Related papers: Shaping and Trimming Branch-and-bound Trees

By extending the breadth first search algorithm to any d-type critical or subcritical irreducible branching forest, we show that such forests may be encoded through d independent, integer valued, d-dimensional random walks. An application…

Strict inequalities in mixed-integer linear optimization can cause difficulties in guaranteeing convergence and exactness. Utilizing that optimal vertex solutions follow a lattice structure we propose a rounding rule for strict inequalities…

We show that there exists a family of instances of the lot-sizing problem, such that any branch-and-bound tree that solves them requires an exponential number of nodes, even in the case when the branchings are performed on general split…

A limited-memory influence diagram (LIMID) generalizes a traditional influence diagram by relaxing the assumptions of regularity and no-forgetting, allowing a wider range of decision problems to be modeled. Algorithms for solving…

A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization…

In this paper, we study the assortment optimization problem under the mixed-logit customer choice model. While assortment optimization has been a major topic in revenue management for decades, the mixed-logit model is considered one of the…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose…

Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…

This paper investigates linear programming based branch-and-bound using general disjunctions, also known as stabbing planes, for solving integer programs. We derive the first sub-exponential lower bound (in the encoding length $L$ of the…

We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…

This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…

In this paper we consider bound-constrained mixed-integer optimization problems where the objective function is differentiable w.r.t.\ the continuous variables for every configuration of the integer variables. We mainly suggest to exploit…

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

In this article, we propose the approach to structural optimization of neural networks, based on the braid theory. The paper describes the basics of braid theory as applied to the description of graph structures of neural networks. It is…

Classification rules can be severely affected by the presence of disturbing observations in the training sample. Looking for an optimal classifier with such data may lead to unnecessarily complex rules. So, simpler effective classification…

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable…