Preference-Based Gradient Estimation for ML-Guided Approximate Combinatorial Optimization

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require high-quality solutions within a given time budget. To address this, we propose a learning-based approach that enhances existing non-learned heuristics for CO. Specifically, we parameterize these heuristics and train graph neural networks (GNNs) to predict parameter values that yield near-optimal solutions. Our method is trained end-to-end in a self-supervised fashion, using a novel gradient estimation scheme that treats the heuristic as a black box. This approach combines the strengths of learning and traditional algorithms: the GNN learns from data to guide the algorithm toward better solutions, while the heuristic ensures feasibility. We validate our method on two well-known combinatorial optimization problems: the travelling salesman problem (TSP) and the minimum k-cut problem. Our results demonstrate that the proposed approach is competitive with state-of-the-art learned CO solvers.

Authors

• Arman Mielke
• Uwe Bauknecht
• Thilo Strauss
• Mathias Niepert University of Stuttgart

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