arXiv subjects

Harsha Nagarajan

Publications and source records attributed to Harsha Nagarajan.

At least 19 recordsLinked to original sources

arXiv2026

Efficient Graph Partitioning under Resource Constraints: A Cutting-Plane Framework for Distribution Grids

This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected subnetworks while ensuring radial connectivity, resource feasibility, and structured leader allocation, which provide structural foundations for distributed controllability, stability, and coordination. The problem is formulated as a mixed-integer program that integrates graph-theoretic constraints, resource flow, and network structural properties to enforce an operational hierarchy. To address the combinatorial complexity of cycle elimination and leader assignment, we propose an iterative cutting-plane framework that ensures convergence to an optimal and feasible network topology. Theoretical guarantees on optimality preservation, feasibility, and convergence are established, ensuring systematic elimination of infeasible configurations while preserving the required coordination structure. Simulations on a modified Iowa 240-bus power distribution grid demonstrate the framework's effectiveness in network reconfiguration under resource constraints. The approach achieves a median speedup of 65.4x and a best-case speedup of over 78x in a 46-switch configuration.

math.OC↗

arXiv2026

A Hybrid Decomposition Approach for Stochastic Unit Commitment with Combined-Cycle Generators

The U.S. power grid is undergoing a paradigm shift as energy demand grows in scale and volatility. In response to this growing need, the U.S. has increased adoption of combined-cycle generators (CCs). CCs are fast-ramping generators that utilize variable configurations of combustion turbines (CTs) and steam turbines (STs) to achieve higher efficiency than traditional CTs. For schedule optimization, modeling these CCs requires the addition of a large number of binary constraints and variables to Unit Commitment (UC) problem formulations. This paper presents a novel hybrid Benders' (BD) and Dantzig-Wolfe (DW) decomposition algorithm, called CRG, for stochastic UC problems with CCs. CRG exploits the separability of the linear constraints in UC through BD and the integer CC constraints through DW. A novel set of valid inequalities are proposed for significantly tightening the lower bound produced by CRG. CRG is tested on the 935-generator FERC test data set, modified to include CC mode data. Results demonstrate better primal solutions than BD on cases with at least 20 load scenarios. CRG scales computationally better than Gurobi's branch-and-bound solver, which exceeds 64GB RAM allocations at 45 scenarios. Results show that the proposed algorithm is a scalable approach for solving large-scale stochastic UC with CCs.

math.OC↗

arXiv2026

Hardware-Aware QUBO Reformulation of Constrained Binary Optimization via the Walsh-Fourier Transform

We present a novel slack-free, penalty-based framework for reformulating constrained binary optimization as Quadratic Unconstrained Binary Optimization (QUBO) on near-term quantum annealing hardware. Given a user-chosen penalty function that most naturally captures a constraint---typically non-quadratic, such as a Heaviside-function surrogate---and a target probability measure over the Boolean hypercube, our method returns the weighted least-squares projection of the chosen penalty function onto the subspace spanned by linear and quadratic Walsh--Fourier characters that correspond to physically realizable couplings on the target hardware graph. Within this restricted family, the resulting quadratic surrogate is uniquely and optimally determined by the normal equations: unlike state-of-the-art approaches, it introduces no per-constraint penalty coefficients to tune and avoids dense all-pairs couplings by construction. Two practical consequences follow. First, the projected penalty respects device connectivity, reducing chain lengths and physical-qubit overhead after minor embedding. Second, we show empirically that this hardware-native surrogate can outperform denser full-pairwise projections, despite being drawn from a strictly smaller approximation space. This advantage widens once the QUBO is embedded and sampled on quantum annealers, yielding samples with the lowest worst-case and mean objective gaps compared to unbalanced penalization and a hardware-blind projection onto all quadratic terms.

quant-ph↗

arXiv2026

Load Block Modeling in Distribution Systems: Network Reconfiguration for Load Restoration

The distribution system restoration (DSR) problem has received considerable attention over the last decade or more. Solutions to the DSR problem identify the best set or sequence of actions to perform on a distribution circuit to restore service after a disruption. The problem is challenging from a computational perspective, with engineering constraints specific to distribution systems, such as radial operations, that are difficult to effectively model. In this paper, we revisit the model for how specific loads are shed, energized and restored--and develop a formulation that more accurately models the requirements of load shedding, load energizing and restoration in distribution systems.

eess.SY↗

arXiv2026

Multi-Region Optimal Energy Storage Arbitrage

The increasing interconnection of power systems through AC and DC links enables energy storage units to access multiple electricity markets yet most existing arbitrage models remain limited to singlemarket participation This gap restricts understanding of the economic value and operational constraints associated with crossborder storage operation To address this an optimal multiregion energy storage arbitrage model is developed for a gridscale battery located at one end of an interconnector linking two distinct dayahead markets The formulation incorporates battery capacity and ramping limits converter and interconnector losses and marketspecific buying and selling prices Using disjunctive linearization of nonlinear terms this work exactly reformulates the multiregion energy arbitrage optimization as a mixedinteger linear programming problem The proposed formulation ensures that the battery either charges or discharges from all participating energy markets simultaneously at any given time Case studies using eight years of BelgianUK price data demonstrate that multiregion participation can increase arbitrage revenue by more than 40% compared to local energy arbitrage operation only while also highlighting the negative impact of interconnector congestion on achievable gains The results indicate that crossborder market access substantially enhances storage profitability while considering the cycle of battery and that the proposed formulation provides a computationally efficient framework for evaluating and operating storage assets in interconnected power systems Finally a pseudoefficiency term is introduced to improve battery utilization by discarding less profitable charging and discharging battery cycles

eess.SY↗

arXiv2026

URSA: The Universal Research and Scientific Agent

Large language models (LLMs) have moved far beyond their initial form as simple chatbots, now carrying out complex reasoning, planning, writing, coding, and research tasks. These skills overlap significantly with those that human scientists use day-to-day to solve complex problems that drive the cutting edge of research. Using LLMs in \quotes{agentic} AI has the potential to revolutionize modern science and remove bottlenecks to progress. In this work, we present URSA, a scientific agent ecosystem for accelerating research tasks. URSA consists of a set of modular agents and tools, including coupling to advanced physics simulation codes, that can be combined to address scientific problems of varied complexity and impact. This work highlights the architecture of URSA, as well as examples that highlight the potential of the system.

cs.AI↗

arXiv2025

Sparse Neural Approximations for Bilevel Adversarial Problems in Power Grids

The adversarial worst-case load shedding (AWLS) problem is pivotal for identifying critical contingencies under line outages. It is naturally cast as a bilevel program: the upper level simulates an attacker determining worst-case line failures, and the lower level corresponds to the defender's generator redispatch operations. Conventional techniques using optimality conditions render the bilevel, mixed-integer formulation computationally prohibitive due to the combinatorial number of topologies and the nonconvexity of AC power flow constraints. To address these challenges, we develop a novel single-level optimal value-function (OVF) reformulation and further leverage a data-driven neural network (NN) surrogate of the follower's optimal value. To ensure physical realizability, we embed the trained surrogate in a physics-constrained NN (PCNN) formulation that couples the OVF inequality with (relaxed) AC feasibility, yielding a mixed-integer convex model amenable to off-the-shelf solvers. To achieve scalability, we learn a sparse, area-partitioned NN via spectral clustering; the resulting block-sparse architecture scales essentially linearly with system size while preserving accuracy. Notably, our approach produces near-optimal worst-case failures and generalizes across loading conditions and unseen topologies, enabling rapid online recomputation. Numerical experiments on the IEEE 14- and 118-bus systems demonstrate the method's scalability and solution quality for large-scale contingency analysis, with an average optimality gap of 5.8% compared to conventional methods, while maintaining computation times under one minute.

eess.SY↗

arXiv2025

Learning for Interval Prediction of Electricity Demand: A Cluster-based Bootstrapping Approach

Accurate predictions of electricity demands are necessary for managing operations in a small aggregation load setting like a Microgrid. Due to low aggregation, the electricity demands can be highly stochastic and point estimates would lead to inflated errors. Interval estimation in this scenario, would provide a range of values within which the future values might lie and helps quantify the errors around the point estimates. This paper introduces a residual bootstrap algorithm to generate interval estimates of day-ahead electricity demand. A machine learning algorithm is used to obtain the point estimates of electricity demand and respective residuals on the training set. The obtained residuals are stored in memory and the memory is further partitioned. Days with similar demand patterns are grouped in clusters using an unsupervised learning algorithm and these clusters are used to partition the memory. The point estimates for test day are used to find the closest cluster of similar days and the residuals are bootstrapped from the chosen cluster. This algorithm is evaluated on the real electricity demand data from EULR(End Use Load Research) and is compared to other bootstrapping methods for varying confidence intervals.

cs.LG↗

arXiv2025

Reconfiguration and Real-Time Operation of Networked Microgrids Under Load Uncertainty

Distribution networks are increasingly exposed to threats such as extreme weather, aging infrastructure, and cyber risks--resulting in more frequent contingencies and outages, a trend likely to persist. Microgrids, particularly dynamic networked microgrids (DNMGs), offer a promising solution to mitigate the impacts of such contingencies and enhance resiliency. However, distribution networks present unique challenges due to their unbalanced nature and the inherent uncertainty in both loads and generation. This paper builds upon our prior work on the two-stage mixed-integer robust optimization problem for configuring DNMGs, improving the solve time and scalability. Furthermore, we present a model-free, real-time optimal power flow algorithm to manage DNMG operations in the time between reconfigurations. A case study on a realistic network based on part of the San Francisco Bay Area demonstrates the scalability of both approaches. The case study also illustrates the ability to maintain power flow feasibility as loads vary and operating conditions change when the methods are used in tandem.

math.OC↗

arXiv2025

Provably Optimal Quantum Circuits with Mixed-Integer Programming

We present a depth-aware optimization framework for quantum circuit compilation that unifies provable optimality with scalable heuristics. For exact synthesis of a target unitary, we formulate a mixed-integer linear program (MILP) that linearly handles global-phase equivalence and uses explicit parallel scheduling variables to certify depth-optimal solutions for small-to-medium circuits. Domain-specific valid constraints, including identity ordering, commuting-gate pruning, short-sequence redundancy cuts, and Hermitian-conjugate linkages, significantly accelerate branch-and-bound, yielding speedups up to 43x on standard benchmarks. The framework supports hardware-aware objectives, enabling fault-tolerant (e.g. T-count) and NISQ-era (e.g. entangling gates) devices. For approximate synthesis, we propose 3 objectives: (i) exact, but non-convex, phase-invariant fidelity maximization; (ii) a linear surrogate that maximizes the real trace overlap, yielding a tight lower bound to fidelity; and (iii) a convex quadratic function that minimizes the circuit's Frobenius error. To scale beyond exact MILP, we propose a novel rolling-horizon optimization (RHO) that rolls primarily in time, caps the active-qubits, and enforces per-qubit closure while globally optimizing windowed segments. This preserves local context, reduces the Hilbert-space dimension, and enables iterative improvements without ancillas. On a 142-gate seed circuit, RHO yields 116 gates, an 18.3% reduction from the seed, while avoiding the trade-off between myopic passes and long run times. Empirically, our exact compilation framework achieves certified depth-optimal circuits on standard targets, high-fidelity Fibonacci-anyon weaves, and a 36% gate-count reduction on multi-body parity circuits. All methods are in the open-source QuantumCircuitOpt, providing a single framework that bridges exact certification and scalable synthesis.

quant-ph↗

arXiv2025

Hierarchical Semi-Markov Models with Duration-Aware Dynamics for Activity Sequences

Residential electricity demand at granular scales is driven by what people do and for how long. Accurately forecasting this demand for applications like microgrid management and demand response therefore requires generative models that can produce realistic daily activity sequences, capturing both the timing and duration of human behavior. This paper develops a generative model of human activity sequences using nationally representative time-use diaries at a 10-minute resolution. We use this model to quantify which demographic factors are most critical for improving predictive performance. We propose a hierarchical semi-Markov framework that addresses two key modeling challenges. First, a time-inhomogeneous Markov \emph{router} learns the patterns of ``which activity comes next." Second, a semi-Markov \emph{hazard} component explicitly models activity durations, capturing ``how long" activities realistically last. To ensure statistical stability when data are sparse, the model pools information across related demographic groups and time blocks. The entire framework is trained and evaluated using survey design weights to ensure our findings are representative of the U.S. population. On a held-out test set, we demonstrate that explicitly modeling durations with the hazard component provides a substantial and statistically significant improvement over purely Markovian models. Furthermore, our analysis reveals a clear hierarchy of demographic factors: Sex, Day-Type, and Household Size provide the largest predictive gains, while Region and Season, though important for energy calculations, contribute little to predicting the activity sequence itself. The result is an interpretable and robust generator of synthetic activity traces, providing a high-fidelity foundation for downstream energy systems modeling.

stat.AP↗

arXiv2025

Strong Partitioning and a Machine Learning Approximation for Accelerating the Global Optimization of Nonconvex QCQPs

We learn optimal instance-specific heuristics for the global minimization of nonconvex quadratically-constrained quadratic programs (QCQPs). Specifically, we consider partitioning-based convex mixed-integer programming relaxations for nonconvex QCQPs and propose the novel problem of strong partitioning to optimally partition variable domains without sacrificing global optimality. Since solving this max-min strong partitioning problem exactly can be very challenging, we design a local optimization method that leverages generalized gradients of the value function of its inner-minimization problem. However, even solving the strong partitioning problem to local optimality can be time-consuming. To address this, we propose a simple and practical machine learning (ML) approximation for homogeneous families of QCQPs. Motivated by practical applications, we conduct a detailed computational study using the open-source global solver Alpine to evaluate the effectiveness of our ML approximation in accelerating the repeated solution of homogeneous QCQPs with fixed structure. Our study considers randomly generated QCQP families, including instances of the pooling problem, that are benchmarked using state-of-the-art global optimization software. Numerical experiments demonstrate that our ML approximation of strong partitioning reduces Alpine's solution time by a factor of 2 to 4.5 on average, with maximum reduction factors ranging from 10 to 200 across these QCQP families.

math.OC↗

arXiv2025

Optimal Trajectory Planning for Space Object Tracking with Collision-Avoidance Constraints

A control optimization approach is presented for a chaser spacecraft tasked with maintaining proximity to a target space object while avoiding collisions. The target object trajectory is provided numerically to account for both passive debris and actively maneuvering spacecraft. Thrusting actions for the chaser object are modeled as discrete (on/off) variables to optimize resources (e.g., fuel) while satisfying spatial, dynamical, and collision-avoidance constraints. The nonlinear equation of motion is discretized directly using a fourth-order Runge-Kutta method without the need for linearized dynamics. The resulting mixed-integer nonlinear programming (MINLP) formulation is further enhanced with scaling techniques, valid constraints based on a perspective convex reformulation, and a combination of continuous relaxations of discrete actions with rounding heuristics to recover high-quality feasible solutions. This methodology enables efficient, collision-free trajectory planning over extended time horizons while reducing computational overhead. The effectiveness and practicality of the proposed approach is validated through a numerical case study.

math.OC↗

arXiv2025

Tightening Quadratic Convex Relaxations for the AC Optimal Transmission Switching Problem

The Alternating Current Optimal Transmission Switching (ACOTS) problem incorporates line switching decisions into the AC Optimal Power Flow (ACOPF) framework, offering well-known benefits in reducing operational costs and enhancing system reliability. ACOTS optimization models contain discrete variables and nonlinear, non-convex constraints, which make it difficult to solve. In this work, we develop strengthened quadratic convex (QC) relaxations for ACOTS, where we tighten the relaxation with several new valid inequalities, including a novel kind of on/off cycle-based polynomial constraints by taking advantage of the network structure. We linearize the sum of on/off trilinear terms in the relaxation using extreme-point representation, demonstrating theoretical tightness, and efficiently incorporate on/off cycle-based polynomial constraints through disjunctive programming-based cutting planes. Combined with an optimization-based bound tightening algorithm, this results in the tightest QC-based ACOTS relaxation to date. We additionally propose a novel maximum spanning tree-based heuristic to improve the computational performance by fixing certain lines to be switched on. Our extensive numerical experiments on medium-scale PGLib instances show significant improvements on relaxation bounds, while tests on large-scale instances with up to 2,312 buses demonstrate substantial performance gains. To our knowledge, this is the first ACOTS relaxation-based approach to demonstrate near-optimal switching solutions on realistic large-scale power grid instances.

math.OC↗

arXiv2025

Leveraging Quantum Computing for Accelerated Classical Algorithms in Power Systems Optimization

The recent advent of commercially available quantum annealing hardware (QAH) has expanded opportunities for research into quantum annealing-based algorithms. In the domain of power systems, this advancement has driven increased interest in applying such algorithms to mixed-integer problems (MIP) like Unit Commitment (UC). UC focuses on minimizing power generator operating costs while adhering to physical system constraints. Grid operators solve UC instances daily to meet power demand and ensure safe grid operations. This work presents a novel hybrid algorithm that leverages quantum and classical computing to solve UC more efficiently. We introduce a novel Benders-cut generation technique for UC, thereby enhancing cut quality, reducing expensive quantum-classical hardware interactions, and lowering qubit requirements. Additionally, we incorporate a $k$-local neighborhood search technique as a recovery step to ensure a higher quality solution than current QAH alone can achieve. The proposed algorithm, QC4UC, is evaluated on a modified instance of the IEEE RTS-96 test system. Results from both a simulated annealer and real QAH are compared, demonstrating the effectiveness of this algorithm in reducing qubit requirements and producing near-optimal solutions on noisy QAH.

math.OC↗

arXiv2024

Spectral Graph Theoretic Methods for Enhancing Network Robustness in Robot Localization

This paper addresses the optimization of edge-weighted networks by maximizing algebraic connectivity to enhance network robustness. Motivated by the need for precise robot position estimation in cooperative localization and pose-graph sparsification in Simultaneous Localization and Mapping (SLAM), the algebraic connectivity maximization problem is formulated as a Mixed Integer Semi-Definite Program (MISDP), which is NP-hard. Leveraging spectral graph theoretic methods, specifically Cheeger's inequality, this work introduces novel "Cheeger cuts" to strengthen and efficiently solve medium-scale MISDPs. Further, a new Mixed Integer Linear Program (MILP) is developed for efficiently computing Cheeger cuts, implemented within an outer-approximation algorithm for solving the MISDP. A greedy k-opt heuristic is also presented, producing high-quality solutions that serve as valid lower bounds for Cheeger cuts. Comprehensive numerical analyses demonstrate the efficacy of strengthened cuts via substantial improvements in run times on synthetic and realistic robot localization datasets.

eess.SY↗

arXiv2024

Robust Partitioning and Operation for Maximal Uncertain-Load Delivery in Distribution Grids

To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids could improve resiliency and maximize load delivery, though the modeling of three-phase unbalanced network physics and computational complexity pose challenges. These challenges are further exacerbated by an increased penetration of uncertain loads. In this paper, we present a two-stage mixed-integer robust optimization problem that configures and operates networked microgrids, and is guaranteed to be robust and feasible to all realizations of loads within a specified uncertainty set, while maximizing load delivery. To solve this problem, we propose a cutting-plane algorithm, with convergence guarantees, which approximates a convex recourse function with sub-gradient cuts. Finally, we provide a detailed case study on the IEEE 37-bus test system to demonstrate the economic benefits of networking microgrids to maximize uncertain-load delivery.

math.OC↗

arXiv2024

Optimal Robust Network Design: Formulations and Algorithms for Maximizing Algebraic Connectivity

This paper focuses on designing edge-weighted networks, whose robustness is characterized by maximizing algebraic connectivity, or the second smallest eigenvalue of the Laplacian matrix. This problem is motivated by cooperative vehicle localization, where accurately estimating relative position measurements and establishing communication links are essential. We also examine an associated problem where every robot is limited by payload, budget, and communication to pick no more than a specified number of relative position measurements. The basic underlying formulation for these problems is nonlinear and is known to be NP-hard. Our approach formulates this problem as a Mixed Integer Semi-Definite Program (MISDP), later reformulated into a Mixed Integer Linear Program (MILP) for obtaining optimal solutions using cutting plane algorithms. We introduce a novel upper-bounding algorithm based on principal minor characterization of positive semi-definite matrices and discuss a degree-constrained lower bounding formulation inspired by robust network structures. In addition, we propose a maximum cost heuristic with low computational complexity to identify high-quality feasible solutions for instances involving up to one hundred nodes. We show extensive computational results corroborating our proposed methods.

eess.SY↗