors employed MILP techniques, evolutionary algorithms, and dynamic simulation to optimize the system design and performance parameters.