arXiv subjects

Anirudh Subramanyam

Publications and source records attributed to Anirudh Subramanyam.

At least 19 recordsLinked to original sources

arXiv2026

Neural Embedded Mixed-Integer Optimization for Location-Routing Problems

We present a framework that combines machine learning with mixed-integer optimization to solve the Capacitated Location-Routing Problem (CLRP), a classical NP-hard problem that integrates strategic facility location with operational vehicle routing decisions. The proposed method trains a neural network to approximate the cost of a Capacitated Vehicle Routing Problem (CVRP) for serving any subset of customers from a candidate facility. The network is trained on an independently generated dataset of CVRP instances from the literature, entirely separate from any CLRP test instances, thereby avoiding the overfitting and information leakage that can affect learning-based methods. The trained network is then embedded as a surrogate within a mixed-integer model for location-allocation decisions, which is solved using off-the-shelf solvers, thus leveraging decades of advances in vehicle routing and the availability of mature solvers. Computational experiments across four benchmark sets show that the method delivers reasonable solution quality and scales well to large instances, where, after a one-time training cost, it reaches solutions close to the best known at a fraction of the runtime of state-of-the-art heuristics. Our results demonstrate the value of routing cost approximations from the neural surrogate in informing high-quality location-allocation decisions. Our code and data are publicly available.

math.OC↗

arXiv2026

Computing Rare Probabilities of Voltage Collapse

This paper introduces a framework based on Large Deviation Theory (LDT) to accurately and efficiently compute the rare probabilities of voltage collapse. We formulate the problem as finding the most probable failure point (the instanton) on the stability boundary and derive both first-order and second-order approximations for the collapse probability. The second-order method incorporates the local curvature of the stability boundary, yielding higher accuracy. This LDT framework generalizes methods based on Mahalanobis distance and is extensible to non-Gaussian uncertainties. We validate our approach on test systems, demonstrating that the LDT estimates converge to Monte Carlo results in the rare-event regime where direct sampling becomes computationally prohibitive.

math.OC↗

arXiv2026

Decision-Scaled Scenario Approach for Rare Chance-Constrained Optimization

Chance-constrained optimization is a suitable modeling framework for safety-critical applications where violating constraints is nearly unacceptable. The scenario approach is a popular solution method for these problems, due to its straightforward implementation and ability to preserve problem structure. However, in the rare-event regime where constraint violations must be kept extremely unlikely, the scenario approach becomes computationally infeasible due to the excessively large sample sizes it demands. We address this limitation with a new yet straightforward decision-scaling method that relies exclusively on original data samples and a single scalar hyperparameter that scales the constraints in a way amenable to standard solvers. Our method leverages large deviation principles under mild nonparametric assumptions satisfied by commonly used distribution families in practice. For a broad class of problems satisfying certain practically verifiable structural assumptions, the method achieves a polynomial reduction in sample size requirements compared to the classical scenario approach, while also guaranteeing asymptotic feasibility in the rare-event regime. Numerical experiments spanning finance and engineering applications show that our decision-scaling method significantly expands the scope of problems that can be solved both efficiently and reliably.

math.OC↗

arXiv2026

Chance-Constrained DC Optimal Power Flow Using Constraint-Informed Statistical Estimation

Chance-constrained optimization has emerged as a promising framework for managing uncertainties in power systems. This work advances its application to the DC Optimal Power Flow (DC-OPF) model, developing a novel approach to uncertainty modeling and estimation. Current methods typically tackle these problems by first modeling random nodal injections using high-dimensional statistical distributions that scale with the number of buses, followed by deriving deterministic reformulations of the probabilistic constraints. We propose an alternative methodology that exploits the constraint structure to inform the uncertainties to be estimated, enabling significant dimensionality reduction. Rather than learning joint distributions of net-load forecast errors across units, we instead directly model the one-dimensional aggregate system forecast error and two-dimensional line errors weighted by power transfer distribution factors. We evaluate our approach under both Gaussian and non-Gaussian distributions on synthetic and real-world datasets, demonstrating significant improvements in statistical accuracy and optimization performance compared to existing methods.

eess.SY↗

arXiv2026

Machine Learning-Enabled Large-Scale Capacity Expansion Planning under Uncertainty

Capacity expansion planning under uncertainty requires selecting a scenario count and representative operational horizon to estimate average production costs. Small choices risk unreliable plans, while large choices become intractable. We propose AutoSCEP, an automated, statistically grounded procedure that, for a fixed plan, selects the minimum sufficient scenario count and horizon length to estimate production costs to a given precision. Using these estimates, we train linear and neural surrogates to approximate expected production costs for arbitrary plans, and embed the surrogates within the planning model. On the continental-scale EMPIRE system, AutoSCEP attains 2% optimality gap on a reduced model and 8% gap on a large model, outperforming parallel progressive hedging under equal wall-clock budgets that include data generation, training, and solve times. Where the reduced model's optimum is available, investment patterns broadly align with the benchmark. Our approach enables high-resolution uncertainty modeling at realistic system scales.

math.OC↗

arXiv2026

Scaling Laws Revisited: Modeling the Role of Data Quality in Language Model Pretraining

Scaling laws for language model training traditionally characterize how performance scales with model size and dataset volume. Prior work has explored architecture variants and data treatments such as dataset filtering and noise injection in language model pretraining; however, these studies have not formalized data quality within a principled scaling law. We introduce a dimensionless data-quality parameter Q, and propose a quality-aware scaling law extending the Chinchilla framework to predict loss as a joint function of model size, data volume, and data quality. The law is motivated by an effective-sample-size and information-theoretic view of noisy or redundant corpora, and it admits two practical estimators for Q: (i) a corruption rate proxy and (ii) a deficiency measure. Through synthetic experiments in neural machine translation and autoregressive modeling -- where we systematically control data quality via multiple levels of noise injection variation -- we show that loss scales predictably with data quality and that higher-quality data can substantially reduce model size and hence compute requirements. Our results demonstrate a sublinear decay of effective data with quality and robustness to moderate data corruption; out-of-sample evaluations further validate the predictive form of the law. Unlike prior empirical analyses, our work establishes an explicit, generalizable law for data quality, offering concrete guidance for balancing data curation effort and model scale in large-scale pretraining.

cs.LG↗

arXiv2026

Extreme-Scale EV Charging Infrastructure Planning for Last-Mile Delivery Using High-Performance Parallel Computing

This paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

math.OC↗

arXiv2025

On Solving Chance-Constrained Models with Gaussian Mixture Distribution

We study linear chance-constrained problems where the coefficients follow a Gaussian mixture distribution. We provide mixed-binary quadratic programs that give inner and outer approximations of the chance constraint based on piecewise linear approximations of the standard normal cumulative density function. We show that $O\left(\sqrt{\ln(1/τ)/τ} \right)$ pieces are sufficient to attain $τ$-accuracy in the chance constraint. We also show that any desired optimality gap can be achieved under a constraint qualification condition by controlling the approximation accuracy. Extensive computations using a commercial solver show that problems with up to one thousand random coefficients specified with up to fifteen Gaussian mixture components, generated under diverse settings, can be solved to near optimality within 18 hours, while satisfying chance constraint satisfaction probabilities of up to $0.999$. The solution times are significantly lower for problems with fewer random coefficients and mixture terms. For example, problems with one hundred random coefficients, ten mixture terms, and a constraint satisfaction probability of $0.999$ can be solved in a minute or less. Sample average approximations fail to provide meaningful solutions even for the smaller problems.

math.OC↗

arXiv2025

LaB-RAG: Label Boosted Retrieval Augmented Generation for Radiology Report Generation

In the current paradigm of image captioning, deep learning models are trained to generate text from image embeddings of latent features. We challenge the assumption that fine-tuning of large, bespoke models is required to improve model generation accuracy. Here we propose Label Boosted Retrieval Augmented Generation (LaB-RAG), a small-model-based approach to image captioning that leverages image descriptors in the form of categorical labels to boost standard retrieval augmented generation (RAG) with pretrained large language models (LLMs). We study our method in the context of radiology report generation (RRG) over MIMIC-CXR and CheXpert Plus. We argue that simple classification models combined with zero-shot embeddings can effectively transform X-rays into text-space as radiology-specific labels. In combination with standard RAG, we show that these derived text labels can be used with general-domain LLMs to generate radiology reports. Without ever training our generative language model or image embedding models specifically for the task, and without ever directly "showing" the LLM an X-ray, we demonstrate that LaB-RAG achieves better results across natural language and radiology language metrics compared with other retrieval-based RRG methods, while attaining competitive results compared to other fine-tuned vision-language RRG models. We further conduct extensive ablation experiments to better understand the components of LaB-RAG. Our results suggest broader compatibility and synergy with fine-tuned methods to further enhance RRG performance.

cs.CV↗

arXiv2025

GDC Cohort Copilot: An AI Copilot for Curating Cohorts from the Genomic Data Commons

The Genomic Data Commons (GDC) provides access to high quality, harmonized cancer genomics data through a unified curation and analysis platform centered around patient cohorts. While GDC users can interactively create complex cohorts through the graphical Cohort Builder, users (especially new ones) may struggle to find specific cohort descriptors across hundreds of possible fields and properties. However, users may be better able to describe their desired cohort in free-text natural language. We introduce GDC Cohort Copilot, an open-source copilot tool for curating cohorts from the GDC. GDC Cohort Copilot automatically generates the GDC cohort filter corresponding to a user-input natural language description of their desired cohort, before exporting the cohort back to the GDC for further analysis. An interactive user interface allows users to further refine the generated cohort. We develop and evaluate multiple large language models (LLMs) for GDC Cohort Copilot and demonstrate that our locally-served, open-source GDC Cohort LLM achieves better results than GPT-4o prompting in generating GDC cohorts. We implement and share GDC Cohort Copilot as a containerized Gradio app on HuggingFace Spaces, available at https://huggingface.co/spaces/uc-ctds/GDC-Cohort-Copilot. GDC Cohort LLM weights are available at https://huggingface.co/uc-ctds. All source code is available at https://github.com/uc-cdis/gdc-cohort-copilot.

cs.CL↗

arXiv2025

Correction to: A Lagrangian dual method for two-stage robust optimization with binary uncertainties

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. We first present a simple counterexample where the original conditions are insufficient, highlight where the original proof fails, and then provide modified conditions along with a correct proof of their validity. Finally, although the original paper discusses modifications to their method for problems that may not satisfy any sufficient conditions, we substantiate that discussion along two directions. We first show that computing an optimal Lagrange multiplier can still be done in polynomial time. We then provide complete and correct versions of the corresponding Benders and column-and-constraint generation algorithms in which the original method is used. We also discuss the implications of our findings on computational performance.

math.OC↗

arXiv2024

Reduced Sample Complexity in Scenario-Based Control System Design via Constraint Scaling

The scenario approach is widely used in robust control system design and chance-constrained optimization, maintaining convexity without requiring assumptions about the probability distribution of uncertain parameters. However, the approach can demand large sample sizes, making it intractable for safety-critical applications that require very low levels of constraint violation. To address this challenge, we propose a novel yet simple constraint scaling method, inspired by large deviations theory. Under mild nonparametric conditions on the underlying probability distribution, we show that our method yields an exponential reduction in sample size requirements for bilinear constraints with low violation levels compared to the classical approach, thereby significantly improving computational tractability. Numerical experiments on robust pole assignment problems support our theoretical findings.

math.OC↗

arXiv2024

Electric Vehicle Supply Equipment Location and Capacity Allocation for Fixed-Route Networks

Electric vehicle (EV) supply equipment location and allocation (EVSELCA) problems for freight vehicles are becoming more important because of the trending electrification shift. Some previous works address EV charger location and vehicle routing problems simultaneously by generating vehicle routes from scratch. Although such routes can be efficient, introducing new routes may violate practical constraints, such as drive schedules, and satisfying electrification requirements can require dramatically altering existing routes. To address the challenges in the prevailing adoption scheme, we approach the problem from a fixed-route perspective. We develop a mixed-integer linear program, a clustering approach, and a metaheuristic solution method using a genetic algorithm (GA) to solve the EVSELCA problem. The clustering approach simplifies the problem by grouping customers into clusters, while the GA generates solutions that are shown to be nearly optimal for small problem cases. A case study examines how charger costs, energy costs, the value of time (VOT), and battery capacity impact the cost of the EVSELCA. Charger equipment costs were found to be the most significant component in the objective function, leading to a substantial reduction in cost when decreased. VOT costs exhibited a significant decrease with rising energy costs. An increase in VOT resulted in a notable rise in the number of fast chargers. Longer EV ranges decrease total costs up to a certain point, beyond which the decrease in total costs is negligible.

math.OC↗

arXiv2023

Network Cascade Vulnerability using Constrained Bayesian Optimization

Measures of power grid vulnerability are often assessed by the amount of damage an adversary can exact on the network. However, the cascading impact of such attacks is often overlooked, even though cascades are one of the primary causes of large-scale blackouts. This paper explores modifications of transmission line protection settings as candidates for adversarial attacks, which can remain undetectable as long as the network equilibrium state remains unaltered. This forms the basis of a black-box function in a Bayesian optimization procedure, where the objective is to find protection settings that maximize network degradation due to cascading. Notably, our proposed method is agnostic to the choice of the cascade simulator and its underlying assumptions. Numerical experiments reveal that, against conventional wisdom, maximally misconfiguring the protection settings of all network lines does not cause the most cascading. More surprisingly, even when the degree of misconfiguration is limited due to resource constraints, it is still possible to find settings that produce cascades comparable in severity to instances where there are no resource constraints.

cs.SI↗

arXiv2022

A Time-Constrained Capacitated Vehicle Routing Problem in Urban E-Commerce Delivery

Electric vehicle routing problems can be particularly complex when recharging must be performed mid-route. In some applications such as the e-commerce parcel delivery truck routing, however, mid-route recharging may not be necessary because of constraints on vehicle capacities and maximum allowed time for delivery. In this study, we develop a mixed-integer optimization model that exactly solves such a time-constrained capacitated vehicle routing problem, especially of interest to e-commerce parcel delivery vehicles. We compare our solution method with an existing metaheuristic and carry out exhaustive case studies considering four U.S. cities -- Austin, TX; Bloomington, IL; Chicago, IL; and Detroit, MI -- and two vehicle types: conventional vehicles and battery electric vehicles (BEVs). In these studies we examine the impact of vehicle capacity, maximum allowed travel time, service time (dwelling time to physically deliver the parcel), and BEV range on system-level performance metrics including vehicle miles traveled (VMT). We find that the service time followed by the vehicle capacity plays a key role in the performance of our approach. We assume an 80-mile BEV range as a baseline without mid-route recharging. Our results show that BEV range has a minimal impact on performance metrics because the VMT per vehicle averages around 72 miles. In a case study for shared-economy parcel deliveries, we observe that VMT could be reduced by 38.8\% in Austin if service providers were to operate their distribution centers jointly.

math.OC↗

arXiv2022

Failure Probability Constrained AC Optimal Power Flow

Despite cascading failures being the central cause of blackouts in power transmission systems, existing operational and planning decisions are made largely by ignoring their underlying cascade potential. This paper posits a reliability-aware AC Optimal Power Flow formulation that seeks to design a dispatch point which has a low operator-specified likelihood of triggering a cascade starting from any single component outage. By exploiting a recently developed analytical model of the probability of component failure, our Failure Probability-constrained ACOPF (FP-ACOPF) utilizes the system's expected first failure time as a smoothly tunable and interpretable signature of cascade risk. We use techniques from bilevel optimization and numerical linear algebra to efficiently formulate and solve the FP-ACOPF using off-the-shelf solvers. Extensive simulations on the IEEE 118-bus case show that, when compared to the unconstrained and N-1 security-constrained ACOPF, our probability-constrained dispatch points can significantly lower the probabilities of long severe cascades and of large demand losses, while incurring only minor increases in total generation costs.

math.OC↗

arXiv2022

A Lagrangian Dual Method for Two-Stage Robust Optimization with Binary Uncertainties

This paper presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.

math.OC↗

arXiv2022

Optimization under rare chance constraints

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe sampling and computational requirements on classical solution methods that render them impractical. This work proposes a novel sampling-free method for solving rare chance constrained optimization problems affected by uncertainties that follow general Gaussian mixture distributions. By integrating modern developments in large deviation theory with tools from convex analysis and bilevel optimization, we propose tractable formulations that can be solved by off-the-shelf solvers. Our formulations enjoy several advantages compared to classical methods: their size and complexity is independent of event rarity, they do not require linearity or convexity assumptions on system constraints, and under easily verifiable conditions, serve as safe conservative approximations or asymptotically exact reformulations of the true problem. Computational experiments on linear, nonlinear and PDE-constrained problems from applications in portfolio management, structural engineering and fluid dynamics illustrate the broad applicability of our method and its advantages over classical sampling-based approaches in terms of both accuracy and efficiency.

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