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Two-stage stochastic integer programs provide a powerful framework for modeling decision-making under uncertainty, but they are notoriously difficult to solve at scale due to their high dimensionality and intrinsic nonconvexity.…
Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…
While Mixed-integer linear programming (MILP) is NP-hard in general, practical MILP has received roughly 100--fold speedup in the past twenty years. Still, many classes of MILPs quickly become unsolvable as their sizes increase, motivating…
This paper focuses on the identical parallel machine scheduling problem with sequence-dependent setup time, with special attention paid to the uncertainty of processing time. In this paper, a mathematical model of the parallel machine…
Integer and mixed-integer nonlinear programming (INLP, MINLP) are central to logistics, energy, and scheduling, but remain computationally challenging. This survey examines how machine learning and reinforcement learning can enhance exact…
Influence diagrams represent decision-making problems with interdependencies between random events, decisions, and consequences. Traditionally, they have been solved using algorithms that determine the expected utility-maximizing decision…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
In model predictive control (MPC) for hybrid systems, solving optimization problems efficiently and with guarantees on worst-case computational complexity is critical to satisfy the real-time constraints in these applications. These…
We consider the least squares regression problem, penalized with a combination of the $\ell_{0}$ and squared $\ell_{2}$ penalty functions (a.k.a. $\ell_0 \ell_2$ regularization). Recent work shows that the resulting estimators are of key…
The aim of this study is to find the optimum of a linear fractional function over the efficient set of a multi-objective linear fractional integer program without generating all efficient solutions. By its nature, it is a global…
Branch and bound algorithms have been developed for reliability analysis of coherent systems. They exhibit a set of advantages; in particular, they can find a computationally efficient representation of a system failure or survival event,…
Influence Diagrams (ID) are a flexible tool to represent discrete stochastic optimization problems, including Markov Decision Process (MDP) and Partially Observable MDP as standard examples. More precisely, given random variables considered…
The closest string problem is an NP-hard problem, whose task is to find a string that minimizes maximum Hamming distance to a given set of strings. This can be reduced to an integer program (IP). However, to date, there exists no known…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
The talent scheduling problem is a simplified version of the real-world film shooting problem, which aims to determine a shooting sequence so as to minimize the total cost of the actors involved. In this article, we first formulate the…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
Over the last few years, there has been a surge in the use of learning techniques to improve the performance of optimization algorithms. In particular, the learning of branching rules in mixed integer linear programming has received a lot…
We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function,…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
Electronic phased-array radars offer new possibilities for radar search pattern optimization by using bi-dimensional beam-forming and beam-steering. Radar search pattern optimization can be approximated as a set cover problem and solved…