arXiv subjects

Juan S. Borrero

Publications and source records attributed to Juan S. Borrero.

3 recordsLinked to original sources

arXiv2026

Graph4BiLO: Graph Neural Network Approximation for Bilevel Mixed-Integer Linear Optimization

Bilevel mixed-integer linear optimization problems model hierarchical decision processes in which a leader anticipates the optimal response of a follower. Although expressive, these problems are computationally challenging because lower-level optimality is embedded in the leader's feasible region. Value-function reformulations replace the nested follower optimization with a constraint involving the follower's optimal value, but evaluating this value function exactly can itself be expensive. This paper introduces Graph4BiLO, a graph neural network (GNN) approach for learning bilevel value functions from variable--constraint graph representations. In contrast to fixed-length multilayer perceptron (MLP) representations, the GNN uses shared message-passing parameters and can therefore be applied across multiple problem sizes with a single trained model. The learned ReLU network is encoded exactly as mixed-integer linear constraints and embedded in an approximate single-level formulation. A repair step subsequently re-solves the follower problem for the selected leader decision to recover a bilevel-feasible follower response. We evaluate Graph4BiLO on knapsack interdiction instances with 20--100 items against the exact MibS solver and the learning-based Neur2BiLO method. Graph4BiLO obtains objective values comparable to Neur2BiLO across all tested sizes while avoiding size-specific neural networks. An additional out-of-distribution experiment demonstrates zero-shot transfer from 20-item training instances to previously unseen 40- and 60-item instances. However, embedding message passing at every graph node substantially increases the resulting mixed-integer formulation size and solve time. These results identify a central tradeoff between size-generalizable graph representations and the computational cost of embedding GNNs within optimization models.

cs.LG↗

arXiv2026

Which Directions Matter? Sparse Design for Affine Robust Optimization

Robust machine learning and optimization rely on the uncertainty model choice. We investigate which uncertainty directions a model must cover when defined by a finite dictionary and a budget constraint. Selecting a subset forms an atomic uncertainty set with a closed form support function, yielding tractable robust programs for affine objectives. We propose a data driven selection rule based on a coverage objective over evaluation directions, including gradients, adversarial perturbations, or shifts observed on held out data. We prove this objective is monotone and submodular, supporting a greedy method with a $(1-1/e)$ approximation guarantee and a matching hardness barrier. We also provide a certificate bounding the loss from the selected subset and a radius calibration rule with out of sample control.

cs.LG↗

arXiv2023

Two-stage Robust Optimization Approach for Enhanced Community Resilience Under Tornado Hazards

Catastrophic tornadoes cause severe damage and are a threat to human wellbeing, making it critical to determine mitigation strategies to reduce their impact. One such strategy, following recent research, is to retrofit existing structures. To this end, in this article we propose a model that considers a decision-maker (a government agency or a public-private consortium) who seeks to allocate resources to retrofit and recover wood-frame residential structures, to minimize the population dislocation due to an uncertain tornado. In the first stage the decision-maker selects the retrofitting strategies, and in the second stage the recovery decisions are made after observing the tornado. As tornado paths cannot be forecast reliably, we take a worst-case approach to uncertainty where paths are modeled as arbitrary line segments on the plane. Under the assumption that an area is affected if it is sufficiently close to the tornado path, the problem is framed as a two-stage robust optimization problem with a mixed-integer non-linear uncertainty set. We solve this problem by using a decomposition column-and-constraint generation algorithm that solves a two-level integer problem at each iteration. This problem, in turn, is solved by a decomposition branch-and-cut method that exploits the geometry of the uncertainty set. To illustrate the model's applicability, we present a case study based on Joplin, Missouri. Our results show that there can be up to 20 percent reductions in worst-case population dislocation by investing 15 million dollars in retrofitting and recovery; that our approach outperforms other retrofitting policies, and that the model is not over-conservative.

math.OC↗