Related papers: A Framework for Handling and Exploiting Symmetry i…
Since its inception, Benders Decomposition (BD) has been successfully applied to a wide range of large-scale mixed-integer (linear) problems. The key element of BD is the derivation of Benders cuts, which are often not unique. In this…
We propose an enhancement to Benders decomposition (BD) that generates valid inequalities for the convex hull of the Benders reformulation, addressing the limitation that classical BD cuts are typically tight only for the continuous…
Various types of communication networks are constantly emerging to improve the connectivity services and facilitate the interconnection of various types of devices. This involves the development of several technologies, such as…
Logic-based Benders decomposition (LBBD) is a substantial generalization of classical Benders decomposition that, in principle, allows the subproblem to be any optimization problem rather than specifically a linear or nonlinear programming…
Benders decomposition is a widely used method for solving large optimization problems, but its performance is often hindered by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating…
The Benders' decomposition algorithm is a technique in mathematical programming for complex mixed-integer linear programming (MILP) problems with a particular block structure. The strategy of Benders' decomposition can be described as a…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
We show how to extract alternative solutions for optimization problems solved by Benders Decomposition. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative…
Generalized Benders decomposition (GBD) is a globally optimal algorithm for mixed integer nonlinear programming (MINLP) problems, which are NP-hard and can be widely found in the area of wireless resource allocation. The main idea of GBD is…
In this paper, we consider a probabilistic set covering problem (PSCP) in which each 0-1 row of the constraint matrix is random with a finite discrete distribution, and the objective is to minimize the total cost of the selected columns…
In this paper, we investigate the probabilistic set covering problem (PSCP) in which the right-hand side is a binary random vector and the covering constraint is required to be satisfied with a prespecified probability. We consider the case…
Benders decomposition is one of the most applied methods to solve two-stage stochastic problems (TSSP) with a large number of scenarios. The main idea behind the Benders decomposition is to solve a large problem by replacing the values of…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Benders decomposition is widely used to solve large mixed-integer problems. This paper takes advantage of machine learning and proposes enhanced variants of Benders decomposition for solving two-stage stochastic security-constrained unit…
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery…
Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to…
Block coordinate descent (BCD) methods approach optimization problems by performing gradient steps along alternating subgroups of coordinates. This is in contrast to full gradient descent, where a gradient step updates all coordinates…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
Scenario-based optimization problems can be solved via Benders decomposition, which separates first-stage (master problem) decisions from second-stage (subproblem) recourse actions and iteratively refines the master problem with Benders…
Coordinate descent algorithms are widely used in machine learning and large-scale data analysis due to their strong optimality guarantees and impressive empirical performance in solving non-convex problems. In this work, we introduce Block…