Time to Rethink AI for Combinatorial Optimization: Classical Algorithms Remain Tough to Match

• URL: http://arxiv.org/abs/2502.03669v2
• Date: Mon, 30 Jun 2025 02:02:59 GMT
• Title: Time to Rethink AI for Combinatorial Optimization: Classical Algorithms Remain Tough to Match
• Authors: Yikai Wu, Haoyu Zhao, Sanjeev Arora,
• Abstract summary: We show that leading AI-inspired methods are consistently outperformed by the state-of-the-art classical solver KaMIS.<n>Non-backtracking AI methods, such as LTFT (based on GNets), end up reasoning similarly to the simplest degree-based greedy.
• Score: 36.092099713670414
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This position paper argues that the machine learning community should fundamentally rethink how AI-inspired methods are developed and evaluated for combinatorial optimization (CO). We present comprehensive empirical benchmarks comparing various recent AI-inspired GPU-based methods with several classical CPU-based solvers on the Maximum Independent Set (MIS) problem. Strikingly, even on in-distribution random graphs, leading AI-inspired methods are consistently outperformed by the state-of-the-art classical solver KaMIS, and some AI-inspired methods frequently fail to surpass even the simplest degree-based greedy heuristic. To better understand the source of these failures, we introduce a novel analysis, serialization, which reveals that non-backtracking AI methods, such as LTFT (based on GFlowNets), end up reasoning similarly to the simplest degree-based greedy heuristic, and thus worse than KaMIS. Our findings reveal three core issues: (1) Limited benchmarks and evaluation - AI-inspired methods are often tested only on small instances with very limited inference time, which covers up issues with scalability and resource usage; (2) Intrinsic hardness and learning limits - even under ideal, in-distribution conditions, learning-based approaches lag behind classical heuristics, highlighting inherent barriers that receive little attention; and (3) Insufficient use and understanding of classical heuristics - current learning frameworks often neglect to incorporate effective classical techniques. Although we use MIS as a testbed, similar gaps and challenges have been reported in other combinatorial optimization problems, suggesting broader relevance for our recommendations. We propose that future research must address these issues by rigorous benchmarking, deepening understanding of learning limitations, and integrating classical heuristics into AI-inspired methods.

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