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DOE OSTI2022

A hybrid robust-stochastic optimization approach for day-ahead scheduling of cascaded hydroelectric system in restructured electricity market

Uncertainties arising from complicated natural and market environments pose great challenges for the efficient operation of cascaded hydroelectric systems. To overcome these challenges, this paper studies the day-ahead scheduling of cascaded hydroelectric systems in a restructured electricity market with the presence of uncertainties in electricity price and natural water inflow. To properly model the uncertainty, we consider the unique characteristics of these two types of uncertainties and capture them via the uncertainty set and stochastic scenarios, respectively. Further, a hybrid robust-stochastic optimization model is developed to simultaneously hedge against these two types of uncertainties, which is formulated as a large-scale non-convex optimization problem with mixed integer recourse. After introducing linearization of nonlinear terms, a tailored hybrid decomposition scheme combining Lagrangian relaxation and Dantzig-Wolfe decomposition is adopted to achieve efficient computation of the proposed model. Two real-world cases are conducted to demonstrate the capability and characteristics of the proposed model and algorithms.

13 HYDRO ENERGY↗

DOE OSTI2024

A Framework for the Optimization of Water Treatment Processes Under Uncertainty Assessed through Process Operability

Conference presentation conveying work conducted on developing a framework for the optimization of water treatment processes after applying robust optimization and process operability tools. The objective of this framework is to optimize treatment processes under the uncertainty of source water conditions. This work contributes to robust optimization and process operability methodologies, allowing for the extension of probability from statistical models to operability calculations.

Barber, Hunter↗

DOE OSTI2016

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total cost of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2015

Robust PET-guided intensity-modulated radiation therapy

Purpose: Functional image guided intensity-modulated radiation therapy has the potential to improve cancer treatment quality by basing treatment parameters such as heterogeneous dose distributions information derived from imaging. However, such heterogeneous dose distributions are subject to imaging uncertainty. In this paper, the authors develop a robust optimization model to design plans that are desensitized to imaging uncertainty. Methods: Starting from the pretreatment fluorodeoxyglucose-positron emission tomography scans, the authors use the raw voxel standard uptake values (SUVs) as input into a series of intermediate functions to transform the SUV into a desired dose. The calculated desired doses were used as an input into a robust optimization model to generate beamlet intensities. For each voxel, the authors assume that the true SUV cannot be observed but instead resides in an interval centered on the nominal (i.e., observed) SUV. Then the authors evaluated the nominal and robust solutions through a simulation study. The simulation considered the effect of the true SUV being different from the nominal SUV on the quality of the treatment plan. Treatment plans were compared on the metrics of objective function value and tumor control probability (TCP). Results: Computational results demonstrate the potential for improvements in tumor control probability and deviation from the desired dose distribution compared to a nonrobust model while maintaining acceptable tissue dose. Conclusions: Robust optimization can help design treatment plans that are more stable in the presence of image value uncertainties.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Controlling risk and demand ambiguity in newsvendor models

We use distributionally robust optimization (DRO) to model a general class of newsvendor problems with unknown demand distribution. The goal is to find an order quantity that minimizes the worst-case expected cost among an ambiguity set of distributions. The ambiguity set consists of those distributions that are not far—in the sense of the total variation distance—from a nominal distribution. The maximum distance allowed in the ambiguity set (called level of robustness) places the DRO between the risk-neutral stochastic programming and robust optimization models. An important problem a decision maker faces is how to determine the level of robustness—or, equivalently, how to find an appropriate level of risk-aversion. We answer this question in two ways. Our first approach relates the level of robustness and risk to the regions of demand that are critical (in a precise sense we introduce) to the optimal cost. Our second approach establishes new quantitative relationships between the DRO model and the corresponding risk-neutral and classical robust optimization models. To achieve these goals, we first focus on a single-product setting and derive explicit formulas and properties of the optimal solution as a function of the level of robustness. Then, we demonstrate the practical and managerial relevance of our results by applying our findings to a healthcare problem to reserve operating room time for cardiovascular surgeries. Finally, we extend some of our results to the multi-product setting and illustrate them numerically.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2017

Robust optimisation-based microgrid scheduling with islanding constraints

This paper proposes a robust optimization based optimal scheduling model for microgrid operation considering constraints of islanding capability. Our objective is to minimize the total operation cost, including generation cost and spinning reserve cost of local resources as well as purchasing cost of energy from the main grid. In order to ensure the resiliency of a microgrid and improve the reliability of the local electricity supply, the microgrid is required to maintain enough spinning reserve (both up and down) to meet local demand and accommodate local renewable generation when the supply of power from the main grid is interrupted suddenly, i.e., microgrid transitions from grid-connected into islanded mode. Prevailing operational uncertainties in renewable energy resources and load are considered and captured using a robust optimization method. With proper robust level, the solution of the proposed scheduling model ensures successful islanding of the microgrid with minimum load curtailment and guarantees robustness against all possible realizations of the modeled operational uncertainties. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator and a battery demonstrate the effectiveness of the proposed scheduling model.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2021

Robust vehicle routing under uncertainty via branch-price-and-cut

Here, this paper contemplates how branch-price-and-cut solvers can be employed along with the robust optimization paradigm to address parametric uncertainty in the context of vehicle routing problems. In this setting, given postulated uncertainty sets for customer demands and vehicle travel times, one aims to identify a set of cost-effective routes for vehicles to traverse, such that the vehicle capacities and customer time window constraints are respected under any anticipated demand and travel time realization, respectively. To tackle such problems, we propose a novel approach that combines cutting-plane techniques with an advanced branch-price-and-cut algorithm. Specifically, we use deterministic pricing procedures to generate "partially robust" vehicle routes and then utilize robust versions of rounded capacity inequalities and infeasible path elimination constraints to guarantee complete robust feasibility of routing designs against demand and travel time uncertainty. In contrast to recent approaches that modify the pricing algorithm, our approach is both modular and versatile. It permits the use of advanced branch-price-and-cut technologies without significant modification, while it can admit a variety of uncertainty sets that are commonly used in robust optimization but could not be previously employed in a branch-price-and-cut setting.

42 ENGINEERING↗

DOE OSTI2016

SU-F-T-205: Effectiveness of Robust Treatment Planning to Account for Inter- Fractional Variation in Intensity Modulated Proton Therapy for Head Neck Cancer

Purpose: To evaluate the potential benefits of robust optimization in intensity modulated proton therapy(IMPT) treatment planning to account for inter-fractional variation for Head Neck Cancer(HNC). Methods: One patient with bilateral HNC previous treated at our institution was used in this study. Ten daily CBCTs were selected. The CT numbers of the CBCTs were corrected by mapping the CT numbers from simulation CT via Deformable Image Registration. The planning target volumes(PTVs) were defined by a 3mm expansion from clinical target volumes(CTVs). The prescription was 70Gy, 54Gy to CTV1, CTV2, and PTV1, PTV2 for robust optimized(RO) and conventionally optimized(CO) plans respectively. Both techniques were generated by RayStation with the same beam angles: two anterior oblique and two posterior oblique angles. The similar dose constraints were used to achieve 99% of CTV1 received 100% prescription dose while kept the hotspots less than 110% of the prescription. In order to evaluate the dosimetric result through the course of treatment, the contours were deformed from simulation CT to daily CBCTs, modified, and approved by a radiation oncologist. The initial plan on the simulation CT was re-replayed on the daily CBCTs followed the bony alignment. The target coverage was evaluated using the daily doses and the cumulative dose. Results: Eight of 10 daily deliveries with using RO plan achieved at least 95% prescription dose to CTV1 and CTV2, while still kept maximum hotspot less than 112% of prescription compared with only one of 10 for the CO plan to achieve the same standards. For the cumulative doses, the target coverage for both RO and CO plans was quite similar, which was due to the compensation of cold and hot spots. Conclusion: Robust optimization can be effectively applied to compensate for target dose deficit caused by inter-fractional target geometric variation in IMPT treatment planning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Designing a Robust MEA-Based Post-Combustion Carbon Capture Process with Capture Rate Guarantees

This work presents an application of the nonlinear two-stage robust optimization solver PyROS to the model-based design and operation of a monoethanolamine scrubbing process for CO2 capture under epistemic uncertainty. Through this application, risk-averse process designs are successfully obtained for CO2 capture targets ranging from 90% to over 99%. In particular, the risk-averse solutions for CO2 capture targets of up to 98% are shown to be only marginally more expensive than their nominally optimal counterparts. Thus, the results demonstrate the utility of recently developed nonlinear robust optimization approaches for the solution of large-scale chemical process models under uncertainty.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2018

Coordination of Wind Farm and Pumped-Storage Hydro for a Self-Healing Power Grid

The increasing penetration of wind energy poses great challenges to the operation of power systems in normal and emergency states. However, energy storage technologies can help accommodate wind power uncertainty and variability due to their flexible characteristics. This paper focuses on the restoration phase, and provides a novel coordination strategy of wind and pumped-storage hydro (PSH) units for a faster and reliable self-healing process. The wind-PSH assisted power system restoration is formulated as a two-stage adaptive robust optimization problem. The first-stage problem determines the start-up sequence of generators and the energization times of transmission paths; and the second-stage problem decides load pickup sequences, wind power dispatch levels, and PSH units' operating modes. The column-and-constraint generation decomposition algorithm is applied to solve the two-stage adaptive robust optimization problem, which has a mixed-integer optimization in the inner-level problem. The developed coordination strategy is tested on the modified IEEE 39-bus system. Numerical results demonstrate that the coordinated wind and PSH units can increase the total energy served, enhance wind power dispatchability, and reduce wind power curtailment.

17 WIND ENERGY↗

DOE OSTI2022

Distributionally Robust Decision Making Leveraging Conditional Distributions

Distributionally robust optimization (DRO) is a powerful tool for decision making under uncertainty. It is particularly appealing because of its ability to leverage existing data. However, many practical problems call for decision-making with some auxiliary information, and DRO in the context of conditional distributions is not straightforward. We propose a conditional kernel distributionally robust optimization (CKDRO) method that enables robust decision making under conditional distributions through kernel DRO and the conditional mean operator in the reproducing kernel Hilbert space (RKHS). In particular, we consider problems where there is a correlation between the unknown variable y and an auxiliary observable variable x. Given past data of the two variables and a queried auxiliary variable, CKDRO represents the conditional distribution P(y|x) as the conditional mean operator in the RKHS space and quantifies the ambiguity set in the RKHS as well, which depends on the size of the dataset as well as the query point. To justify the use of RKHS, we demonstrate that the ambiguity set defined in RKHS can be viewed as a ball under a metric that is similar to the Wasserstein metric. The DRO is then dualized and solved via a finite dimensional convex program. The proposed CKDRO approach is applied to a generation scheduling problem and shows that the result of CKDRO is superior to common benchmarks in terms of quality and robustness.

Chen, Yuxiao↗

DOE OSTI2024

Optimal and robust reconstruction of BAO, redshift-space distortions and the Alcock-Paczynski effect

The goal of this project is to optimally reconstruct cosmological information that has been lost from large-scale clustering of galaxies due to cosmic structure growth. The outcome of our research will be used to improve dark energy and other cosmological constraints from the ongoing extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the upcoming Dark Energy Spectroscopic Instrument (DESI). The large-scale galaxy clustering data contain two important features: the Baryon Acoustic Oscillations (BAO) and the overall shape from small to large scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

NUHOMS{sup R} EOS (Extended Optimized Storage): Robust, Advanced, and Dual Purpose Dry Storage System - 16472

AREVA TN has completed the design, analysis, and US NRC license submittal for the NUHOMS{sup R} Extended Optimized Storage (EOS) system. NUHOMS{sup R} EOS offers a large capacity and high heat load dry storage and transportation solution for UNF. EOS is not a new system, but an evolution of the already-proven safe and low-risk horizontal NUHOMS{sup R} storage system, which is one of the most widely used UNF dry storage systems in the United States. The EOS system features a 37PTH dry shielded canister (DSC) for 37 PWR UNF assemblies and an 89BTH DSC for the 89 BWR UNF assemblies. The EOS DSCs will be stored inside a horizontal storage module (HSM) that is a robust, fortress-like concrete storage overpack. Designed with the lessons learned from the Fukushima event in Japan in mind, EOS has robust margins for beyond design basis (BDB) events and offers the lowest risk and highest safety margin of any dry storage system design for recovery from BDB events. EOS also offers innovative aging management features with an aging management program (AMP) to assure safe and low dose long-term storage at the utility sites. EOS incorporates ports for AMP inspections and offers the option of using duplex stainless steel (DSS) for the DSC shell in order to negate corrosion issues. EOS is stored horizontally and above ground, making it easy and quick to access for visual inspection, monitoring, and mitigating actions during AMP. NUHOMS{sup R} EOS is optimized for high capacity, high burnup, high enrichments, and very low cooling times for UNF assemblies. It enables the highest heat load per canister (50 kW) and low dose rates. Even with high heat loads, EOS has significant margins to design basis limits. As the future of used fuel disposition will require the need to move fuel off-site to interim or consolidated storage, EOS is the ideal solution as it enables on-site loading and unloading operations that mitigate risk when transferring fuel on-site or transporting fuel off-site. The EOS design can be safely located in a traditional outdoor setting with fortress-like concrete reinforced modules that offer superior resistance to attack or can be safely operated inside of a building enclosure for those utilities desiring a more discreet siting for its used fuel storage systems. EOS has an innovative basket design that is made of high strength low alloy (HSLA) material and is easy to fabricate due to its non-welded design. Its innovative inlet and outlet air vent design, which incorporates dose reduction hardware, allows for optimal ambient airflow for highly efficient heat transfer with minimal radiation dose. The NUHOMS{sup R} EOS storage modules are interlocked in a side-by-side configuration offering superior and robust seismic performance. The license application for NUHOMS{sup R} EOS is currently under US NRC review and this system will be available for deployment in 2017. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Designing Operationally Flexible Diafiltration Membrane Systems for Critical Mineral Separations

This talk presents the design of operationally flexible diafiltration membrane systems for Li/Co recovery, and applies robust optimization methodologies using these flexible systems to generate optimal designs immune to membrane manufacturing variability and uncertain process inlet conditions. The results highlight the use of robust optimization to find design strategies and insights that may reduce technical risks arising from model uncertainties.

Yao, Jason↗

DOE OSTI2024

Treatment and Mineral Recovery from Combustion Residual Leachate and Produced Water

Able, Chad↗

DOE OSTI2017

Testing the robustness of optimal access vessel fleet selection for operation and maintenance of offshore wind farms

Optimising the operation and maintenance (O&M) and logistics strategy of offshore wind farms implies the decision problem of selecting the vessel fleet for O&M. Different strategic decision support tools can be applied to this problem, but much uncertainty remains regarding both input data and modelling assumptions. Our paper aims to investigate and ultimately reduce this uncertainty by comparing four simulation tools, one mathematical optimisation tool and one analytic spreadsheet-based tool applied to select the O&M access vessel fleet that minimizes the total O&M cost of a reference wind farm. The comparison shows that the tools generally agree on the optimal vessel fleet, but only partially agree on the relative ranking of the different vessel fleets in terms of total O&M cost. The robustness of the vessel fleet selection to various input data assumptions was tested, and the ranking was found to be particularly sensitive to the vessels' limiting significant wave height for turbine access. Also the parameter with the greatest discrepancy between the tools, implies that accurate quantification and modelling of this parameter is crucial. The ranking is moderately sensitive to turbine failure rates and vessel day rates but less sensitive to electricity price and vessel transit speed.

17 WIND ENERGY↗

DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗