The Optical Stochastic Cooling Program at Fermilab
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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Results for “Stochastic programming”
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Stochastic Unit Commitment: Model Reduction via Learning
As weather-dependent renewable generation increases its share in the generation mix of most electric energy systems, a stochastic unit commitment becomes the natural day-ahead scheduling tool. However, such a tool is generally computationally intractable if a detailed uncertainty description is considered. Taking this into account, we proposed a learning method to make the stochastic unit commitment problem tractable. Here, recent advances in statistical learning and machine learning to address optimization problems can be advantageously applied to the rather intractable stochastic unit commitment problem. Considering these advances, we explore simple learning techniques to drastically reduce the size of a stochastic unit commitment problem without significantly altering its optimal solution. The considered stochastic unit commitment problem is formulated as a two-stage stochastic programming problem. The first stage represents commitment decisions, while the second one represents the operation conditions under different scenarios. Taking into account historical solved instances (or proxies for them), we reduce the size (measured by numbers of constraints and variables) of the stochastic unit commitment problem by (i) fixing unchanged binary variables and by (ii) eliminating inactive inequality constraints. Our numerical results show that the reduced problem generally requires significantly less time to solve while obtaining high-quality solutions, which are very close to or indistinguishable from the one obtained by solving the original problem. We use an Illinois 200-bus system to illustrate and characterize the performance of the proposed problem-reduction method.
42 ENGINEERING↗
A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market
In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.
Bilevel multistage stochastic programming problem↗
Routing Problem for Unmanned Aerial Vehicle Patrolling Missions - A Progressive Hedging Algorithm
This paper presents a two-stage stochastic program to model a routing problem involving an Unmanned Aerial Vehicle (UAV) in the context of patrolling missions. In particular, given a set of targets and a set of supplemental targets corresponding to each target, the first stage decisions involve finding the sequence in which the vehicle has to visit the set of targets. Upon reaching each target, the UAV collects information and if the operator of the UAV deems that the information collected is not of sufficient fidelity, then the UAV has to visit all the supplemental targets corresponding to that target to collect additional information before proceeding to visit the next target. The problem is solved using a progressive hedging algorithm and extensive computational results corroborating the effectiveness of the proposed model and the solution methodology is presented.
33 ADVANCED PROPULSION SYSTEMS↗
A Stochastic Charging Station Deployment Model for Electrified Taxi Fleets in Coupled Urban Transportation and Power Distribution Networks
Metropolitansworldwide are increasingly adopting electric taxis (ET) to address concerns about transportation-related emissions. However, the widespread deployment of electric taxis presents challenges in terms of increased electricity demand and changing demand profiles. This transition impacts both the urban transportation network (TN) and the electricity power distribution network (PDN), highlighting the interdependence between these two systems. Here, in this paper, we propose a two-stage stochastic programming planning model that aims to optimize both the TN and PDN, enabling efficient deployment of charging stations and grid upgrades. Our model seeks to strike a balance between meeting ET drivers' charging preferences, minimizing the costs associated with infrastructure deployment and grid expansion, and harmonizing the coordination between the TN and PDN. Additionally, we explore the potential benefits of utilizing an autonomous ET fleet to enhance overall system performance.
33 ADVANCED PROPULSION SYSTEMS↗
State-of-the-Art Techniques for Large-Scale Stochastic Unit Commitment
Recent advances in deterministic unit commitment, both formulaic and algorithmic, along with modern algorithmic approaches for stochastic programming, have enabled the solution of stochastic unit commitment problems with hundreds of scenarios on large-scale transmission networks. In this presentation, we will give an overview of these methods, including lazy transmission constraint generation, lower-bounding techniques, and heuristics, all of which can be executed in concert with customized decomposition approaches for optimization under uncertainty. We demonstrate the effectiveness of these techniques on the TAMU Texas7K synthetic transmission network, leveraging realistic high-resolution forecasts based on NREL renewable resource availability data. The software leveraged for these demonstrations is available via the open-source software packages EGRET (for electrical grid optimization) and mpi-sppy (for optimization under uncertainty).
27 ARPA - Advanced Research Projects Agency-Energy↗
A Comprehensive Scheduling Framework using SP-ADMM for Residential Demand Response with Weather and Consumer Uncertainties
This paper presents a comprehensive scheduling framework for residential demand response (DR) programs considering both the day-ahead and real-time electricity markets. In the first stage, residential customers determine the operating status of their responsive devices such as heating, ventilation, and air conditioning (HVAC) systems and electric water heaters (EWHs), while the distribution system operator (DSO) computes the amount of electricity to be purchased in the day-ahead electricity market. In the second stage, the DSO purchases insufficient (or sells surplus) electricity in the real-time electricity market to maintain the supply-demand balance. Due to its computational complexity and data privacy issues, the proposed model cannot be directly solved in a centralized manner, especially with a large number of uncertain scenarios. Therefore, this paper proposes a combination of stochastic programming (SP) and the alternating direction method of multipliers (ADMM) algorithm, called SP-ADMM, to decompose the original model and then solve each sub-problem in a distributed manner while considering multiple uncertain scenarios. The simulation study is performed on the IEEE 33-bus system including 121 residential houses. Here, the results demonstrate the effectiveness of the proposed approach for large-scale residential DR applications under weather and consumer uncertainties.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Tri-level hybrid interval-stochastic optimal scheduling for flexible residential loads under GAN-assisted multiple uncertainties
Various building loads, such as heating, ventilation, and air conditioners (HVACs), electric water heaters (EWHs), and electric vehicles (EVs), can introduce opportunities for improving the flexibility of electricity consumption while satisfying the needs of building owners as well as benefiting the resilience of distribution system. To utilize such flexibility, a tri-level distribution market framework is established, including residential consumers, load aggregators (LAs), and the distribution system operator (DSO). In this work, the uncertainties from all three levels are considered. The random consumption behavior at the consumer level is modeled as a Gaussian noise that is also aggregated and transmitted to the LA level. The weather temperature in the LA level is forecasted as an interval, and the photovoltaic (PV) power in the market-clearing level is modeled by a set of power scenarios generated by Generative Adversarial Networks (GANs). Then, a hybrid interval-stochastic programming is proposed to transform the uncertain problems in the first two levels into deterministic ones. For real-time implementations, a rolling horizon optimization (RHO) scheme is employed to continuously optimize the power consumption based on the latest operating information. Finally, case studies on a modified IEEE 69-bus system validate the effectiveness of the proposed uncertainty modeling strategies and the RHO scheme.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Microgrid design and multi-year dispatch optimization under climate-informed load and renewable resource uncertainty
Microgrids are an increasingly popular solution to provide energy resilience in response to increasing grid dependency and the growing impacts of climate change on grid operations. However, existing microgrid models do not currently consider the uncertain and long-term impacts of climate change when determining a set of design and operational decisions to minimize long-term costs or meet a resilience threshold. In this paper, we develop a novel scenario generation method that accounts for the uncertain effects of (i) climate change on variable renewable energy availability, (ii) extreme heat events on site load, and (iii) population and electrification trends on load growth. Additionally, we develop a two-stage stochastic programming extension of an existing microgrid design and dispatch optimization model to obtain uncertainty-informed and climate-resilient energy system decisions that minimizes long-term costs. Use of sample average approximation to validate our two case studies illustrates that the proposed methodology produces high-quality solutions that add resilience to systems with existing backup generation while reducing expected long-term costs.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Random field optimization
Herein we present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges.
97 MATHEMATICS AND COMPUTING↗
Resource distribution under spatiotemporal uncertainty of disease spread: Stochastic versus robust approaches
We consider the problem of optimizing locations of distribution centers (DCs) and plans for distributing resources such as test kits and vaccines, under spatiotemporal uncertainties of disease spread and demand for the resources. We aim to balance the operational cost (including costs of deploying facilities, shipping, and storage) and quality of service (reflected by demand coverage), while ensuring equity and fairness of resource distribution across multiple populations. We compare a sample-based stochastic programming (SP) approach with a distributionally robust optimization (DRO) approach using a moment-based ambiguity set. Numerical studies are conducted on instances of distributing COVID-19 vaccines in the United States and test kits, to compare SP and DRO models with a deterministic formulation using estimated demand and with the current resource distribution plans implemented in the US. We demonstrate the results over distinct phases of the pandemic to estimate the cost and speed of resource distribution depending on scale and coverage, and show the “demand-driven” properties of the SP and DRO solutions. Furthermore, our results further indicate that if the worst-case unmet demand is prioritized, then the DRO approach is preferred despite of its higher overall cost. Nevertheless, the SP approach can provide an intermediate plan under budgetary restrictions without significant compromises in demand coverage.
97 MATHEMATICS AND COMPUTING↗
Modular supply chain optimization considering demand uncertainty to manage risk
Supply chain under demand uncertainty has been a challenging problem due to increased competition and market volatility in modern markets. Flexibility in planning decisions makes modular manufacturing a promising way to address this problem. We report the problem of multiperiod process and supply chain network design is considered under demand uncertainty. A mixed integer two-stage stochastic programming problem is formulated with integer variables indicating the process design and continuous variables to represent the material flow in the supply chain. The problem is solved using a rolling horizon approach. Benders decomposition is used to reduce the computational complexity of the optimization problem. To promote risk-averse decisions, a downside risk measure is incorporated in the model. The results demonstrate the several advantages of modular designs in meeting product demands. A pareto-optimal curve for minimizing the objectives of expected cost and downside risk is obtained.
42 ENGINEERING↗
Impacts of floating-point non-associativity on reproducibility for HPC and deep learning applications
Run to run variability in parallel programs caused by floating-point non-associativity has been known to significantly affect reproducibility in iterative algorithms, due to accumulating errors. Non-reproducibility can critically affect the efficiency and effectiveness of correctness testing for stochastic programs. Recently, the sensitivity of deep learning training and inference pipelines to floating-point non-associativity has been found to sometimes be extreme. It can prevent certification for commercial applications, accurate assessment of robustness and sensitivity, and bug detection. New approaches in scientific computing applications have coupled deep learning models with high-performance computing, leading to an aggravation of debugging and testing challenges. Here we perform an investigation of the statistical properties of floating-point non-associativity within modern parallel programming models, and analyze performance and productivity impacts of replacing atomic operations with deterministic alternatives on GPUs. We examine the recently-added deterministic options in PyTorch within the context of GPU deployment for deep learning, uncovering and quantifying the impacts of input parameters triggering run to run variability and reporting on the reliability and completeness of the documentation. Finally, we evaluate the strategy of exploiting automatic determinism that could be provided by deterministic hardware, using the Groq LPUTM accelerator for inference portions of the deep learning pipeline. We demonstrate the benefits that a hardware-based strategy can provide within reproducibility and correctness efforts.
Shanmugavelu, Sanjif↗
A Data-Driven Methodology for Contextual Unit Commitment Using Regression Residuals
Day after day, system operators are faced with the challenge of taking unit commitment (UC) decisions under uncertain net load conditions. The standard operating procedure for taking UC decisions begins by leveraging auxiliary data on covariates (such as the day of the week or latest weather information) to generate a point prediction for net load, which is used in solving a deterministic UC problem. Such an approach, however, is known to deliver a notoriously poor out-of-sample (OOS) performance, as it completely disregards the stochastic nature of net load. While stochastic programming models explicitly represent uncertainty, they mostly do so using a generic set of scenarios that neglect covariate observations, squandering useful auxiliary data that could be harnessed to glean insights into uncertainty. In this article, we discuss a contextual stochastic optimization approach to UC, which effectively exploits covariate observations while explicitly assessing uncertainty so as to boost the OOS performance of UC decisions. The key thrust of our approach is to leverage regression models, along with their empirical residuals, to set up and solve sample average approximation problems. Not only do we prove that our approach satisfies the requisite conditions for asymptotic optimality and consistency laid out in (Kannan et al., 2022), but we also assess its performance on several case studies conducted using real-world data collected in California ISO and New York ISO grids. In conclusion, results show that the proposed approach can significantly improve OOS performance compared to alternative methods proposed in the literature under varying dataset sizes.
Yurdakul, Ogun↗
An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians
In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.
97 MATHEMATICS AND COMPUTING↗
Optimizing Power Line Undergrounding Decisions under Varying Wildfire Risk and Weather Scenarios
Abstract—The threat of wildfire ignitions from electric power equipment has led utilities to increasingly turn to preemptive power shutoffs, which, while effective in reducing grid-induced wildfire risk, can cause significant load loss. Undergrounding power lines is an alternative strategy for preventing grid-induced wildfires. However, undergrounding lines is costly, so an efficient undergrounding plan must balance reductions in wildfire risk and load loss with the cost of undergrounding lines. We propose a robust optimization model to identify which power lines to underground to maximize load served while limiting wildfire risk across a range of wildfire risk and weather scenarios. Since solving this problem may be computationally heavy for large power grids and many operating scenarios, we present a delayed constraint generation algorithm to iteratively add scenarios until an optimal solution is found. We evaluate the performance of this framework on the RTS-GMLC with scenarios representing a year of operating conditions and compare it with a stochastic programming formulation. Our results indicate that our undergrounding model is successful in reducing load shed and risk compared to baseline cases in which no mitigation action is taken and only power shutoffs are implemented (no undergrounding). The robust formulation also reduces more load shed than the stochastic formulation in the most extreme scenarios. Index Terms—grid resilience, optimization, transmission systems, underground power lines, wildfire risk.
Taylor, S. [Department of Electrical and Computer ↗
A Sequential Quadratic Programming Algorithm for Nonsmooth Problems with Upper- \({\boldsymbol{\mathcal{C}^2}}\) Objective
An optimization algorithm for nonsmooth nonconvex constrained optimization problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objective functions is proposed and analyzed. Upper- \({\boldsymbol{\mathcal{C}^2}}\) is a weakly concave property that exists in difference of convex (DC) functions and arises naturally in many applications, particularly certain classes of solutions to parametric optimization problems e.g., recourse of stochastic programming and projection onto closed sets. The algorithm can be viewed as an extension of sequential quadratic programming (SQP) to nonsmooth problems with upper- \({\boldsymbol{\mathcal{C}^2}}\) objectives or a simplified bundle method. It is globally convergent with bounded algorithm parameters that are updated with a trust-region criterion. The algorithm handles general smooth constraints through linearization and uses a line search to ensure progress. The potential inconsistencies from the linearization of the constraints are addressed through a penalty method. In conclusion, the capabilities of the algorithm are demonstrated by solving both simple upper- \({\boldsymbol{\mathcal{C}^2}}\) problems and a real-world optimal power flow problem used in current power grid industry practices.
97 MATHEMATICS AND COMPUTING↗
Marine energy supported multi-energy system planning and operation optimization for sustainable coastal community
The growing need for sustainable energy solutions in coastal areas necessitates the development of integrated systems that leverage abundant marine resources. In this study, a standalone Marine Energy Supported Multi-Energy System (MRE-MES) is designed for sustainable coastal community development, utilizing renewable marine resources, including offshore wind, wave, and solar energy, to address the energy needs of electricity, heat, freshwater, and hydrogen. The proposed MRE-MES incorporates a co-optimization model that simultaneously balances capacity planning and operational efficiency to minimize costs and environmental impacts. The system is tested under different renewable energy penetration levels and demand uncertainties, using a two-stage stochastic programming to account for variability in renewable resources and consumption needs. The experimental results indicate that in the optimal system capacity configuration, the percentage of total renewable energy generation is around 80 %, with or without capacity limitation constraints on PV, water tank, and hydrogen storage. Compared to the worst-case scenario in Monte Carlo experiments, two-stage stochastic optimization results in a more robust decision that effectively mitigates the risks posed by future uncertain demand conditions. In conclusion, the findings highlight the viability of marine energy for providing a resilient, comprehensive energy solution to coastal communities.
Capacity planning↗