Related papers: Parameterizing Branch-and-Bound Search Trees to Le…
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…
Local branching is an improvement heuristic, developed within the context of branch-and-bound algorithms for MILPs, which has proved to be very effective in practice. For the binary case, it is based on defining a neighbourhood of the…
We consider an expected-value ranking and selection (R&S) problem where all k solutions' simulation outputs depend on a common parameter whose uncertainty can be modeled by a distribution. We define the most probable best (MPB) to be the…
We analyze a tree search problem with an underlying Markov decision process, in which the goal is to identify the best action at the root that achieves the highest cumulative reward. We present a new tree policy that optimally allocates a…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…
This paper develops a measure for bounding the performance of AND/OR search algorithms for solving a variety of queries over graphical models. We show how drawing a connection to the recent notion of hypertree decompositions allows to…
Current work in explainable reinforcement learning generally produces policies in the form of a decision tree over the state space. Such policies can be used for formal safety verification, agent behavior prediction, and manual inspection…
A branch-and-bound (BB) tree certifies a dual bound on the value of an integer program. In this work, we introduce the tree compression problem (TCP): Given a BB tree T that certifies a dual bound, can we obtain a smaller tree with the same…
Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…
Data-driven decision making is rapidly gaining popularity, fueled by the ever-increasing amounts of available data and encouraged by the development of models that can identify beyond linear input-output relationships. Simultaneously the…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
Iterative refinement has been a promising paradigm to enable large language models (LLMs) to resolve difficult reasoning and problem-solving tasks. One of the key challenges, however, is how to effectively search through the enormous search…
In this paper, we describe a comprehensive algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) using a generalized branch-and-cut approach. The framework presented merges features from existing…
The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width…
Decision tree ensembles are widely used in critical domains, making robustness and sensitivity analysis essential to their trustworthiness. We study the feature sensitivity problem, which asks whether an ensemble is sensitive to a specified…
This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent)…
Graph neural networks (GNNs) have been widely used to predict properties and heuristics of mixed-integer linear programs (MILPs) and hence accelerate MILP solvers. This paper investigates the capacity of GNNs to represent strong branching…
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…
Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…