arXiv subjects

Alessandro Zocca

Publications and source records attributed to Alessandro Zocca.

At least 19 recordsLinked to original sources

arXiv2026

Exact and Evolutionary Algorithms for Sequential Multi-Objective Transmission Topology Planning

We study day-ahead transmission topology control for high-voltage grid operation under $N-1$ security constraints. The operational task is to select, over a 24-hour horizon, a sequence of substation topologies obtained via busbar-coupler switching to relieve line overloads while limiting switching effort and topological complexity. We formulate this task as a sequential multi-objective optimization problem with four objectives used in TSO decision making: worst-case $N-1$ line loading, maximum topological depth, number of topology changes, and time spent outside the reference topology. We propose an exact block algorithm that exploits the temporal structure of topology plans: consecutive hours with the same topology are represented as blocks, enabling enumeration of the complete Pareto front over the admissible set of topologies under fixed operational bounds on depth and switching. We also develop a tailored NSGA-III-based evolutionary heuristic and evaluate it against the exact front. Using real operational data from the Dutch high-voltage transmission grid operated by TenneT, the block algorithm computes the exact front for a highly congested day in under three minutes after topology-level load-flow preprocessing. The exact front reveals low-switching plans with no DC $N-1$ thermal overloads that the tested evolutionary search fails to find. The proposed method, therefore, provides both a practical day-ahead decision-support tool for transmission operators and a benchmark for heuristic and learning-based topology-control methods.

math.OC↗

arXiv2026

Random Walks with Traversal Costs: Variance-Aware Performance Analysis and Network Optimization

We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the accumulated weight along a path independently of the routing behavior. Crucially, we derive closed-form expressions for the mean and variance of weighted first passage times and weighted Kemeny constants, together with their partial derivatives with respect to both the weight and transition matrices. These results hold for both deterministic and stochastic weights with no distributional assumptions. We demonstrate the framework through two applications, highlighting the dual role of variance. In surveillance networks, we introduce the surprise index, a coefficient-of-variation metric quantifying patrol unpredictability, and show how maximizing it yields policies that are both efficient and hard to anticipate. In traffic networks subject to cascading edge failures, we develop a minimal-intervention framework that adjusts speed limits to preserve connectivity under three increasingly flexible regulatory policies.

math.OC↗

arXiv2026

LOTUS: A Warm-Start Framework for Powering Dual Decomposition in Large-Scale Two-Stage Stochastic Programs

Solving large two-stage stochastic mixed-integer programs is computationally challenging. We propose LOTUS, a subset-based warm-start framework that enhances Dual Decomposition under fixed time budgets. By initializing the dual search with informed multipliers, LOTUS accelerates primal convergence and partially alleviates the impact of weak LP relaxations. Through an extensive computational study on production planning instances, we show that, within two hours, LOTUS yields significantly better primal solutions in 45.83% of cases, while being outperformed by Dual Decomposition in only 4.17%.

math.OC↗

arXiv2026

A Fast Heuristic for Stochastic Steiner Tree Problems

Network design under uncertainty arises in countless real-world settings and can be captured by the Stochastic Steiner Tree Problem (SSTP). Although there are a few approaches specifically tailored to this stochastic optimization problem, there are considerably more state-of-the-art heuristics for its deterministic variant, the Steiner Tree Problem (STP). In this work, we show how to leverage an existing STP heuristic in building a novel method for solving its stochastic variant, the SSTP. This approach is a powerful, yet simple and easy-to-implement way of solving this complex problem. We test our method using benchmark instances from the literature. Numerical results show considerably faster computation times compared to the state-of-the-art, with a gap of approximately 5%.

math.OC↗

arXiv2026

Metastable opinion dynamics with hidden preferences: an Ising model with neutral agents

We introduce a new Ising-type framework for opinion dynamics that explicitly separates private preferences from publicly expressed binary opinions and naturally incorporates neutral agents. Each individual is endowed with an immutable hidden preference, while public opinions evolve through Metropolis dynamics on a finite graph. This formulation extends classical sociophysical Ising models by capturing the tension between internal conviction, social conformity, and neutrality. Focusing on highly symmetric grid networks and spatially structured hidden-preference patterns, we analyze the resulting low-temperature dynamics using the pathwise approach to metastability. We provide a complete characterization of stable and metastable configurations, identify the maximal stability level of the energy landscape, and derive sharp asymptotics for hitting and mixing times. A central technical contribution is a new family of isoperimetric inequalities for polyominoes on the torus, which emerge from a geometric representation of opinion clusters and play a key role in determining critical configurations and energy barriers. Our results provide a quantitative understanding of how spatial heterogeneity in hidden preferences qualitatively reshapes collective opinion transitions and illustrate the power of geometric and probabilistic methods in the study of complex interacting systems.

math.PR↗

arXiv2025

Optimizing Power Grid Topologies with Reinforcement Learning: A Survey of Methods and Challenges

Power grid operation is becoming increasingly complex due to the rising integration of renewable energy sources and the need for more adaptive control strategies. Reinforcement Learning (RL) has emerged as a promising approach to power network control (PNC), offering the potential to enhance decision-making in dynamic and uncertain environments. The Learning To Run a Power Network (L2RPN) competitions have played a key role in accelerating research by providing standardized benchmarks and problem formulations, leading to rapid advancements in RL-based methods. This survey provides a comprehensive and structured overview of RL applications for power grid topology optimization, categorizing existing techniques, highlighting key design choices, and identifying gaps in current research. Additionally, we present a comparative numerical study evaluating the impact of commonly applied RL-based methods, offering insights into their practical effectiveness. By consolidating existing research and outlining open challenges, this survey aims to provide a foundation for future advancements in RL-driven power grid optimization.

eess.SY↗

arXiv2024

A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems"), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.

math.OC↗

arXiv2024

Dynamic Dimensioning of Frequency Containment Reserves: The Case of the Nordic Grid

One of the main responsibilities of a Transmission System Operator (TSO) operating an electric grid is to maintain a designated frequency (e.g., 50 Hz in Europe). To achieve this, TSOs have created several products called frequency-supporting ancillary services. The Frequency Containment Reserve (FCR) is one of these ancillary service products. This article focuses on the TSO problem of determining the volume procured for FCR. Specifically, we investigate the potential benefits and impact on grid security when transitioning from a traditionally \textit{static} procurement method to a \textit{dynamic} strategy for FCR volume. We take the Nordic synchronous area in Europe as a case study and use a diffusion model to capture its frequency development. We introduce a controlled mean reversal parameter to assess changes in FCR obligations, in particular for the Nordic FCR-N ancillary service product. We establish closed-form expressions for exceedance probabilities and use historical frequency data as input to calibrate the model. We show that a dynamic dimensioning approach for FCR has the potential to significantly reduce the exceedance probabilities (up to $37\%$) while maintaining the total yearly procured FCR volume equal to that of the current static approach. Alternatively, a dynamic dimensioning approach could significantly increase security at limited extra cost.

eess.SY↗

arXiv2024

A First-Order Gradient Approach for the Connectivity Optimization of Markov Chains

Graphs are commonly used to model various complex systems, including social networks, power grids, transportation networks, and biological systems. In many applications, the connectivity of these networks can be expressed through the Mean First Passage Times (MFPTs) of a Markov chain modeling a random walker on the graph. In this paper, we generalize the network metrics based on Markov chains' MFPTs and extend them to networks affected by uncertainty, in which edges may fail and hence not be present according to a pre-determined stochastic model. To find optimally connected Markov chains, we present a parameterization-free method for optimizing the MFPTs of the Markov chain. More specifically, we present an efficient Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm in the context of Markov chain optimization. The proposed algorithm is suitable for both fixed and random networks. Using various numerical experiments, we demonstrate scalability compared to established benchmarks. Importantly, our algorithm finds an optimal solution without requiring prior knowledge of edge failure probabilities, allowing for an online optimization approach.

math.OC↗

arXiv2023

Future-proof ship pipe routing: navigating the energy transition

The maritime industry must prepare for the energy transition from fossil fuels to sustainable alternatives. Making ships future-proof is necessary given their long lifetime, but it is also complex because the future fuel type is uncertain. Within this uncertainty, one typically overlooks pipe routing, although it is a crucial driver for design time and costs. Therefore, we propose a mathematical approach for modeling uncertainty in pipe routing with deterministic, stochastic, and robust optimization. All three models are based on state-of-the-art integer linear optimization models for the Stochastic Steiner Forest Problem and adjusted to the maritime domain using specific constraints for pipe routing. We compare the models using both artificial and realistic instances and show that considering uncertainty using stochastic optimization and robust optimization leads to cost reductions of up to 22% in our experiments.

math.OC↗

arXiv2023

Generating synthetic power grids using exponential random graphs models

Synthetic power grids enable secure, real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power grids using Exponential Random Graph (ERG) models. Our two main contributions are: (1) the formulation of an ERG model tailored specifically for capturing the topological nuances of power grids, and (2) a general procedure for estimating the parameters of such a model conditioned on working with connected graphs. From a modeling perspective, we identify the edge counts per bus type and $k$-triangles as crucial topological characteristics for synthetic power grid generation. From a technical perspective, we develop a rigorous methodology to estimate the parameters of an ERG constrained to the space of connected graphs. The proposed model is flexible, easy to implement, and successfully captures the desired topological properties of power grids.

eess.SY↗

arXiv2023

Multi-Agent Reinforcement Learning for Power Grid Topology Optimization

Recent challenges in operating power networks arise from increasing energy demands and unpredictable renewable sources like wind and solar. While reinforcement learning (RL) shows promise in managing these networks, through topological actions like bus and line switching, efficiently handling large action spaces as networks grow is crucial. This paper presents a hierarchical multi-agent reinforcement learning (MARL) framework tailored for these expansive action spaces, leveraging the power grid's inherent hierarchical nature. Experimental results indicate the MARL framework's competitive performance with single-agent RL methods. We also compare different RL algorithms for lower-level agents alongside different policies for higher-order agents.

cs.LG↗

arXiv2023

Critical configurations of the hard-core model on square grid graphs

We consider the hard-core model on a finite square grid graph with stochastic Glauber dynamics parametrized by the inverse temperature $\beta$. We investigate how the transition between its two maximum-occupancy configurations takes place in the low-temperature regime $\beta\to\infty$ in the case of periodic boundary conditions. The hard-core constraints and the grid symmetry make the structure of the critical configurations, also known as essential saddles, for this transition very rich and complex. We provide a comprehensive geometrical characterization of the set of critical configurations that are asymptotically visited with probability one. In particular, we develop a novel isoperimetric inequality for hard-core configurations with a fixed number of particles and we show how not only their size but also their shape determines the characterization of the saddles.

math.PR↗

arXiv2023

Uncovering Load-Altering Attacks Against N-1 Secure Power Grids: A Rare-Event Sampling Approach

Load-altering attacks targetting a large number of IoT-based high-wattage devices (e.g., smart electric vehicle charging stations) can lead to serious disruptions of power grid operations. In this work, we aim to uncover spatiotemporal characteristics of LAAs that can lead to serious impact. The problem is challenging since existing protection measures such as $N-1$ security ensures that the power grid is naturally resilient to load changes. Thus, strategically injected load perturbations that lead to network failure can be regarded as \emph{rare events}. To this end, we adopt a rare-event sampling approach to uncover LAAs distributed temporally and spatially across the power network. The key advantage of this sampling method is the ability of sampling efficiently from multi-modal conditional distributions with disconnected support. Furthermore, we systematically compare the impacts of static (one-time manipulation of demand) and dynamic (attack over multiple time periods) LAAs. We perform extensive simulations using benchmark IEEE test simulations. The results show (i) the superiority and the need for rare-event sampling in the context of uncovering LAAs as compared to other sampling methodologies, (ii) statistical analysis of attack characteristics and impacts of static and dynamic LAAs, and (iii) cascade sizes (due to LAA) for different network sizes and load conditions.

eess.SY↗

arXiv2023

Analysis of Cascading Failures Due to Dynamic Load-Altering Attacks

Large-scale load-altering attacks (LAAs) are known to severely disrupt power grid operations by manipulating several internet-of-things (IoT)-enabled load devices. In this work, we analyze power grid cascading failures induced by such attacks. The inherent security features in power grids such as the $N-1$ design philosophy dictate LAAs that can trigger cascading failures are \emph{rare} events. We overcome the challenge of efficiently sampling critical LAAs scenarios for a wide range of attack parameters by using the so-called ``skipping sampler'' algorithm. We conduct extensive simulations using a three-area IEEE-39 bus system and provide several novel insights into the composition of cascades due to LAAs. Our results highlight the particular risks to modern power systems posed by strategically designed coordinated LAAs that exploit their structural and real-time operating characteristics.

cs.CR↗

arXiv2022

Ising model on clustered networks: A model for opinion dynamics

We study opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other individuals in the network. To model such dynamics, we consider the Ising model with an external magnetic field on a family of finite networks with a clustered structure. Assuming a unit strength for the interactions inside each community, we assume that the strength of interaction across different communities is described by a scalar $\epsilon \in [-1,1]$, which allows a weaker but possibly antagonistic effect between communities. We are interested in the stochastic evolution of this system described by a Glauber-type dynamics parameterized by the inverse temperature $\beta$. We focus on the low-temperature regime $\beta\rightarrow\infty$, in which homogeneous opinion patterns prevail and, as such, it takes the network a long time to fully change opinion. We investigate the different metastable and stable states of this opinion dynamics model and how they depend on the values of the parameters $\epsilon$ and $h$. More precisely, using tools from statistical physics, we derive rigorous estimates in probability, expectation, and law for the first hitting time between metastable (or stable) states and (other) stable states, together with tight bounds on the mixing time and spectral gap of the Markov chain describing the network dynamics. Lastly, we provide a full characterization of the critical configurations for the dynamics, i.e., those which are visited with high probability along the transitions of interest.

math.PR↗

arXiv2022

RangL: A Reinforcement Learning Competition Platform

The RangL project hosted by The Alan Turing Institute aims to encourage the wider uptake of reinforcement learning by supporting competitions relating to real-world dynamic decision problems. This article describes the reusable code repository developed by the RangL team and deployed for the 2022 Pathways to Net Zero Challenge, supported by the UK Net Zero Technology Centre. The winning solutions to this particular Challenge seek to optimize the UK's energy transition policy to net zero carbon emissions by 2050. The RangL repository includes an OpenAI Gym reinforcement learning environment and code that supports both submission to, and evaluation in, a remote instance of the open source EvalAI platform as well as all winning learning agent strategies. The repository is an illustrative example of RangL's capability to provide a reusable structure for future challenges.

cs.LG↗

arXiv2022

Interface Networks for Failure Localization in Power Systems

Transmission power systems usually consist of interconnected sub-grids that are operated relatively independently. When a failure happens, it is desirable to localize its impact within the sub-grid where the failure occurs. This paper introduces three interface networks to connect sub-grids, achieving better failure localization while maintaining robust network connectivity. The proposed interface networks are validated with numerical experiments on the IEEE 118-bus test network under both DC and AC power flow models.

eess.SY↗