Distributionally robust optimization with correlated data from vector autoregressive processes
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Dou, Xialiang↗
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Results for “Stochastic optimization”
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Efficient Parameterization of Density Functional Tight-Binding for 5 f -Elements: A Th–O Case Study
Density functional tight binding (DFTB) models for f-element species are challenging to parametrize owing to the large number of adjustable parameters. The explicit optimization of the terms entering the semiempirical DFTB Hamiltonian related to f orbitals is crucial to generating a reliable parametrization for f-block elements, because they play import roles in bonding interactions. However, since the number of parameters grows quadratically with the number of orbitals, the computational cost for parameter optimization is much more expensive for the f-elements than for the main group elements. In this work we present a set of efficient approaches for mitigating the hurdle imposed by the large size of the parameter space. A novel group-by-orbital correction functions for two-center bond integrals was developed. With this approach the number of parameters is reduced, and it grows linearly with the number of elements, maintaining the accuracy and the number of parameters, in the case of f elements, by more than 40%. The parameter optimization step was accelerated by means of the mini-batch BFGS method. This method allows parameter optimizations with much larger training sets than other single batch methods. A stochastic optimizer was employed that helped overcome shallow local minima in the objective function. The proposed algorithm was used to parametrize the DFTB Hamiltonian for the Th–O system, which was subsequently applied to the study of ThO 2 nanoparticles. The training set consisted of 6322 unique structures, which is barely feasible with conventional optimization methods. The optimized parameter set, LANL-ThO, displays good agreement with DFT-calculated properties such as energies, forces, and structures for both clusters and bulk ThO 2 . Benefiting from the fewer number of parameters and lower computational costs for objective function evaluations, this new approach shows its potential applications in DFTB parametrization for elements with high angular momentum, which present a challenge to conventional methods.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Variational design principles for nonequilibrium colloidal assembly
Using large deviation theory and principles of stochastic optimal control, we show that rare molecular dynamics trajectories conditioned on assembling a specific target structure encode a set of interactions and external forces that lead to enhanced stability of that structure. Such a relationship can be formulated into a variational principle, for which we have developed an associated optimization algorithm and have used it to determine optimal forces for targeted self-assembly within nonequilibrium steady-states. We illustrate this perspective on inverse design in a model of colloidal cluster assembly within linear shear flow. We find that colloidal clusters can be assembled with high yield using specific short-range interactions of tunable complexity. Shear decreases the yields of rigid clusters, while small values of shear increase the yields of nonrigid clusters. The enhancement or suppression of the yield due to shear is rationalized with a generalized linear response theory. Furthermore, by studying 21 unique clusters made of six, seven, or eight particles, we uncover basic design principles for targeted assembly out of equilibrium.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Stochastic Methods Applied to Power System Operations with Renewable Energy: A Review
Renewable energy resources have been rapidly integrated into power systems in many parts of the world, contributing to a cleaner and more sustainable supply of electricity. Wind and solar resources also introduce new challenges for system operations and planning in terms of economics and reliability because of their variability and uncertainty. Operational strategies based on stochastic optimization have been developed recently to address these challenges. In general terms, these stochastic strategies either embed uncertainties into the scheduling formulations (e.g., the unit commitment [UC] problem) in probabilistic forms or develop more appropriate operating reserve strategies to take advantage of advanced forecasting techniques. Other approaches to address uncertainty are also proposed, where operational feasibility is ensured within an uncertainty set of forecasting intervals. In this report, a comprehensive review is conducted to present the state of the art through Spring 2015 in the area of stochastic methods applied to power system operations with high penetration of renewable energy. Chapters 1 and 2 give a brief introduction and overview of power system and electricity market operations, as well as the impact of renewable energy and how this impact is typically considered in modeling tools. Chapter 3 reviews relevant literature on operating reserves and specifically probabilistic methods to estimate the need for system reserve requirements. Chapter 4 looks at stochastic programming formulations of the UC and economic dispatch (ED) problems, highlighting benefits reported in the literature as well as recent industry developments. Chapter 5 briefly introduces alternative formulations of UC under uncertainty, such as robust, chance-constrained, and interval programming. Finally, in Chapter 6, we conclude with the main observations from our review and important directions for future work.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Optimal mitigation and control over power system dynamics for stochastic grid resilience
Optimal mitigation planning for highly disruptive contingencies to a transmission-level power system requires optimization with dynamic power system constraints, due to the key role of dynamics in system stability to major perturbations. We formulate a generalized disjunctive program to determine optimal grid component hardening choices for protecting against major failures, with differential algebraic constraints representing system dynamics (specifically, differential equations representing generator and load behavior and algebraic equations representing instantaneous power balance over the transmission system). We optionally allow stochastic optimal pre-positioning across all considered failure scenarios, and optimal emergency control within each scenario. This novel formulation allows, for the first time, analyzing the resilience interdependencies of mitigation planning, preventive control, and emergency control. Using all three strategies in concert is particularly effective at maintaining robust power system operation under severe contingencies, as we demonstrate on the western system coordinating council 9-bus test system using synthetic multi-device outage scenarios.
30 DIRECT ENERGY CONVERSION↗
Reliability-Based Design Optimization of a Composite Airframe Component
A stochastic design optimization methodology (SDO) has been developed to design components of an airframe structure that can be made of metallic and composite materials. The design is obtained as a function of the risk level, or reliability, p. The design method treats uncertainties in load, strength, and material properties as distribution functions, which are defined with mean values and standard deviations. A design constraint or a failure mode is specified as a function of reliability p. Solution to stochastic optimization yields the weight of a structure as a function of reliability p. Optimum weight versus reliability p traced out an inverted-S-shaped graph. The center of the inverted-S graph corresponded to 50 percent (p = 0.5) probability of success. A heavy design with weight approaching infinity could be produced for a near-zero rate of failure that corresponds to unity for reliability p (or p = 1). Weight can be reduced to a small value for the most failure-prone design with a reliability that approaches zero (p = 0). Reliability can be changed for different components of an airframe structure. For example, the landing gear can be designed for a very high reliability, whereas it can be reduced to a small extent for a raked wingtip. The SDO capability is obtained by combining three codes: (1) The MSC/Nastran code was the deterministic analysis tool, (2) The fast probabilistic integrator, or the FPI module of the NESSUS software, was the probabilistic calculator, and (3) NASA Glenn Research Center s optimization testbed CometBoards became the optimizer. The SDO capability requires a finite element structural model, a material model, a load model, and a design model. The stochastic optimization concept is illustrated considering an academic example and a real-life raked wingtip structure of the Boeing 767-400 extended range airliner made of metallic and composite materials.
Patnaik, Surya N.↗
Analytical and experimental performance of optimal controller designs for a supersonic inlet
The techniques of modern optimal control theory were applied to the design of a control system for a supersonic inlet. The inlet control problem was approached as a linear stochastic optimal control problem using as the performance index the expected frequency of unstarts. The details of the formulation of the stochastic inlet control problem are presented. The computational procedures required to obtain optimal controller designs are discussed, and the analytically predicted performance of controllers designed for several different inlet conditions is tabulated. The experimental implementation of the optimal control laws is described, and the experimental results obtained in a supersonic wind tunnel are presented. The control laws were implemented with analog and digital computers. Comparisons are made between the experimental and analytically predicted performance results. Comparisons are also made between the results obtained with continuous analog computer controllers and discrete digital computer versions.
Zeller, J. R.↗
Multiobjective Modular Biorefinery Configuration under Uncertainty
With increasing interest in using biomass as a raw material for fuel, the development of biorefineries is an active area of research. However, increasing market competition, uncertainty, and environmental concerns are a few of the challenges that need to be addressed. In this work, mathematical optimization formulations are proposed to address these challenges simultaneously. A multiobjective deterministic optimization framework is proposed to address economic and environmental objectives. A two-stage stochastic optimization framework is proposed to account for uncertainties in material flow and product yields. To model the environmental objective, an environmental risk metric is proposed. Finally, as modularization is gaining popularity in the process industry due to its ability to save capital cost because of standardization and reduce time to market, a formulation for simultaneously achieving modular process design and biorefinery configuration is proposed. Furthermore, the results demonstrate the efficacy of the proposed approach.
09 BIOMASS FUELS↗
Suboptimal stochastic controller for an n-body spacecraft
The problem is studied of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector, can be easily implemented, and enables system performance to be significantly improved.
Larson, V.↗
A suboptimal stochastic controller for an N-body spacecraft
Considerable attention, in the open literature, is being focused on the problem of developing a suitable set of deterministic dynamical equations for a complex spacecraft. This paper considers the problem of determining a stochastic optimal controller for an n-body spacecraft. The approach used in obtaining the stochastic controller involves the application, interpretation, and combination of advanced dynamical principles and the theoretical aspects of modern control theory. The stochastic controller obtained herein for a complicated model of a spacecraft uses sensor angular measurements associated with the base body to obtain smoothed estimates of the entire state vector. It can be easily implemented, and it enables system performance to be significantly improved.
Larson, V.↗
Data centers as dispatchable loads to harness stranded power
Here, we analyze how traditional data center placement and optimal placement of dispatchable data centers affect power grid efficiency. We use detailed network models, stochastic optimization formulations, and diverse renewable generation scenarios to perform our analysis. Our results reveal that significant spillage and stranded power will persist in power grids as wind power levels are increased. A counter-intuitive finding is that collocating data centers with inflexible loads next to wind farms has limited impacts on renewable portfolio standard (RPS) goals because it provides limited system-level flexibility. Such an approach can, in fact, increase stranded power and fossil-fueled generation. In contrast, optimally placing data centers that are dispatchable provides system-wide flexibility, reduces stranded power, and improves efficiency. In short, optimally placed dispatchable computing loads can enable better scaling to high RPS. In our case study, we find that these dispatchable computing loads are powered to 60-80% of their requested capacity, indicating that there are significant economic incentives provided by stranded power.
97 MATHEMATICS AND COMPUTING↗
WE-AB-303-06: Combining DAO with MV + KV Optimization to Improve Skin Dose Sparing with Real-Time Fluoroscopy
Purpose: Real-time fluoroscopy may allow for improved patient positioning and tumor tracking, particularly in the treatment of lung tumors. In order to mitigate the effects of the imaging dose, previous studies have demonstrated the effect of including both imaging dose and imaging constraints into the inverse treatment planning object function. That method of combined MV+kV optimization may Result in plans with treatment beams chosen to allow for more gentle imaging beam-on times. Direct-aperture optimization (DAO) is also known to produce treatment plans with fluence maps more conducive to lower beam-on times. Therefore, in this work we demonstrate the feasibility of a combination of DAO and MV+kV optimization for further optimized real-time kV imaging. Methods: Therapeutic and imaging beams were modeled in the EGSnrc Monte Carlo environment, and applied to a patient model for a previously treated lung patient to provide dose influence matrices from DOSXYZnrc. An MV + kV IMRT DAO treatment planning system was developed to compare DAO treatment plans with and without MV+kV optimization. The objective function was optimized using simulated annealing. In order to allow for comparisons between different cases of the stochastically optimized plans, the optimization was repeated twenty times. Results: Across twenty optimizations, combined MV+kV IMRT resulted in an average of 12.8% reduction in peak skin dose. Both non-optimized and MV+kV optimized imaging beams delivered, on average, mean dose of approximately 1 cGy per fraction to the target, with peak doses to target of approximately 6 cGy per fraction. Conclusion: When using DAO, MV+kV optimization is shown to Result in improvements to plan quality in terms of skin dose, when compared to the case of MV optimization with non-optimized kV imaging. The combination of DAO and MV+kV optimization may allow for real-time imaging without excessive imaging dose. Financial support for the work has been provided in part by NIH Grant T32 EB002103, ACS RSG-13-313-01-CCE, and NIH S10 RR021039 and P30 CA14599 grants. The contents of this submission do not necessarily represent the official views of any of the supporting organizations.
60 APPLIED LIFE SCIENCES↗
Adaptive Multi-Agent Systems for Constrained Optimization
Product Distribution (PD) theory is a new framework for analyzing and controlling distributed systems. Here we demonstrate its use for distributed stochastic optimization. First we review one motivation of PD theory, as the information-theoretic extension of conventional full-rationality game theory to the case of bounded rational agents. In this extension the equilibrium of the game is the optimizer of a Lagrangian of the (probability distribution of) the joint state of the agents. When the game in question is a team game with constraints, that equilibrium optimizes the expected value of the team game utility, subject to those constraints. The updating of the Lagrange parameters in the Lagrangian can be viewed as a form of automated annealing, that focuses the MAS more and more on the optimal pure strategy. This provides a simple way to map the solution of any constrained optimization problem onto the equilibrium of a Multi-Agent System (MAS). We present computer experiments involving both the Queen s problem and K-SAT validating the predictions of PD theory and its use for off-the-shelf distributed adaptive optimization.
Macready, William↗
A linear stochastic model of the human operator
A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.
Durrett, J. C.↗
An application of different dioids in public key cryptography
Dioids provide a natural framework for analyzing a broad class of discrete event dynamical systems such as the design and analysis of bus and railway timetables, scheduling of high-throughput industrial processes, solution of combinatorial optimization problems, the analysis and improvement of flow systems in communication networks. They have appeared in several branches of mathematics such as functional analysis, optimization, stochastic systems and dynamic programming, tropical geometry, fuzzy logic. In this paper we show how to involve dioids in public key cryptography. The main goal is to create key – exchange protocols based on dioids. Additionally the digital signature scheme is presented.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Storage ring nonlinear dynamics optimization with multi-objective multi-generation Gaussian process optimizer
Nonlinear beam dynamics optimization is essential in a low emittance storage ring design. Multi-objective optimization algorithms are needed in order to simultaneously optimize the dynamic aperture and the momentum aperture. In this study we demonstrate the application of a highly efficient stochastic optimization algorithm, the multi-generation Gaussian process optimizer (MG-GPO), to storage ring nonlinear dynamics optimization by successfully applying the method to the SPEAR3 upgrade lattice. It is shown that the new method, owing to its capability of selecting high rank candidates from a large number of trial solutions, converges significantly faster than the commonly used traditional algorithms, multi-objective genetic algorithms (MOGA) and particle swarm optimization (PSO).
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
On the minimax feedback control of uncertain dynamic systems.
In this paper the problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
Bertsekas, D. P.↗
Sufficiently informative functions and the minimax feedback control of uncertain dynamic systems.
The problem of optimal feedback control of uncertain discrete-time dynamic systems is considered where the uncertain quantities do not have a stochastic description but instead are known to belong to given sets. The problem is converted to a sequential minimax problem and dynamic programming is suggested as a general method for its solution. The notion of a sufficiently informative function, which parallels the notion of a sufficient statistic of stochastic optimal control, is introduced, and conditions under which the optimal controller decomposes into an estimator and an actuator are identified.
Bertsekas, D. P.↗