We developed an objective parameter optimization system for a coupled sea ice-ocean model based on a genetic algorithm. The system is set up to optimize 15 model parameters simultaneously by minimizing a cost function composed of the model-observation misfit of three sea ice quantities (concentration, drift and thickness). The system is applied for a domain covering the entire Arctic and northern North Atlantic Ocean with an optimization window of about two decades (1990 - 2012). It successfully improves the simulated sea ice properties not only during the period of optimization but also in a validation period (2013 - 2016). We also examined the uniqueness of the optimal parameter sets by independent optimization experiments. Regardless of the striking similarity of the values of the cost function and optimized sea ice fields, the corresponding optimal parameters exhibit a large spread, showing the existence of multiple optimal solutions. The result shows that the utilized sea ice observations, even though covering more than two decades, cannot constrain the process parameters towards an unique solution. A correlation analysis shows that the optimal parameters are inter-related and covariant. A principal component analysis reveals that the first three (six) principal components explain 70% (90%) of the total variance of the optimal parameter sets, indicating a contraction of the parameter space.