In this paper, we study a latticized optimization problem with fuzzy relational inequality constraints where the feasible region is formed as the intersection of two inequality fuzzy systems and Sugeno - Weber family of t - norms is considered as fuzzy composition. Sugeno - Weber family of t - norms and t - conorms is one of the most applied one in various fuzzy modelling problems. Thi s family of t - norms and t - conorms was suggested by Weber for modeling intersection and union of fuzzy sets. Also, the t - conorms were suggested as addition rules by Sugeno for so - called - fuzzy measures. The resolution of the feasible region of the problem is firstly investigated when it is defined with max - Sugeno - Weber composition and a necessary and sufficient condition is presented for determining the feasibility. Then, based on some theoretical properties of the problem, an algorithm is presented for sol ving this nonlinear problem. It is proved that the algorithm can find the exact optimal solution and an example is presented to illustrate the proposed algorithm.

Standard evaluation protocols in robotic manipulation typically assess policy performance over curated, in-distribution test sets, offering limited insight into how systems fail under plausible variation. We introduce Geometric Red-Teaming (GRT), a red-teaming framework that probes robustness through object-centric geometric perturbations, automatically generating CrashShapes -- structurally valid, user-constrained mesh deformations that trigger catastrophic failures in pre-trained manipulation policies. The method integrates a Jacobian field-based deformation model with a gradient-free, simulator-in-the-loop optimization strategy. Across insertion, articulation, and grasping tasks, GRT consistently discovers deformations that collapse policy performance, revealing brittle failure modes missed by static benchmarks. By combining task-level policy rollouts with constraint-aware shape exploration, we aim to build a general purpose framework for structured, object-centric robustness evaluation in robotic manipulation. We additionally show that fine-tuning on individual CrashShapes, a process we refer to as blue-teaming, improves task success by up to 60 percentage points on those shapes, while preserving performance on the original object, demonstrating the utility of red-teamed geometries for targeted policy refinement. Finally, we validate both red-teaming and blue-teaming results with a real robotic arm, observing that simulated CrashShapes reduce task success from 90% to as low as 22.5%, and that blue-teaming recovers performance to up to 90% on the corresponding real-world geometry -- closely matching simulation outcomes. Videos and code can be found on our project website: https://georedteam.github.io/ .

Oddvar Kloster, Bjørnar Luteberget, Carlo Mannino, Giorgio SartorAbstract Optimization-based decision support systems have a significant potential to reduce delays, and thus improve efficiency on the railways, by automatically re-routing and re-scheduling trains after delays have occurred. The operations research community has dedicated a lot of effort to developing optimization algorithms for this problem, but each study is typically tightly connected with a specific industrial use case. Code and data are seldom shared publicly. This fact hinders reproducibility, and has led to a proliferation of papers describing algorithms for more or less compatible problem definitions, without any real opportunity for readers to assess their relative performance. Inspired by the successful communities around MILP, SAT, TSP, VRP, etc., we introduce a common problem definition and file format, DISPLIB, which captures all the main features of train re-routing and re-scheduling. We have gathered problem instances from multiple real-world use cases and made them openly available. In this paper, we describe the problem definition, the industrial instances, and a reference solver implementation. This allows any researcher or developer to work on the train dispatching problem without an industrial connection, and enables the research community to perform empirical comparisons between solvers.

The Internet of Electric Vehicles (IoEV) envisions a tightly coupled ecosystem of electric vehicles (EVs), charging infrastructure, and grid services, yet it remains vulnerable to cyberattacks, unreliable battery-state predictions, and opaque decision processes that erode trust and performance. To address these challenges, we introduce a novel Agentic Artificial Intelligence (AAI) framework tailored for IoEV, where specialized agents collaborate to deliver autonomous threat mitigation, robust analytics, and interpretable decision support. Specifically, we design an AAI architecture comprising dedicated agents for cyber-threat detection and response at charging stations, real-time State of Charge (SoC) estimation, and State of Health (SoH) anomaly detection, all coordinated through a shared, explainable reasoning layer; develop interpretable threat-mitigation mechanisms that proactively identify and neutralize attacks on both physical charging points and learning components; propose resilient SoC and SoH models that leverage continuous and adversarial-aware learning to produce accurate, uncertainty-aware forecasts with human-readable explanations; and implement a three-agent pipeline, where each agent uses LLM-driven reasoning and dynamic tool invocation to interpret intent, contextualize tasks, and execute formal optimizations for user-centric assistance. Finally, we validate our framework through comprehensive experiments across diverse IoEV scenarios, demonstrating significant improvements in security and prediction accuracy. All datasets, models, and code will be released publicly.

The optimal control problem of stochastic systems is commonly solved via robust [2, 21] or scenario-based [7, 19, 17] optimization methods, which are both challenging to scale to long optimization horizons due to their open-loop nature. Dynamic programming formulations [4], while applicable to stochastic systems, typically involve nonconvex optimization problems and do not support specifying the terminal distribution. Polynomial optimization has been proposed for deterministic nonlinear [11] and hybrid systems [16]. We extend the method to stochastic systems using a weak formulation of the Fokker-Planck equation. As a cost function, we propose to use the Christoffel polynomial, which can be estimated from data.

Arithmetic circuits, such as adders and multipliers, are fundamental components of digital systems, directly impacting the performance, power efficiency, and area footprint. However, optimizing these circuits remains challenging due to the vast design space and complex physical constraints. While recent deep learning-based approaches have shown promise, they struggle to consistently explore high-potential design variants, limiting their optimization efficiency. To address this challenge, we propose AC-Refiner, a novel arithmetic circuit optimization framework leveraging conditional diffusion models. Our key insight is to reframe arithmetic circuit synthesis as a conditional image generation task. By carefully conditioning the denoising diffusion process on target quality-of-results (QoRs), AC-Refiner consistently produces high-quality circuit designs. Furthermore, the explored designs are used to fine-tune the diffusion model, which focuses the exploration near the Pareto frontier. Experimental results demonstrate that AC-Refiner generates designs with superior Pareto optimality, outperforming state-of-the-art baselines. The performance gain is further validated by integrating AC-Refiner into practical applications.

HiLAB (Hybrid inverse-design with Latent-space learning, Adjoint-based partial optimizations, and Bayesian optimization) is a new paradigm for inverse design of nanophotonic structures. Combining early-terminated topological optimization (TO) with a Vision Transformer-based variational autoencoder (VAE) and a Bayesian search, HiLAB addresses multi-functional device design by generating diverse freeform configurations at reduced simulation costs. Shortened adjoint-driven TO runs, coupled with randomized physical parameters, produce robust initial structures. These structures are compressed into a compact latent space by the VAE, enabling Bayesian optimization to co-optimize geometry and physical hyperparameters. Crucially, the trained VAE can be reused for alternative objectives or constraints by adjusting only the acquisition function. Compared to conventional TO pipelines prone to local optima, HiLAB systematically explores near-global optima with considerably fewer electromagnetic simulations. Even after accounting for training overhead, the total number of full simulations decreases by over an order of magnitude, accelerating the discovery of fabrication-friendly devices. Demonstrating its efficacy, HiLAB is used to design an achromatic beam deflector for red, green, and blue wavelengths, achieving balanced diffraction efficiencies of ~25% while mitigating chromatic aberrations-a performance surpassing existing demonstrations. Overall, HiLAB provides a flexible platform for robust, multi-parameter photonic designs and rapid adaptation to next-generation nanophotonic challenges.

Quantum variational circuits have gained significant attention due to their applications in the quantum approximate optimization algorithm and quantum machine learning research. This work introduces a novel class of classical probabilistic circuits designed for generating approximate solutions to combinatorial optimization problems constructed using two-bit stochastic matrices. Through a numerical study, we investigate the performance of our proposed variational circuits in solving the Max-Cut problem on various graphs of increasing sizes. Our classical algorithm demonstrates improved performance for several graph types to the quantum approximate optimization algorithm. Our findings suggest that evaluating the performance of quantum variational circuits against variational circuits with sub-universal gate sets is a valuable benchmark for identifying areas where quantum variational circuits can excel.

We propose FACTORS, a framework that combines design of experiments with Shapley decomposition to address performance and stability issues that are sensitive to combinations of training factors. Our approach consistently estimates main effects and two-factor interactions, then integrates them into a risk-adjusted objective function that jointly accounts for uncertainty and cost, enabling reliable selection of configurations under a fixed budget. Effect estimation is implemented through two complementary paths: a plug-in path based on conditional means, and a least-squares path that reconstructs Shapley contributions from samples. These paths are designed to work complementarily even when design density and bias levels differ. By incorporating standardization of estimates, bias correction, and uncertainty quantification, our procedure ensures comparability across heterogeneous factor spaces and designs, while a lightweight search routine yields configurations within practical time even for large factor spaces. On the theoretical side, we provide error decompositions, sample complexity analysis, and upper bounds on optimality gaps. On the interpretive side, we summarize main effects and interactions in map form, highlighting adjustment priorities and safe improvement pathways. Across diverse datasets and design conditions, our approach improves rank preservation and optimal configuration identification, reduces decision-making risks, and offers a tuning foundation that delivers interpretable justification alongside stable performance gains even under budget constraints.

This work proposes a bid shading strategy for first-price auctions as a measure-valued optimization problem. We consider a standard parametric form for bid shading and formulate the problem as convex optimization over the joint distribution of shading parameters. After each auction, the shading parameter distribution is adapted via a regularized Wasserstein-proximal update with a data-driven energy functional. This energy functional is conditional on the context, i.e., on publisher/user attributes such as domain, ad slot type, device, or location. The proposed algorithm encourages the bid distribution to place more weight on values with higher expected surplus, i.e., where the win probability and the value gap are both large. We show that the resulting measure-valued convex optimization problem admits a closed form solution. A numerical example illustrates the proposed method.