Data-driven individual and joint chance-constrained optimization via kernel smoothing

Calfa, Bruno A.; Grossmann, Ignacio E.; Agarwal, Anshul; Bury, Scott J.; Wassick, John M.

doi:10.1016/j.compchemeng.2015.04.012

Cited by 62 publications

(63 citation statements)

References 20 publications

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“…This method can become computationally difficult as the dimensions of the problem grow. Another method applies kernel density estimators (KDEs) to the samples to obtain a nonlinear approximation of the chance constraint 32,33 . KDEs result in a nonlinear constraint that becomes increasingly less conservative relative to the chance constraint as the number of samples grows, but have the disadvantage of potentially violating the bounds of the chance constraint unlike the method of References 26‐28.…”

Section: Introductionmentioning

confidence: 99%

Method for solving chance constrained optimal control problems using biased kernel density estimators

Keil

Miller

Kumar³

et al. 2020

Optim Control Appl Methods

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SummaryA method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation transforms the chance constrained optimal control problem into a deterministic optimal control problem that can be solved numerically. The new method developed in this paper approximates the chance constraints using Markov Chain Monte Carlo sampling and kernel density estimators whose kernels have integral functions that bound the indicator function. The nonlinear constraints resulting from the application of kernel density estimators are designed with bounds that do not violate the bounds of the original chance constraint. The method is tested on a nontrivial chance constrained modification of a soft lunar landing optimal control problem and the results are compared with results obtained using a conservative deterministic formulation of the optimal control problem. Additionally, the method is tested on a complex chance constrained unmanned aerial vehicle problem. The results show that this new method can be used to reliably solve chance constrained optimal control problems.

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Section: Introductionmentioning

confidence: 99%

Method for solving chance constrained optimal control problems using biased kernel density estimators

Keil

Miller

Kumar³

et al. 2020

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…Reliability-based design is of crucial importance in engineering design. Hence, numerous methods have been proposed to systematically treat uncertainties in product design and carry out stochastic [8][9][10][11] or reliability-based [12] design optimization [13][14][15]. Stochastic methodology has already been applied in powertrain development.…”

Section: Introductionmentioning

confidence: 99%

A stochastic design optimization methodology to reduce emission spread in combustion engines

Mourat

Eckstein

Koch

2020

Automot. Engine Technol.

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This paper introduces a method for efficiently solving stochastic optimization problems in the field of engine calibration. The main objective is to make more conscious decisions during the base engine calibration process by considering the system uncertainty due to component tolerances and thus enabling more robust design, low emissions, and avoiding expensive recalibration steps that generate costs and possibly postpone the start of production. The main idea behind the approach is to optimize the design parameters of the engine control unit (ECU) that are subject to uncertainty by considering the resulting output uncertainty. The premise is that a model of the system under study exists, which can be evaluated cheaply, and the system tolerance is known. Furthermore, it is essential that the stochastic optimization problem can be formulated such that the objective function and the constraint functions can be expressed using proper metrics such as the value at risk (VaR). The main idea is to derive analytically closed formulations for the VaR, which are cheap to evaluate and thus reduce the computational effort of evaluating the objective and constraints. The VaR is therefore learned as a function of the input parameters of the initial model using a supervised learning algorithm. For this work, we employ Gaussian process regression models. To illustrate the benefits of the approach, it is applied to a representative engine calibration problem. The results show a significant improvement in emissions compared to the deterministic setting, where the optimization problem is constructed using safety coefficients. We also show that the computation time is comparable to the deterministic setting and is orders of magnitude less than solving the problem using the Monte-Carlo or quasi-Monte-Carlo method.

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“…This is typically more appropriate for short-term scheduling problems where feasibility is a major concern and where there is little scope for corrective action . Chance-constrained optimization also has a similar emphasis on constraint feasibility; specifically, some of the constraints must be satisfied with at least a given level of probability for all possible outcomes of the uncertain parameters present in those respective constraints (Calfa et al, 2015). As our intended applications are long-term planning problems in which corrective action is essential and probabilistic constraints are not required, we focus on a stochastic programming framework to effectively hedge against parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties

Apap

Grossmann

2017

Computers & Chemical Engineering

102

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This dissertation addresses the modeling and solution of mixed-integer linear multistage stochastic programming problems involving both endogenous and exogenous uncertain parameters. We propose a composite scenario tree that captures both types of uncertainty, and we exploit its unique structure to derive new theoretical properties that can drastically reduce the number of non-anticipativity constraints (NACs). Since the reduced model is often still intractable, we discuss two special solution approaches. The first is a sequential scenario decomposition heuristic in which we sequentially solve endogenous MILP subproblems to determine the binary investment decisions, fix these decisions to satisfy the first-period and exogenous NACs, and then solve the resulting model to obtain a feasible solution. The second approach is Lagrangean decomposition. We present numerical results for a process network planning problem and an oilfield development planning problem. The results clearly demonstrate the efficiency of the special solution methods over solving the reduced model directly. To further generalize this work, we also propose a graph-theory algorithm for non-anticipativity constraint reduction in problems with arbitrary scenario sets. Finally, in a break from the rest of the thesis, we present the basics of stochastic programming for non-expert users.

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Data-driven individual and joint chance-constrained optimization via kernel smoothing

Cited by 62 publications

References 20 publications

Method for solving chance constrained optimal control problems using biased kernel density estimators

Method for solving chance constrained optimal control problems using biased kernel density estimators

A stochastic design optimization methodology to reduce emission spread in combustion engines

Models and computational strategies for multistage stochastic programming under endogenous and exogenous uncertainties

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