Related papers: Improving the filtering of Branch-And-Bound MDD so…
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose…
In this paper, we surveyed the existing literature studying different approaches and algorithms for the four critical components in the general branch and bound (B&B) algorithm, namely, branching variable selection, node selection, node…
We apply a branch-and-bound (B\&B) algorithm to the D-optimality problem based on a convex mixed-integer nonlinear formulation. We discuss possible methodologies to accelerate the convergence of the B\&B algorithm, by combining the use of…
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…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
Branch and bound methods which are based on the principle "divide and conquer" are a well established solution approach in single-objective integer programming. In multi-objective optimization branch and bound algorithms are increasingly…
Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…
We consider the resolution of learning problems involving $\ell_0$-regularization via Branch-and-Bound (BnB) algorithms. These methods explore regions of the feasible space of the problem and check whether they do not contain solutions…
The Maximum s-Bundle Problem (MBP) addresses the task of identifying a maximum s-bundle in a given graph. A graph G=(V, E) is called an s-bundle if its vertex connectivity is at least |V|-s, where the vertex connectivity equals the minimum…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
This paper develops an exact solution framework for the choice-based time slot management problem under mixed logit demand in attended home delivery systems. The problem jointly optimizes delivery slot offerings, price discounts, and…
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…
The full strong branching (FSB) rule is well known to produce extremely small branch-and-bound trees. This rule guides branching decisions based exclusively on the information regarding local gains in the linear programming (LP) bounds. We…
Decision trees, without appropriate constraints, can easily become overly complex and prone to overfit, capturing noise rather than generalizable patterns. To resolve this problem,pruning operation is a crucial part in optimizing decision…
Decision diagrams are an increasingly important tool in cutting-edge solvers for discrete optimization. However, the field of decision diagrams is relatively new, and is still incorporating the library of techniques that conventional…
The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous…
Lagrangian decomposition (LD) is a relaxation method that provides a dual bound for constrained optimization problems by decomposing them into more manageable sub-problems. This bound can be used in branch-and-bound algorithms to prune the…
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper…
An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when…
We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…