Related papers: Machine Learning for Cutting Planes in Integer Pro…
We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
Attack trees (ATs) are an important tool in security analysis, and an important part of AT analysis is computing metrics. However, metric computation is NP-complete in general. In this paper, we showcase the use of mixed integer linear…
Efficient branching policies are essential for accelerating Mixed Integer Linear Programming (MILP) solvers. Their design has long relied on hand-crafted heuristics, and now machine learning has emerged as a promising paradigm to automate…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However,…
Cutting-plane methods are well-studied localization(and optimization) algorithms. We show that they provide a natural framework to perform machinelearning ---and not just to solve optimization problems posed by machinelearning--- in…
We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles…
Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have…
Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which…
Inspection planning is concerned with computing the shortest robot path to inspect a given set of points of interest (POIs) using the robot's sensors. This problem arises in a wide range of applications from manufacturing to medical…
Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the…
Even though it is well known that for most relevant computational problems different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic…
Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…
Mixed Integer Linear Programming (MILP) is a fundamental class of NP-hard problems that has garnered significant attention from both academia and industry. The Branch-and-Bound (B\&B) method is the dominant approach for solving MILPs and…
Optical emission spectroscopy of laser-produced plasmas, commonly known as laser-induced breakdown spectroscopy (LIBS), is an emerging analytical tool for rapid soil analysis. However, specific challenges with LIBS exist, such as matrix…
Mixed-integer linear programming (MILP) plays a crucial role in artificial intelligence, biochemistry, finance, cryptography, etc. Notwithstanding popular for decades, the researches of MILP solvers are still limited by the resource…
Branch-and-cut is the most widely used algorithm for solving integer programs, employed by commercial solvers like CPLEX and Gurobi. Branch-and-cut has a wide variety of tunable parameters that have a huge impact on the size of the search…
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…