Abstract: The increasing demand for polar scientific exploration and Arctic maritime transportation has intensified the need for advanced polar heavy icebreakers capable of operating efficiently under extreme environmental and highly variable loading conditions. As a critical component of the shipboard power system, the hybrid energy storage system plays an essential role in mitigating power fluctuations, improving energy utilization efficiency, and enhancing operational reliability. A multi-objective optimization model is developed for the capacity configuration of the HESS in a polar heavy icebreaker. The proposed model simultaneously minimizes the cost of the energy storage system, reduces the lifetime loss of energy storage components, and improves the power-balance performance of the shipboard power supply system. An adaptive mutation-based Multi-Objective Particle Swarm Optimization(MOPSO) algorithm is employed to solve the optimization problem. The algorithm incorporates an adaptive inertia weight factor to accelerate convergence velocity and introduces a targeted mutation operator to prevent premature convergence. Subsequently, a tri-objective cost-effectiveness method was applied to evaluate the Pareto-optimal solution set and identify the most suitable capacity configuration scheme. The results demonstrate that the optimized configuration satisfies the power demand requirements under representative icebreaking operating conditions. In addition, the proposed approach reduces energy storage system costs, extending the service life of lithium batteries and significantly improving the stability of the power system bus voltage of icebreakers.