Attention Mechanisms in Physics-Inspired Graph Neural Networks for the Max-Cut Problem

Categories Combinatorial Optimization, Graphs and Matroids, Network Optimization Tags , , ,

Physics-Inspired Graph Neural Networks (PI-GNNs) reformulate MAX-CUT as QUBO energy minimization, training a GNN to produce soft binary node assignments without labeled data. The baseline PI-GCN uses static, degree-normalized aggregation, while its attention-augmented counterpart PI-GAT—built on GATv2—introduces additional hyperparameters whose effects remain uncharacterized. This paper addresses that gap through controlled experiments on five Gset benchmark … Read more

Random-Key Optimization for 2D Irregular Packing with Reusable Area Evaluation

Categories Applications - OR and Management Sciences, Meta Heuristics, Parallel Algorithms, Production and Logistics Tags , ,

The diverse constraints of industrial applications lead to variants of 2D irregular packing problems that require tailored solution methods. This paper addresses a real-world industrial challenge by proposing a new problem definition, the Maximum Reusable Contiguous Area Problem (MRCAP), and a novel metric, the Maximum Contiguous Area, developed to measure and maximize the contiguous unused … Read more

Robust Chance-Constrained Optimization using a Continuous Parameter Space Wasserstein-2 Ambiguity Set of Gaussian Mixtures

Categories Nonlinear Optimization, Robust Optimization, Stochastic Programming Tags , , , ,

We study distributionally robust linear chance-constrained problems in which uncertainty is modeled by a Gaussian mixture model (GMM). Finite-support distributionally robust (FDR) formulations, widely used in data-driven robust optimization, robustify over empirical mixture support points and therefore primarily stress-test the fitted nominal mixture. This can be insufficient when service reliability depends on structural misspecification of … Read more

Tight Conic Relaxations for Rank-one Doubly Nonnegative Matrix Completion

Categories Cone Programming, Global Optimization Applications, Quadratic Programming Tags , , , ,

We study tight conic relaxations for a quadratically constrained quadratic programming (QCQP) formulation of rank-one doubly nonnegative (DNN) matrix completion. Motivated by sparse QCQPs whose lifted matrix variables include elements not directly specified by the objective or constraints, we interpret tightness as a rank-one completion property for the unspecified elements. For sparsity patterns whose blocks … Read more

Approximate solution of infinite-horizon risk-sensitive Markov decision processes

Categories Dynamic Programming, Other Topics Tags , ,

Infinite-horizon risk-sensitive Markov decision processes (MDPs) under the discounted cost criterion are challenging to solve because the optimal policy may be non- stationary. Existing solution methods reformulate the problem as a continuous-state (risk-neutral) MDP and solve it using state-discretization or value function approximation. Such approaches typically lack explicit stopping conditions or error bounds. In this … Read more

Exploring polynomial models in the Search Step of Direct Multisearch

Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

Direct Multisearch (DMS) is a class of direct-search algorithms designed for multiobjective derivative-free optimization. Its framework consists of an optional search step and a poll step, the latter ensuring the corresponding theoretical convergence properties. Recently, a search strategy based on the minimization of quadratic polynomial models, constructed from previously evaluated points, was proposed to improve … Read more

Model-Uncertainty-Aware Residuals-Based Sample Average Approximation

Categories Robust Optimization, Stochastic Programming Tags , , ,

We consider a contextual stochastic optimization (CSO) problem, where one has observations of the uncertain parameters together with concurrent observations of covariates, and the goal is to choose decisions that minimize expected cost conditioned on new covariate observations. The empirical residuals-based sample average approximation (ER-SAA) of the CSO problem constructs scenarios of uncertainty by combining … Read more

Accelerated Kernel Stein Discrepancy with Rényi Landmark Selection for GAN Training

Categories Data Science Algorithms

Our project investigates replacing the classical adversarial discriminator in GAN training with a kernel-based distance metric, namely Kernel Stein Discrepancy (KSD). We assess whether a kernelized objective can improve training stability and efficiency without compromising sample quality, and we evaluate accelerated Nystrom approximations with Renyi landmark selection on CIFAR-10. ArticleDownload View PDF

PaNGEA: Parallel Node Generation and Exploration Algorithm

Categories (Mixed) Integer Linear Programming, Integer Programming Tags ,

Primal heuristics for finding high-quality feasible solutions are an important component in mixed-integer optimization (MIO) solvers. Recent advances in GPU-accelerated optimization algorithms show the potential of GPU acceleration for continuous optimization. In this paper, we introduce the Parallel Node Generation and Exploration Algorithm (PaNGEA), a GPU-friendly MIO primal heuristic. PaNGEA explores restricted subproblems by combining … Read more

A Dynamic-Programming Labeling Approach to Hydrogen-Powered Route Selection in Aviation Networks

Categories Airline Optimization, Applications - OR and Management Sciences Tags , ,

We study passenger routing in an aviation network that blends hydrogen‐ and kerosene‐powered aircraft. Under our assumptions, hydrogen enables carbon‐free short‐ and medium‐haul flights but requires capital‐intensive supply facilities, which lead to varying prices and availabilities of hydrogen at specific airports, creating strong interdependencies between routing, technology choice, and infrastructure availability. To capture these trade‐offs, … Read more