Related papers: On the Complexity of Inverse Mixed Integer Linear …
Many real-world problems can be efficiently modeled as Mixed Integer Linear Programs (MILPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MILP backdoors, small sets of variables such that prioritizing…
Discrete black-box optimization problems are challenging for model-based optimization (MBO) algorithms, such as Bayesian optimization, due to the size of the search space and the need to satisfy combinatorial constraints. In particular,…
This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…
Given real numbers whose sum is an integer, we study the problem of finding integers which match these real numbers as closely as possible, in the sense of L^p norm, while preserving the sum. We describe the structure of solutions for this…
An integer program is called ideal if its continuous relaxation coincides with its convex hull allowing the problem to be solved as a continuous program and offering substantial computational advantages. Proving idealness analytically can…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
Mixed integer linear programming (MILP) is a powerful tool for planning and control problems because of its modeling capability and the availability of good solvers. However, for large models, MILP methods suffer computationally. In this…
The alternating-current unit commitment problem provides a realistic representation of power system operations, which is a nonconvex mixed-integer nonlinear programming problem and hence is computationally intractable. A common relaxation…
Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its…
It is a very challenging task to identify the objectives on which a certain decision was based, in particular if several, potentially conflicting criteria are equally important and a continuous set of optimal compromise decisions exists.…
Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the…
A data-driven inverse optimization problem (DDIOP) seeks to estimate an objective function (i.e., weights) that is consistent with observed optimal-solution data, and is important in many applications, including those involving mixed…
Finding optimal join orders is among the most crucial steps to be performed by query optimisers. Though extensively studied in data management research, the problem remains far from solved: While query optimisers rely on exhaustive search…
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 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…
In this paper we provide a computation algorithm to get a global solution for the maximum rank correlation estimator using the mixed integer programming (MIP) approach. We construct a new constrained optimization problem by transforming all…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…
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…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
Mixed Integer Linear Programming (MILP) can be considered the backbone of the modern power system optimization process, with a large application spectrum, from Unit Commitment and Optimal Transmission Switching to verifying Neural Networks…