Related papers: Branch-and-Bound Solves Random Binary IPs in Polyt…

This paper presents a method to certify the computational complexity of a standard Branch and Bound method for solving Mixed-Integer Quadratic Programming (MIQP) problems defined as instances of a multi-parametric MIQP. Beyond previous…

Branch-and-bound approaches in integer programming require ordering portions of the space to explore next, a problem known as node comparison. We propose a new siamese graph neural network model to tackle this problem, where the nodes are…

We investigate how the numerical properties of the LP relaxations evolve throughout the solution procedure in a solver employing the branch-and-cut algorithm. The long-term goal of this work is to determine whether the effect on the…

We develop a branch-and-bound algorithm for the integer D-optimality problem, a central problem in statistical design theory, based on two convex relaxations, employing variable-bound tightening and fast local-search procedures, testing our…

Combinatorial sequential decision making problems are typically modeled as mixed integer linear programs (MILPs) and solved via branch and bound (B&B) algorithms. The inherent difficulty of modeling MILPs that accurately represent…

When solving numerical constraints such as nonlinear equations and inequalities, solvers often exploit pruning techniques, which remove redundant value combinations from the domains of variables, at pruning steps. To find the complete…

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…

State-of-the-art Mixed Integer Linear Program (MILP) solvers combine systematic tree search with a plethora of hard-coded heuristics, such as the branching rule. The idea of learning branching rules from data has received increasing…

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To…

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solvers for integer linear programming (ILP) problems.…

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…

This paper explores reoptimization techniques for solving sequences of similar mixed integer programs (MIPs) more effectively. Traditionally, these MIPs are solved independently, without capitalizing on information from previously solved…

The incorporation of cutting planes within the branch-and-bound algorithm, known as branch-and-cut, forms the backbone of modern integer programming solvers. These solvers are the foremost method for solving discrete optimization problems…

Mixed Integer Linear Programming (MILP) is a fundamental tool for modeling combinatorial optimization problems. Recently, a growing body of research has used machine learning to accelerate MILP solving. Despite the increasing popularity of…

Algebraic Branching Programs(ABPs) are standard models for computing polynomials. Syntactic multilinear ABPs (smABPs) are restrictions of ABPs where every variable is allowed to occur at most once in every path from the start to the…

Mixed Integer Linear Programs (MILPs) are essential tools for solving planning and scheduling problems across critical industries such as construction, manufacturing, and logistics. However, their widespread adoption is limited by long…

Covering problems are well-studied in the domain of Operations Research, and, more specifically, in Location Science. When the location space is a network, the most frequent assumption is to consider the candidate facility locations, the…

The Multiprocessor Scheduling Problem (MSP) is an NP-Complete problem with significant applications in computer and operations systems. We provide a survey of the wide array of polynomial-time approximation, heuristic, and meta-heuristic…

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…

Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…