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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

SPAROW: Stochastic Programming and Related Optimization Workflows

SAND2026-16703O SPAROW: Stochastic Programming and Related Optimization Workflows is a Python library tool that facilitates the development and solution of stochastic programming problems. It provides a user-friendly class structure for defining stochastic programs through scenario-based representations of uncertainties. SPAROW incorporates multiple optimization strategies, including integer programming with all scenarios, progressive hedging, Benders decomposition, and Snoglode, a novel technique developed by Carnegie Mellon University. It also features interfaces to external solvers and functions that are commonly used in analysis workflows, making it applicable to a wide range of scientific and engineering design challenges, particularly in power grid planning. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Hart, William [Sandia National Lab. (SNL-NM), Albu↗
DOE OSTI2026

Quantum Stochastic Programming [SWR-26-040]

The Quantum Stochastic Programming tool contains quantum computing algorithms for two-stage stochastic optimization, with a focus on the Unit Commitment (UC) problem in power systems. The algorithms combine Discrete Quantum Annealing (DQA) with Quantum Amplitude Estimation (QAE) to compute expected-value objective functions over a probability distribution of wind-power scenarios. Based on: arXiv 2402.15029 - "Quantum algorithms for the two-stage stochastic unit commitment problem"

Maack, Jonathan [National Laboratory of the Rockie↗
DOE OSTI2022

A multi-stage stochastic programming model for adaptive biomass processing operation under uncertainty

Variations of physical and chemical characteristics of biomass reduce equipment utilization and increase operational costs of biomass processing. Biomass processing facilities use sensors to monitor the changes in biomass characteristics. Integrating sensory data into the operational decisions in biomass processing will increase its flexibility to the changing biomass conditions. In this paper, we propose a multi-stage stochastic programming model that minimizes the expected operational costs by identifying the initial inventory level and creating an operational decision policy for equipment speed settings. These policies take the sensory information data and the current biomass inventory level as inputs to dynamically adjust inventory levels and equipment settings according to the changes in the biomass' characteristics. We ensure that a prescribed target reactor utilization is consistently achieved by penalizing the violation of the target reactor feeding rate. A case study is developed using real-world data collected at Idaho National Laboratory's biomass processing facility. We show the value of multi-stage stochastic programming from an extensive computational experiment. Our sensitivity analysis indicates that updating the infeed rate of the system, the processing speed of equipment, and bale sequencing based on the moisture level of biomass improves the processing rate of the reactor and reduces operating costs.

09 BIOMASS FUELS↗
DOE OSTI2023

Projective Hedging Algorithms for Multistage Stochastic Programming, Supporting Distributed and Asynchronous Implementation

Here we propose a decomposition algorithm for multistage stochastic programming that resembles the progressive hedging method of Rockafellar and Wets but is provably capable of several forms of asynchronous operation. We derive the method from a class of projective operator splitting methods fairly recently proposed by Combettes and Eckstein, significantly expanding the known applications of those methods. Our derivation assures convergence for convex problems whose feasible set is compact, subject to some standard regularity conditions and a mild “fairness” condition on subproblem selection. The method’s convergence guarantees are deterministic and do not require randomization, in contrast to other proposed asynchronous variations of progressive hedging. Computational experiments described in an online appendix show the method to outperform progressive hedging on large-scale problems in a highly parallel computing environment.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Two-Stage Stochastic Programming Approach for the Design of Renewable Ammonia Supply Chain Networks

This work considers the incorporation of renewable ammonia manufacturing sites into existing ammonia supply chain networks while accounting for ammonia price uncertainty from existing producers. We propose a two-stage stochastic programming approach to determine the optimal investment decisions such that the ammonia demand is satisfied and the net present cost is minimized. We apply the proposed approach to a case study considering deploying in-state renewable ammonia manufacturing in Minnesota’s supply chain network. We find that accounting for price uncertainty leads to supply chains with more ammonia demand met via renewable production and thus lower costs from importing ammonia from existing producers. These results show that the in-state renewable production of ammonia can act as a hedge against the volatility of the conventional ammonia market.

Mitrai, Ilias (ORCID:0000000289896864)↗
DOE OSTI2023

Airport Infrastructure Planning Using Multi-Stage Stochastic Programming

The Athena project, funded by the Department of Energy, has worked to identify the critical infrastructure at Dallas Fort Worth (DFW) Airport which influences mobility between the airport and the surrounding city of Dallas. Using scalable methods that can leverage HPC resources we have developed a multi-stage stochastic infrastructure expansion model for determining parking and curb modifications to the DFW Airport over a 20-year horizon. Additionally, we have explored the impacts of congestion pricing in conjunction with infrastructure modifications. Our multi-stage stochastic model is implemented using the mpi-sppy software and solved in parallel using progressive hedging on the National Renewable Energy Laboratory's HPC system Eagle. In this talk we present results from solving this model at scale.

airport planning↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASA's Dawn mission. The Dawn trajectory was designed with the DDP-based Static/Dynamic Optimal Control algorithm used in the Mystic software.1 Another recently developed method, Hybrid Differential Dynamic Programming (HDDP),2, 3 is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS2016

Hybrid Differential Dynamic Programming with Stochastic Search

Differential dynamic programming (DDP) has been demonstrated as a viable approach to low-thrust trajectory optimization, namely with the recent success of NASAs Dawn mission. The Dawn trajectory was designed with the DDP-based Static Dynamic Optimal Control algorithm used in the Mystic software. Another recently developed method, Hybrid Differential Dynamic Programming (HDDP) is a variant of the standard DDP formulation that leverages both first-order and second-order state transition matrices in addition to nonlinear programming (NLP) techniques. Areas of improvement over standard DDP include constraint handling, convergence properties, continuous dynamics, and multi-phase capability. DDP is a gradient based method and will converge to a solution nearby an initial guess. In this study, monotonic basin hopping (MBH) is employed as a stochastic search method to overcome this limitation, by augmenting the HDDP algorithm for a wider search of the solution space.

Aziz, Jonathan↗
NASA NTRS2010

Automated Flight Routing Using Stochastic Dynamic Programming

Airspace capacity reduction due to convective weather impedes air traffic flows and causes traffic congestion. This study presents an algorithm that reroutes flights in the presence of winds, enroute convective weather, and congested airspace based on stochastic dynamic programming. A stochastic disturbance model incorporates into the reroute design process the capacity uncertainty. A trajectory-based airspace demand model is employed for calculating current and future airspace demand. The optimal routes minimize the total expected traveling time, weather incursion, and induced congestion costs. They are compared to weather-avoidance routes calculated using deterministic dynamic programming. The stochastic reroutes have smaller deviation probability than the deterministic counterpart when both reroutes have similar total flight distance. The stochastic rerouting algorithm takes into account all convective weather fields with all severity levels while the deterministic algorithm only accounts for convective weather systems exceeding a specified level of severity. When the stochastic reroutes are compared to the actual flight routes, they have similar total flight time, and both have about 1% of travel time crossing congested enroute sectors on average. The actual flight routes induce slightly less traffic congestion than the stochastic reroutes but intercept more severe convective weather.

Ng, Hok K.↗
DOE OSTI2025

The Optical Stochastic Cooling Program at Fermilab

Recently, Optical Stochastic Cooling (OSC) became the first demonstrated method for ultra-high-bandwidth stochastic cooling. The initial experiments at Fermilab’s IOTA ring explored the essential physics of the method and demonstrated cooling, heating and manipulation of beams and single particles. Having been validated in practice, with continued development, OSC carries the potential for dramatic advances in the state-of-the-art performance and flexibility for beam cooling and control. The ongoing program at Fermilab is now focused on the development of an OSC system that includes high-gain optical amplification, which promises a two-order-of-magnitude increase in the strength of the OSC force. Here we review the progress and plans for the amplified OSC program. This includes detailed lattice designs and tracking simulations for the various experimental configurations, designs and status for the various hardware systems, and near-term operational plans and use cases.

Jarvis, J. [Fermilab]↗
DOE OSTI2024

Progressive Hedging Decomposition for Solutions of Large-Scale Process Family Design Problems

In previous work, we have introduced a mathematical model for solving a discretized version of the process family design problem. This involves two sets of decision variables. One set selects which unit module designs are included in the process platform out of a candidate set of options; the other set determines which of these unit module designs are assigned to each variant. In this work, we exploit a parallelized Progressive Hedging (PH) algorithm to solve even larger scale design problems. PH is a well-known algorithm traditionally used to solve stochastic programming problems. While our problem is not a two-stage stochastic programming problem, the structure is similar, and it can be directly mapped to the PH approach, which we employ here to solve this deterministic optimization problem. We decompose our problem by process variant. We treat the platform unit module design variables as first-stage and the assignment of unit module designs to variants as second-stage, solving the problem using mpi-sppy. We demonstrate this approach on case studies of CC, water desalination, and refrigeration.

Stinchfield, Georgia↗
DOE OSTI2023

A parallel hub-and-spoke system for large-scale scenario-based optimization under uncertainty

Practical solution of stochastic programming problems generally requires the use of parallel computing resources. Here, we describe the open source package mpi-sppy, in which efficient and scalable parallelization is a central feature. We report computational experiments that demonstrate the ability to solve very large stochastic programming problems - including mixed-integer variants - in minutes of wall clock time, efficiently leveraging significant parallel computing resources. We report results for the largest publicly available instances of stochastic mixed-integer unit commitment problems, solving to provably tight optimality gaps. In addition, we introduce a novel software architecture that facilitates combinations of methods for accelerating convergence that can be combined in plug-and-play manner. Finally, the mpi-sppy package is written in Python, leverages the widely used Pyomo (http://www.pyomo.org) library for modeling mathematical programs, builds on existing MPI implementations to ensure efficiency and scalability, and is available via http://github.com/Pyomo/mpi-sppy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

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↗
DOE OSTI2025

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↗
DOE OSTI2022

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↗
DOE OSTI2023

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↗