Improved Rank-One-Based Relaxations and Bound Tightening Techniques for the Pooling Problem

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

Mixed-Integer Programming Approaches to Generalized Submodular Optimization and its Applications

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

An approximation algorithm for multi-objective mixed-integer convex optimization

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

Variable Selection for Kernel Two-Sample Tests

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

Γ-robust Optimization of Project Scheduling Problems

\(\) 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

Stochastic Programming Models for a Fleet Sizing and Appointment Scheduling Problem with Random Service and Travel Times

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

A polyhedral study of multivariate decision trees

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

Evaluating Mixed-Integer Programming Models over Multiple Right-hand Sides

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

Dynamic Rebalancing Optimization for Bike-sharing Systems: A Modeling Framework and Empirical Comparison

Bike-sharing systems have been implemented in multiple major cities, offering a low-cost and environmentally friendly transportation alternative to vehicles. Due to the stochastic nature of customer trips, stations are often unbalanced, resulting in unsatisfied demand. As a remedy, operators employ trucks to rebalance bikes among unbalanced stations. Given the complexity of the dynamic rebalancing planning, … Read more