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We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
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…
Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…
The selection of branching variables is a key component of branch-and-bound algorithms for solving Mixed-Integer Programming (MIP) problems since the quality of the selection procedure is likely to have a significant effect on the size of…
Mixed-integer optimization is at the core of many online decision-making systems that demand frequent updates of decisions in real time. However, due to their combinatorial nature, mixed-integer linear programs (MILPs) can be difficult to…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
In this work we propose an improvement of the $x$-space algorithm developed for solving a class of min--max bilevel optimization problems (Tang Y., Richard J.P.P., Smith J.C. (2016), A class of algorithms for mixed-integer bilevel min--max…
We'll measure the differences of the dual variables and the gain of the objective function when creating new problems, which each has one inequality more than the starting LP-instance. These differences of the dual variables are naturally…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…
As machine learning (ML) applications grow increasingly complex in recent years, modern ML frameworks often need to address multiple potentially conflicting objectives with coupled decision variables across different layers. This creates a…
Mixed integer nonlinear programming (MINLP) problems are encountered in modeling a physical/industrial process consisting both nonlinearity and discrete selective parameters. There are variety of algorithms for solving MINLP problems most…
We consider a bilevel optimization problem in which the ground set is partitioned between two decision makers, a leader and a follower, whose optimization problems are interleaved. We study the Bilevel Independent Set problem, and its…
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…
In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of…
Oil products are the main source of energy in the world today. Distribution of these products is one of the main issues in the industry. The main tools for this work are pipelines, and along with it, railways, shipping and roads are also…
In this work, we aim to compare different methods and formulations to solve a problem in air traffic management to global optimality. In particular, we focus on the aircraft deconfliction problem, where we are given n aircraft, their…
Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level…