In a recent paper, Basu, Hildebrand, and Molinaro established that the set of continuous minimal functions for the 1-dimensional Gomory-Johnson infinite group relaxation possesses a dense subset of extreme functions. The n-dimensional version of this result was left as an open question. In the present paper, we settle this query in the affirmative: for any … Read more
We consider the Resource Constrained Shortest Path problem arising as a subproblem in state-of-the-art Branch-Cut-and-Price algorithms for vehicle routing problems. We propose a variant of the bi-directional label correcting algorithm in which the labels are stored and extended according to so-called bucket graph. Such organization of labels helps to decrease significantly the number of dominance … Read more
The Cell Suppression Problem (CSP) is a challenging Mixed-Integer Linear Problem arising in statistical tabular data protection. Medium sized instances of CSP involve thousands of binary variables and million of continuous variables and constraints. However, CSP has the typical structure that allows application of the renowned Benders’ decomposition method: once the “complicating” binary variables are … Read more
We present a flexible framework for general mixed-integer nonlinear programming (MINLP), called Minotaur, that enables both algorithm exploration and structure exploitation without compromising computational efficiency. This paper documents the concepts and classes in our framework and shows that our implementations of standard MINLP techniques are efficient compared with other state-of-the-art solvers. We then describe structure-exploiting … Read more
Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be … Read more
We study pseudo-polynomial formulations for the classical bin packing and cutting stock problems. We first propose an overview of dominance and equivalence relations among the main pattern-based and pseudo-polynomial formulations from the literature. We then introduce reflect, a new formulation that uses just half of the bin capacity to model an instance and needs significantly … Read more
We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs. The proposed algorithm is developed based on the Triangle Splitting Method (Boland et al. 2015b) which can find a full representation of the nondominated frontier of any bi-objective mixed integer … Read more
This paper addresses the manufacturing and distribution of short-lived radio-pharmaceuticals which are mainly used in diagnostic imaging studies. We develop a mixed integer nonlinear optimization model that is flexible enough to capture the complex underlying nuclear physics of the production process of fludeoxyglucose (FDG), which is widely used in oncology and cardiology, as well as … Read more
It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram, once the optimal value is known. The structure of a decision diagram facilitates rapid processing of … Read more
In this paper, we present lower bounds on the rank of the split closure, the multi-branch closure and the lattice-free closure for packing sets as a function of the integrality gap. We also provide a similar lower bound on the split rank of covering polyhedra. These results indicate that whenever the integrality gap is high, … Read more