Related papers: Branch-and-bound for D-Optimality with fast local …
Branch and Bound (B&B) is the exact tree search method typically used to solve Mixed-Integer Linear Programming problems (MILPs). Learning branching policies for MILP has become an active research area, with most works proposing to imitate…
Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…
This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…
In this paper, a branch and bound algorithm that incorporates the decision maker's preference information is proposed for multiobjective optimization. In the proposed algorithm, a new discarding test is designed to check whether a box…
Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
Mixed-Integer Linear Programming (MILP) lies at the core of many real-world combinatorial optimization (CO) problems, traditionally solved by branch-and-bound (B&B). A key driver influencing B&B solvers efficiency is the variable selection…
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…
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…
In contrast to the many continuous global optimization methods that assume the objective function and constraints are factorable, we study how to find globally maximal solutions to problems that are not factorable, focusing on a particular…
Branch-and-bound is the workhorse of all state-of-the-art mixed integer linear programming (MILP) solvers. These implementations of branch-and-bound typically use variable branching, that is, the child nodes are obtained by fixing some…
Branch-and-Bound (B\&B) is an exact method in integer programming that recursively divides the search space into a tree. During the resolution process, determining the next subproblem to explore within the tree-known as the search…
This paper considers decentralized optimization of convex functions with mixed affine equality constraints involving both local and global variables. Constraints on global variables may vary across different nodes in the network, while…
A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection can affect the size of the resulting search trees by orders of magnitude. A…
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…
The classical branch-and-bound algorithm for the integer feasibility problem has exponential worst case complexity. We prove that it is surprisingly efficient on reformulated problems, in which the columns of the constraint matrix are…