The interdiction defense (ID) problem solves a defender-attacker-defender model where the defender and attacker share the same set of components to harden and target. We build upon the best response intersection (BRI) algorithm by developing the BRI with suboptimal solutions (BRI-SS) algorithm to solve the ID problem. The BRI-SS algorithm utilizes off-the-shelf optimization solvers that … Read more
Mixed-Integer Linear Programming (MIP) is applicable to such a wide range of real-world decision problems that the competition for the best code to solve such problems has lead to tremendous progress over the last decades. While current solvers can solve some of the problems that seemed completely out-of-reach just 10 years ago, there are always … 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
This paper investigates the a-posteriori analysis of Branch-and-Bound (BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible region, systematically constructed from a BB tree. These are: a tight formulation based on disjunctive programming, a branching-based formulation derived from the tree’s branching … 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
TitleDiscovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling Authorsİbrahim Oğuz Çetinkaya^1; İ. Esra Büyüktahtakın^1*; Parshin Shojaee^2; Chandan K. Reddy^2 Affiliations^1 Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA^2 Department of Computer Science, Virginia Tech, Arlington, VA, USA Abstract: Our study contributes to the scheduling and combinatorial optimization … Read more
We introduce the Expeditionary Logistics Network Design Problem (ELNDP), a new formulation for operational-level planning in expeditionary environments where multi-modal vehicle coordination is critical and penalties for unmet demand dominate transportation costs. ELNDP extends the classical Scheduled Service Network Design Problem by incorporating flexible commodity sourcing and heterogeneous vehicle capabilities, both essential in military logistics. … Read more
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We show how to extract alternative solutions for optimization problems solved by Benders Decom- position. In practice, alternative solutions provide useful insights for complex applications; some solvers do support generation of alternative solutions but none appear to support such generation when using Benders Decomposition. We propose a new post-processing method that extracts multiple optimal and … Read more
In mathematical optimization, we want to find the best possible solution for a decision-making problem. Curiously, these problems are harder to solve if they have discrete decisions. Imagine that you would like to buy chocolate: you can buy no chocolate or one chocolate bar, but typically you cannot buy just half of a bar. Now … Read more