arXiv Machine Learning By Mourchid Adegbindin, Brenda Dietrich, Jamol Pender, Andrea Lodi

When Solvers Get Moody: Quantifying and Predicting Performance Variability in Mixed Integer Programming

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The paper introduces the Weighted Variability Score (WVS), a metric that aggregates dispersion in runtime, optimality gap, LP iterations, and branch‑and‑bound nodes across repeated runs of MIP solvers. Experiments on 100 randomized runs of MIPLIB 2017 instances show a right‑skewed distribution, with many instances stable but some exhibiting large variability not explained by basic properties. A tree‑based predictor using static and root‑level features achieves a mean absolute error of 0.058 and Spearman rank correlation of 0.65, with root degeneracy, matrix structure, coefficient ranges, and presolve reductions identified as key drivers of high WVS.

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