Hybrid Quantum Annealing Approach for High-Dimensional and Multi-Criteria Constrained Quadratic Optimization in Arctic Ship Routing

TL;DR

The paper tackles Arctic ship routing under dynamic sea-ice conditions by integrating Copernicus CMEMS environmental data into a Constrained Quadratic Model and solving it with D-Wave’s hybrid quantum–classical solver. It leverages a high-resolution H3 hex grid to discretize the Arctic, and benchmarks against classical MIQP solvers (Gurobi, CPLEX), demonstrating orders of magnitude faster convergence and improved route quality. The main contributions include a physics-informed, multi-criteria cost framework that couples CMEMS variables with curvature penalties, a scalable H3-based Arctic graph, and extensive benchmarking showing faster, smoother, and shorter routes with meaningful CO2 reductions. The work suggests a practical, real-time capable decision-support paradigm for Arctic navigation and lays groundwork for future enhancements with higher-resolution data and safety/regulatory layers.

Abstract

The opening of Arctic sea routes presents unprecedented opportunities for global trade but poses significant operational and computational challenges due to the dynamic nature of sea ice conditions. This study formulates a multi criteria Arctic route optimization problem that integrates Copernicus Marine Environment Monitoring Service (CMEMS) variables into a Constrained Quadratic Model (CQM) and solves it using D Wave's hybrid quantum classical solver. We benchmark the feasibility and scalability of this approach against classical Mixed Integer Quadratic Programming (MIQP) solvers such as Gurobi and CPLEX. Results show that the CQM formulation achieves feasible solutions with stable runtimes as quadratic density increases, demonstrating 10 to 100 times faster convergence and reduced computational time compared with classical solvers, while also improving route smoothness by approximately 10 percent and reducing total length by approximately 1 percent. This reflects the effectiveness of the hybrid quantum annealing approach for Arctic routing problems.

Figures (11)

• Figure 1: Scalability of the H3 hierarchical grid applied to the Arctic Ocean. (a) Global context highlighting the Barents and Kara Seas region. (b-d) progressive refinement from coarse H3 resolution 3 to fine H3 resolution 6. The nested structure maintains hexagonal adjacency and spatial continuity across levels, enabling scalable integration of sea-ice and oceanographic datasets for Arctic routing.
• Figure 2: Comparison of spatial discretization schemes: (a) triangular, (b) square, and (c) hexagonal (H3-based) lattices. The hexagonal configuration preserves isotropy and eliminates diagonal edge ambiguity, ensuring uniform neighbor connectivity and consistent step costs, which are essential for Arctic routing and spatial analysis. Figure adapted from Vaidheeswaran2025HexGridRL.
• Figure 3: End-to-end workflow of the Arctic ship routing framework. (a) H3 ocean hexagonization process, including corridor polygon input, antimeridian normalization, H3 grid generation and land filtering using the Global Self-consistent, Hierarchical, High-Resolution Geography (GSHHS) dataset. (b) Feature-to-constraint mapping, where CMEMS sea-ice variables are mapped to H3 cells through preprocessing and variable extraction. (c) Optimization modeling pipeline, consisting of network graph construction, objective design, and hybrid quantum execution via the D-Wave CQM solver, followed by path recovery and GeoJSON route export. (d) Evaluation stage, including route projection on a real map, visualization, and computation of evaluation metrics such as zigzag proxy and cost.
• Figure 4: Overview of the implemented H3 ocean hexagonalization and land-sea masking process. (a) Integration of area of interest (AOI) boundary extraction, GSHHS shoreline masking, and H3 hexagonal network generation. (b) Land-sea differentiation using the GSHHS dataset, where green regions indicate continental and island landmasses, and blue-shaded areas denote ocean surfaces. This vector-based representation enables accurate separation between terrestrial and marine domains, ensuring that only oceanic regions are retained for subsequent spatial analysis and route optimization.
• Figure 5: Filtered hexagonal corridors produced after masking with GSHHS vectors. Each black hexagon represents a navigable ocean H3 cell retained for subsequent feature extraction and optimization.