Sakarya, I. E.Kundakcıoğlu, Ömer Erhun2023-09-112023-09-112023-020925-5001http://hdl.handle.net/10679/8783https://doi.org/10.1007/s10898-022-01219-yThe purpose of this study is to solve the multi-instance classification problem by maximizing the area under the Receiver Operating Characteristic (ROC) curve obtained for witness instances. We derive a mixed integer linear programming model that chooses witnesses and produces the best possible ROC curve using a linear ranking function for multi-instance classification. The formulation is solved using a commercial mathematical optimization solver as well as a fast metaheuristic approach. When the data is not linearly separable, we illustrate how new features can be generated to tackle the problem. We present a comprehensive computational study to compare our methods against the state-of-the-art approaches in the literature. Our study reveals the success of an optimal linear ranking function through cross validation for several benchmark instances.engrestrictedAccessarticle85235137500083953240000110.1007/s10898-022-01219-yArea under curveMixed integer linear programmingMulti-instance learning2-s2.0-85135837389