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

•Reformulation of individual and joint chance constraints using kernel smoothing.•Method to calculate the divergence tolerance based on kernel smoothing estimation.•Initialization scheme for joint chance-constrained problems.•Application in production planning with variability in production rates. W...

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Bibliographic Details
Published in:Computers & chemical engineering Vol. 78; pp. 51 - 69
Main Authors: Calfa, B.A., Grossmann, I.E., Agarwal, A., Bury, S.J., Wassick, J.M.
Format: Journal Article
Language:English
Published: Elsevier Ltd 12.07.2015
Subjects:
Confidence
Data-driven chance constraint
Density
Distribution functions
Estimates
Kernel smoothing
Kernels
Mathematical models
Optimization
Process systems engineering
Smoothing
ϕ-Divergence
Data-driven chance constraint
90C90
90C15
ϕ-Divergence
Process systems engineering
Kernel smoothing
ISSN:0098-1354, 1873-4375
Online Access:Get full text
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Summary:•Reformulation of individual and joint chance constraints using kernel smoothing.•Method to calculate the divergence tolerance based on kernel smoothing estimation.•Initialization scheme for joint chance-constrained problems.•Application in production planning with variability in production rates. We propose a data-driven, nonparametric approach to reformulate (conditional) individual and joint chance constraints with right-hand side uncertainty into algebraic constraints. The approach consists of using kernel smoothing to approximate unknown true continuous probability density/distribution functions. Given historical data for continuous univariate or multivariate random variables (uncertain parameters in an optimization model), the inverse cumulative distribution function (quantile function) and the joint cumulative distribution function are estimated for the univariate and multivariate cases, respectively. The approach relies on the construction of a confidence set that contains the unknown true distribution. The distance between the true distribution and its estimate is modeled via ϕ-divergences. We propose a new way of specifying the size of the confidence set (i.e., the ϕ-divergence tolerance) based on point-wise standard errors of the smoothing estimates. The approach is illustrated with a motivating and an industrial production planning problem with uncertain plant production rates.
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ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2015.04.012