Related papers: Learning to Choose Branching Rules for Nonconvex M…
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,…
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…
Asymptotically-optimal motion planners such as RRT* have been shown to incrementally approximate the shortest path between start and goal states. Once an initial solution is found, their performance can be dramatically improved by…
We consider integer programming problems with bounded general-integer variables belonging to the general class of network flow problems. For those, we computationally investigate the effect on mixed-integer linear programming (MIP) solvers…
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer…
Data-driven algorithm design is a paradigm that uses statistical and machine learning techniques to select from a class of algorithms for a computational problem an algorithm that has the best expected performance with respect to some…
Model-based Reinforcement Learning (RL) is a popular learning paradigm due to its potential sample efficiency compared to model-free RL. However, existing empirical model-based RL approaches lack the ability to explore. This work studies a…
This article considers nonconvex global optimization problems subject to uncertainties described by continuous random variables. Such problems arise in chemical process design, renewable energy systems, stochastic model predictive control,…
Strong Branching (SB) is a cornerstone of all modern branching rules used in the Branch-and-Bound (BnB) algorithm, which is at the center of Mixed-Integer Programming solvers. In its full form, SB evaluates all variables to branch on and…
In line with the growing trend of using machine learning to help solve combinatorial optimisation problems, one promising idea is to improve node selection within a mixed integer programming (MIP) branch-and-bound tree by using a learned…
Psychiatric neuroscience is increasingly aware of the need to define psychopathology in terms of abnormal neural computation. The central tool in this endeavour is the fitting of computational models to behavioural data. The most prominent…
Branch and cut is the dominant paradigm for solving a wide range of mathematical programming problems -- linear or nonlinear -- combining efficient search (via branch and bound) and relaxation-tightening procedures (via cutting planes, or…
We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
Training Large Language Models (LLMs) with Group Relative Policy Optimization (GRPO) encounters a significant challenge: models often fail to produce accurate responses, particularly in small-scale architectures. This limitation not only…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Modern mixed-integer programming solvers use the branch-and-cut framework, where cutting planes are added to improve the tightness of the linear programming (LP) relaxation, with the expectation that the tighter formulation would produce…
Optimization problems with norm-bounding constraints arise in a variety of applications, including portfolio optimization, machine learning, and feature selection. A common approach to these problems involves relaxing the norm constraint…
In this paper, we propose a Bi-layer Predictionbased Reduction Branch (BP-RB) framework to speed up the process of finding a high-quality feasible solution for Mixed Integer Programming (MIP) problems. A graph convolutional network (GCN) is…
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…