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The classical hinge-loss support vector machines (SVMs) model is sensitive to outlier observations due to the unboundedness of its loss function. To circumvent this issue, recent studies have focused on non-convex loss functions, such as the hard-margin loss, which associates a constant penalty to any misclassified or within-margin sample. Applying this loss function yields much-needed robustness for critical applications but it also leads to an NP-hard model that makes training difficult, since current exact optimization algorithms show limited scalability, whereas heuristics are not able to find high-quality solutions consistently. Against this background, we propose new integer programming strategies that significantly improve our ability to train the hard-margin SVM model to global optimality.We introduce an iterative sampling and decomposition approach, in which smaller subproblems are used to separate combinatorial Benders' cuts. Those cuts, used within a branch-and-cut algorithm, permit to converge much more quickly towards a global optimum. Through extensive numerical analyses on classical benchmark data sets, our solution algorithm solves, for the first time, 117 new data sets to optimality and achieves a reduction of 50% in the average optimality gap for the hardest datasets of the benchmark.

Recently, hybrid metaheuristics have become a trend in operations research. A successful example combines the Greedy Randomized Adaptive Search Procedures (GRASP) and data mining techniques, where frequent patterns found in high‐quality solutions can lead to an efficient exploration of the search space, along with a significant reduction of computational time. In this paper, a GRASP‐based state‐of‐the‐art heuristic for the minimum latency problem is improved by means of data mining techniques. Computational experiments showed that the hybrid heuristic with data mining was able to match or improve the solution quality for a large number of instances, together with a substantial reduction of running time. Besides, 32 new best‐known solutions are introduced to the literature. To support our results, statistical significance tests, analyses over the impact of mined patterns, comparisons based on running time as stopping criterion, and time‐to‐target plots are provided.

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