{"ID":2825347,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20915","arxiv_id":"2512.20915","title":"Towards a General Framework for Predicting and Explaining the Hardness of Graph-based Combinatorial Optimization Problems using Machine Learning and Association Rule Mining","abstract":"This study introduces GCO-HPIF, a general machine-learning-based framework to predict and explain the computational hardness of combinatorial optimization problems that can be represented on graphs. The framework consists of two stages. In the first stage, a dataset is created comprising problem-agnostic graph features and hardness classifications of problem instances. Machine-learning-based classification algorithms are trained to map graph features to hardness categories. In the second stage, the framework explains the predictions using an association rule mining algorithm. Additionally, machine-learning-based regression models are trained to predict algorithmic computation times. The GCO-HPIF framework was applied to a dataset of 3287 maximum clique problem instances compiled from the COLLAB, IMDB, and TWITTER graph datasets using five state-of-the-art algorithms, namely three exact branch-and-bound-based algorithms (Gurobi, CliSAT, and MOMC) and two graph-neural-network-based algorithms (EGN and HGS). The framework demonstrated excellent performance in predicting instance hardness, achieving a weighted F1 score of 0.9921, a minority-class F1 score of 0.878, and an ROC-AUC score of 0.9083 using only three graph features. The best association rule found by the FP-Growth algorithm for explaining the hardness predictions had a support of 0.8829 for hard instances and an overall accuracy of 87.64 percent, underscoring the framework's usefulness for both prediction and explanation. Furthermore, the best-performing regression model for predicting computation times achieved a percentage RMSE of 5.12 and an R2 value of 0.991.","short_abstract":"This study introduces GCO-HPIF, a general machine-learning-based framework to predict and explain the computational hardness of combinatorial optimization problems that can be represented on graphs. The framework consists of two stages. In the first stage, a dataset is created comprising problem-agnostic graph features...","url_abs":"https://arxiv.org/abs/2512.20915","url_pdf":"https://arxiv.org/pdf/2512.20915v1","authors":"[\"Bharat Sharman\",\"Elkafi Hassini\"]","published":"2025-12-24T03:43:54Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.CO\"]","methods":"[]","has_code":false}