Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Ning, Chao; You, Fengqi

doi:10.1016/j.compchemeng.2019.03.034

Cited by 262 publications

(104 citation statements)

References 216 publications

(270 reference statements)

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“…18 Stochastic programming (SP), as another popular mathematical optimization approach, optimizes the expected value of the cost function, 19,20 based on the exact distribution of the disturbance and thus does not incorporate distribution ambiguity into the calculation. 10,21 However, the actual distribution of the random variables is typically unknown, 22 and hence some Monte Carlo sampling approaches have to be adopted for approximation. 23 For example, sample average approximation (SAA) method is widely utilized to estimate the expectation of the measure through empirical mean of historical data.…”

Section: Introductionmentioning

confidence: 99%

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Lee

You

2020

AIChE Journal

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This article proposes a novel distributionally robust optimization (DRO)‐based soft‐constrained model predictive control (MPC) framework to explicitly hedge against unknown external input terms in a linear state‐space system. Without a priori knowledge of the exact uncertainty distribution, this framework works with a lifted ambiguity set constructed using machine learning to incorporate the first‐order moment information. By adopting a linear performance measure and considering input and state constraints robustly with respect to a lifted support set, the DRO‐based MPC is reformulated as a robust optimization problem. The constraints are softened to ensure recursive feasibility. Theoretical results on optimality, feasibility, and stability are further discussed. Performance and computational efficiency of the proposed method are illustrated through motion control and building energy control systems, showing 18.3% less cost and 78.8% less constraint violations, respectively, while requiring one third of the CPU time compared to multi‐stage scenario based stochastic MPC.

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Section: Introductionmentioning

confidence: 99%

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Lee

You

2020

AIChE Journal

Self Cite

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“…This kind of long-term analysis allows capturing the irregularities in the patterns of weather conditions, habits of consumption, and other key variables, a thing that cannot be achieved by forecasting in the short-term. Recently, several statistical techniques have been employed to address this issue, one of the most prominent ones being stochastic programming [5]. Stochastic programming takes into account a variety of scenarios, characterized by a distribution of probability.…”

Section: Context and Definitionsmentioning

confidence: 99%

A Comprehensive Model for the Design of a Microgrid under Regulatory Constraints Using Synthetical Data Generation and Stochastic Optimization

et al. 2020

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As renewable energy installation costs decrease and environmentally-friendly policies are progressively applied in many countries, distributed generation has emerged as the new archetype of energy generation and distribution. The design and economic feasibility of distributed generation systems is constrained by the operation of the microgrid, which has to consider the uncertainty of renewable energy sources, consumption habits and electricity market prices. In this paper, a mathematical model intended to optimize the design and economic feasibility of a microgrid is proposed. After a search in the state-of-the-art, weaknesses and strengths of existing models have been identified and taken into account for building the present model. The present model should be seen as a basis on which other models can be built upon, hence a complete definition of the different sub-models is stated: uncertainty modelling, optimization technique, physical constraints and regulatory framework. One of the main features presented is the generation of synthetic data in uncertainty modelling, employed to enhance the reliability of the model by taking into account a longer time horizon and a shorter time step. Results show significant details about energy management and prove the suitability of using a stochastic approach rather than deterministic or intuitive ones to perform the optimization.

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“…However, if it is not the case, [15] provides a comprehensive review of optimisation under uncertainty, especially on the modelling and sampling of the aleatoric uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust calibration of numerical models based on relative regret

Trappler¹,

Arnaud²,

Vidard³

et al. 2021

Journal of Computational Physics

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Classical methods of calibration usually imply the minimisation of an objective function with respect to some control parameters. This function measures the error between some observations and the results obtained by a numerical model. In the presence of uncontrollable additional parameters that we model as random inputs, the objective function becomes a random variable, and notions of robustness have to be introduced for such an optimisation problem. In this paper, we are going to present how to take into account those uncertainties by defining the relative-regret. This quantity allow us to compare the value of the objective function to its best performance achievable given a realisation of the random additional parameters. By controlling this relative-regret using a probabilistic constraint, we can then define a new family of estimators, whose robustness with respect to the random inputs can be adjusted.

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Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

Cited by 262 publications

References 216 publications

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

Soft‐constrained model predictive control based on data‐driven distributionally robust optimization

A Comprehensive Model for the Design of a Microgrid under Regulatory Constraints Using Synthetical Data Generation and Stochastic Optimization

Robust calibration of numerical models based on relative regret

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