The hybrid absorption-compression heat pump (HACHP) system has garnered widespread attention due to its unique advantage of combining absorption and compression heat pump technologies, allowing it to operate over a wider temperature range and exhibit higher system efficiency. However, the distinct characteristics of the HACHP system's performance curves, the nonlinear coupling between variables, and the diverse performance indicators present significant challenges for system optimization. To address these challenges, this paper proposes a simulation-based optimization framework specifically tailored for HACHP systems, using a multiobjective evolutionary algorithm (MOEA) to tackle constrained multi-objective optimization problems (CMOP). The framework integrates three innovative algorithms: differential evolution optimized symbolic regression (DEOSR), constrained range adaptive sampling (CRAS), and variable speed mutation (VSM). The DEOSR algorithm models the constraint relationships between system variables through inequality fitting, and after comparing various mutation strategies, achieves an optimal fitting result with an R2 of 0.9964 and an RMSE of 1.9912. The CRAS algorithm enhances the diversity of the initial population through a classified sampling strategy, significantly improving the population's coverage in the value space and effectively preventing the risk of missing boundary optima in the HACHP system. The VSM algorithm dynamically adjusts the mutation rate during the optimization process, balancing global and local search capabilities, and effectively addresses the abrupt changes often observed in heat pump performance curves. Additionally, the framework incorporates a strategy based on non-dominated sorting and reference points method (RPM), enabling it to efficiently handle high-dimensional multi-objective optimization problems. Ultimately, this framework was successfully applied to a thermally coupled HACHP system.