In recent years, the integration of Machine Learning (ML) models with Operation Research (OR) tools has gained popularity across diverse applications, including cancer treatment, algorithmic configuration, and chemical process optimization. In this domain, the combination of ML and OR often relies on representing the ML model output using Mixed Integer Programming (MIP) formulations. Numerous studies … Read more
Robust combinatorial optimization with budget uncertainty is one of the most popular approaches for integrating uncertainty into optimization problems. The existence of a compact reformulation for (mixed-integer) linear programs and positive complexity results give the impression that these problems are relatively easy to solve. However, the practical performance of the reformulation is quite poor when … Read more
This mini survey covers optimization, heuristic, and sampling methods for political districting. CitationAccepted for publication in the Encyclopedia of Optimization (Springer, 3rd edition) edited by Panos M. Pardalos and Oleg A. Prokopyev. ArticleDownload View PDF
The CONGEST and CONGEST-CLIQUE models have been carefully studied to represent situations where the communication bandwidth between processors in a network is severely limited. Messages of only \( O(log(n)) \) bits of information each may be sent between processors in each round. The quantum versions of these models allow the processors instead to communicate and … Read more
The set partitioning problem and its decision variant (i.e., the exact cover problem) are combinatorial optimization problems that were historically crucial in the quantum optimization community. This problem is also employed in the main problem of the branch-and-price approach in many real-world optimization problems, including, but not limited to, redistricting and scheduling. Motivated by recent … Read more
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show similar results for a wide variety of discrete optimization problems for which SDP relaxations have been derived. Based on a … Read more
A common assumption in the models for the vehicle routing problem with stochastic demands is that all demands must be satisfied. This is achieved by including recourse actions in two-stage stochastic programming formulations or by ensuring with a high probability that all demand fits within the vehicle capacity (chance-constrained formulations). In this work, we relax … Read more
In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing. Meanwhile, the structure of neural networks converged back to simpler representations based on piecewise constant and piecewise linear functions such as the Rectified … Read more
Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint intersections. We propose an iterative process based on projections onto the subsets which generate the intersections. The process … Read more
In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence an adversary whose objective is to minimize the maximum coverage by p cameras in response to input provided by n autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution … Read more