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This article presents an optimization-based approach for sizing and composition of an Arctic offshore drilling support fleet considering cost-efficiency. The approach studies the main types of duties related to Arctic offshore drillings: supply, towing, anchor handling, standby, oil spill response, firefighting, and ice management. The approach considers the combined effect of the expected costs of accidental events, the versatility of individual support vessels, and ice management. The approach applies an Artificial Bee Colony algorithm-based optimization procedure. As demonstrated through case studies, the approach may help to find a range of cost-efficient fleet compositions. Some of the obtained solutions are similar to corresponding real-life fleets, indicating that the approach works in principle. Sensitivity analyses indicate that the consideration of the expected costs from accidental events significantly impacts the obtained solution, and that investments to reduce these costs may improve the overall cost-efficiency of an Arctic offshore drilling support fleet.