The uniqueness of optimal parameter sets of an Arctic sea ice simulation is investigated. A set of parameter optimization experiments is performed using an automatic parameter optimization system, which simultaneously optimizes 15 dynamic and thermodynamic process parameters. The system employs a stochastic approach (genetic algorithm) to find the global minimum of a cost function. The cost function is defined by the model–observation misfit and observational uncertainties of three sea ice properties (concentration, thickness, drift) covering the entire Arctic Ocean over more than two decades. A total of 11 independent optimizations are carried out to examine the uniqueness of the minimum of the cost function and the associated optimal parameter sets. All 11 optimizations asymptotically reduce the value of the cost functions toward an apparent global minimum and provide strikingly similar sea ice fields. The corresponding optimal parameters, however, 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 toward a unique solution. A correlation analysis shows that the optimal parameters are interrelated 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. Analysis of the associated ocean fields exhibits a large spread of these fields over the 11 optimized parameter sets, suggesting an importance of ocean properties to achieve a dynamically consistent view of the coupled sea ice–ocean system.