Related papers: Benders decomposition for the large-scale probabil…
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…
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…
Mixed integer Model Predictive Control (MPC) problems arise in the operation of systems where discrete and continuous decisions must be taken simultaneously to compensate for disturbances. The efficient solution of mixed integer MPC…
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…
Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating…
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…
In this paper, we introduce a mixed integer quadratic formulation for the congested variant of the partial set covering location problem, which involves determining a subset of facility locations to open and efficiently allocating customers…
The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses…
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 p-median problem is a classic discrete location problem with several applications. It aims to open p sites while minimizing the sum of the distances of each client to its nearest open site. We study a Benders decomposition of the most…
Benders' decomposition (BD) is a framework for solving optimization problems by removing some variables and modeling their contribution to the original problem via so-called Benders cuts. While many advanced optimization techniques can be…
We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set…
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 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…
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…
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…
Second order conic programming (SOCP) has been used to model various applications in power systems, such as operation and expansion planning. In this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model for the…
The necessary decarbonization efforts in energy sectors entail the integration of flexibility assets, as well as increased levels of uncertainty for the planning and operation of power systems. To cope with this in a cost-effective manner,…
We consider electricity capacity expansion models, which optimize investment and retirement decisions by minimizing both investment and operation costs. In order to provide credible support for planning and policy decisions, these models…
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…