Numerous industrial fields, like supply chain management, face mixed-integer optimization problems on a regular basis. Such problems typically show a sparse structure and vary in size, as well as complexity. However, in order to satisfy customer demands, it is crucial to find good solutions to all such problems quickly. Current research often focuses on the … Read more
The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in some intermediate tanks, and mixed again to obtain the final products with desired specifications. The analysis of the pooling … Read more
Submodularity is an important concept in integer and combinatorial optimization. A classical submodular set function models the utility of selecting homogenous items from a single ground set, and such selections can be represented by binary variables. In practice, many problem contexts involve choosing heterogenous items from more than one ground set or selecting multiple copies … Read more
In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more
We consider the variable selection problem for two-sample tests, aiming to select the most informative variables to distinguish samples from two groups. To solve this problem, we propose a framework based on the kernel maximum mean discrepancy (MMD). Our approach seeks a group of variables with a pre-specified size that maximizes the variance-regularized MMD statistics. … Read more
\(\) In this paper, we investigate the problem of finding a robust baseline schedule for the project scheduling problem under uncertain process times. We assume that the probability distribution for the duration is unknown but an estimation together with an interval in which this time can vary is given. At most $ \Gamma $ of … Read more
We propose a new stochastic mixed-integer linear programming model for a home service fleet sizing and appointment scheduling problem (HFASP) with random service and travel times. Specifically, given a set of providers and a set of geographically distributed customers within a service region, our model solves the following decision problems simultaneously: (i) a fleet sizing … Read more
Decision trees are a widely used tool for interpretable machine learning. Multivariate decision trees employ hyperplanes at the branch nodes to route datapoints throughout the tree and yield more compact models than univariate trees. Recently, mixed-integer programming (MIP) has been applied to formulate the optimal decision tree problem. To strengthen MIP formulations, it is crucial … Read more
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A critical measure of model quality for a mixed-integer program (MIP) is the difference, or gap, between its optimal objective value and that of its linear programming relaxation. In some cases, the right-hand side is not known exactly; however, there is no consensus metric for evaluating a MIP model when considering multiple right-hand sides. In … Read more