Arctic shipping route design with CO2-black carbon trade-offs

Arctic shipping growth along the Northern Sea Route raises pressing environmental concerns, particularly regarding black carbon (BC), a short-lived climate forcer rarely modeled as a distinct routing objective. This paper develops a two-stage stochastic multi-objective optimization model that simultaneously minimizes expected cost, CO 2 , and BC emissions under sea ice uncertainty, with strategic deployment fixed before uncertainty realization and operational decisions adjusted afterward. A Criterion-Space Benders Decomposition (CSBD) algorithm reuses optimality cuts across Pareto frontier regions and solves bounded scalarized subproblems to proven optimality within prescribed MIP tolerances. Experiments on 16 synthetic and three AIS-informed instances confirm that CO 2 alone is an inadequate proxy for BC: bi-objective models produce 20 to 128% more BC at matched cost or CO 2 levels. Between 56.5% and 84.6% of BC can be reduced through operating plan selection without route redesign, though near-complete elimination requires cost premiums up to 500%, highlighting the practical value of explicit BC-cost trade-off analysis for Arctic emission governance.