Many large-scale optimization problems decompose into a master problem and scenario subproblems, a structure that can be exploited by Benders decomposition. In Benders decomposition, each iteration may generate many cuts from scenario subproblems, and adding all of them as constraints then causes the master problem to grow rapidly. These are constraints that may need to … Read more
Modern energy grid expansion planning, by necessity, includes timeseries data to accurately model storage and renewable assets. Representative time periods are commonly used as a way to decrease problem size and therefore mitigate the increased complexity from this inclusion. However, there are many choices around these representative periods: length; location in planning horizon; boundary conditions. … Read more
We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we … Read more
We consider a two-stage optimization problem with sparsity constraints, motivated by a common challenge in packaging logistics: minimizing the volume of transported air by optimizing the size and number of available packaging boxes, given the demand for order items. In the first stage, we select the optimal dimensions of the boxes, while in the second … Read more
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 applied in a BD framework, one central technique has not been applied systematically in BD: symmetry handling. The main reason for this … Read more
The Stochastic Unit Commitment (SUC) problem models the scheduling of power generation units under uncertainty, typically using a two-stage stochastic program with integer first-stage and continuous second-stage variables. We propose a new Benders decomposition approach that leverages an extended formulation based on interval variables, enabling decomposition by both unit and time interval under mild technical … Read more
In the aftermath of an earthquake, one of the most critical needs is medical care for the injured. A large number of individuals require immediate attention, often overwhelming the available healthcare resources. The sudden surge in demand, coupled with limited resources, route congestion and infrastructure damage, makes immediate medical care provision a significant challenge. This … Read more
Tsunamis, primarily triggered by earthquakes, pose critical threats to coastal populations due to their rapid onset and limited evacuation time. Two main protective actions exist: sheltering in place, which requires substantial retrofitting investments, and evacuation, which is often hindered by congestion, mixed travel modes, and tight inundation times. Given pedestrians’ slower movement and restricted evacuation … Read more
Bulk-robust optimization is a recent paradigm for addressing problems in which the structure of a system is affected by uncertainty. It considers the case in which a finite and discrete set of possible failure scenarios is known in advance, and the decision maker aims to activate a subset of available resources of minimum cost so … Read more
Benders decomposition is a technique to solve large-scale mixed-integer optimization problems by decomposing them into a pure-integer master problem and a continuous separation subproblem. To accelerate convergence, we propose Random Partial Benders Decomposition (RPBD), a decomposition method that randomly retains a subset of the continuous variables within the master problem. Unlike existing problem-specific approaches, RPBD … Read more