Finite Adaptability in Data-Driven Robust Optimization for Production Scheduling: A Case Study of the Ethylene Plant

Data-driven adaptive robust optimization for energy systems in ethylene plant under demand uncertainty

Mathematical functions are often used to define an engineering design problem and these models are also used to find an optimal solution for the problem. The optimal solutions thus achieved are deterministic in nature and often neglect aberrations in design data as well as in design variables themselves. These uncertainties can manifest in a variety of forms including manufacturing errors, mechanical inaccuracies, and stochasticity in design parameters. This paper presents different robust design optimization methodologies followed by their application on a numerical optimization problem. Some modifications on the existing methods will also be presented. It will be shown that robust design optimization provides a strong framework for handling uncertainty since actual environments parameters are subject to these uncertainties. The methodologies will present robust optimization techniques that will result in designs that are minimally sensitive to input variations making them suitable for problems with uncertain parameters. Ten different robust optimal design methodologies will be briefly discussed and implemented on a quartic multimodal nonlinear test objective - chosen to be Himmelblau’s function. Since many problems arising in engineering design are nonlinear and multimodal, the methodologies discussed can be applied to similar design and quality engineering problems. It will be seen that different robust optimization methodologies vary substantially not only in terms of requirements but also in terms of the solutions they achieve. A summary of these results will be presented at the end.

Adaptive and robust radiation therapy optimization for lung cancer

Aircraft robust multidisciplinary design optimization methodology based on fuzzy preference function

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Robust optimization of geoenergy production using data-driven deep recurrent auto-encoder and fully-connected neural network proxy

Robust nonlinear optimization with conic representable uncertainty set

This paper proposes a two-stage distributionally robust optimization model for the joint energy and reserve dispatch (D-RERD for short) of bulk power systems with significant renewable energy penetration. Distinguished from the prevalent uncertainty set-based and worst-case scenario oriented robust optimization methodology, we assume that the output of volatile renewable generation follows some ambiguous distribution with known expectations and variances, the probability distribution function (pdf) is restricted in a functional uncertainty set. D-RERD aims at minimizing the total expected production cost in the worst renewable power distribution. In this way, D-RERD inherits the advantages from both stochastic optimization and robust optimization: statistical characteristic is taken into account in a data-driven manner without requiring the exact pdf of uncertain factors. We present a convex optimization-based algorithm to solve the D-RERD, which involves solving semidefinite programming (SDP), convex quadratic programming (CQP), and linear programming (LP). The performance of the proposed approach is compared with the emerging adaptive robust optimization (ARO)-based model on the IEEE 118-bus system. Their respective features are discussed in case studies.

Purpose:Accuracy of dose calculation models and robustness under various uncertainties are key factors influencing the quality of intensity modulated proton therapy (IMPT) plans. In this work, a robust IMPT optimization based on accurate Monte Carlo (MC) dose calculation is developed.Methods:We used an in‐house developed and graphics processing unit (GPU) accelerated MC for dose calculation. For robust optimization, dose volume histograms (DVHs) were computed for each uncertainty scenario at each optimization iteration. A gradient based adaptive method was used to improve the DVHs with adjustable scenario weights. GPUs were employed to accelerate the optimization process. Uncertainties in patient setup and proton range were considered in all cases studied. Additionally, the uncertainty of intra‐fraction relative shift between fields was considered for craniospinal irradiation cases. The adaptive robust optimization method was compared with for clinical cases at several different disease sites.Results:Comparing with the traditional optimization target volume (OTV) based method, the adaptive robust optimization spared critical structures better while maintain the target coverage in clinical cases. For example, the right parotid hot spot dose was reduced from 78.5Gy to 74.5Gy as shown in Fig. 1. For craniospinal irradiation, the adaptive method found the robust solution at field junctions without manual feathering of the match lines. Even for relatively large head‐and‐neck cases and craniospinal cases, the whole process of MC dose calculation and robust optimization can be done within 30 minutes on a system of 100 Nvidia GeForce GTX Titan cards.Conclusion:A robust IMPT treatment planning system is developed utilizing an adaptive method. The treatment planning optimization is based on MC dose calculation and is accelerated by GPU to be clinically viable.This work is supported in part by Varian Medical Systems.

In this paper, we propose a data-driven outlier-insensitive adaptive robust optimization framework that leverages big data in industries. A Bayesian nonparametric model - the Dirichlet process mixture model - is adopted to extract the information embedded within uncertainty data via a variational inference algorithm. We then devise data-driven uncertainty sets for adaptive robust optimization. This Bayesian nonparametric model is seamlessly integrated with adaptive optimization approach through a novel four-level robust optimization framework. This framework explicitly considers the correlation, asymmetry and multimode of uncertainty data, and as a result generates less conservative solutions. Additionally, this framework is robust not only to parameter variations, but also to data outliers. An efficient tailored column-and-constraint generation algorithm is proposed for the resulting problem that cannot be solved by any off-the-shelf optimization solvers. The effectiveness and advantages of the modeling framework and solution algorithm are demonstrated through an industrial application in batch process scheduling.

An adaptive robust optimization scheme for water-flooding optimization in oil reservoirs using residual analysis

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.

We develop a modular and tractable framework for solving an adaptive distributionally robust linear optimization problem, where we minimize the worst-case expected cost over an ambiguity set of probability distributions. The adaptive distributionally robust optimization framework caters for dynamic decision making, where decisions adapt to the uncertain outcomes as they unfold in stages. For tractability considerations, we focus on a class of second-order conic (SOC) representable ambiguity set, though our results can easily be extended to more general conic representations. We show that the adaptive distributionally robust linear optimization problem can be formulated as a classical robust optimization problem. To obtain a tractable formulation, we approximate the adaptive distributionally robust optimization problem using linear decision rule (LDR) techniques. More interestingly, by incorporating the primary and auxiliary random variables of the lifted ambiguity set in the LDR approximation, we can significantly improve the solutions, and for a class of adaptive distributionally robust optimization problems, exact solutions can also be obtained. Using the new LDR approximation, we can transform the distributionally adaptive robust optimization problem to a classical robust optimization problem with an SOC representable uncertainty set. Finally, to demonstrate the potential for solving management decision problems, we develop an algebraic modeling package and illustrate how it can be used to facilitate modeling and obtain high-quality solutions for medical appointment scheduling and inventory management problems. The electronic companion is available at https://doi.org/10.1287/mnsc.2017.2952 . This paper was accepted by Noah Gans, optimization.

Optimization techniques combined with uncertainty quantification are computationally expensive for robust aerodynamic optimization due to expensive CFD costs. Surrogate model technology can be used to improve the efficiency of robust optimization. In this paper, non-intrusive polynomial chaos method and Kriging model are used to construct a surrogate model that associate stochastic aerodynamic statistics with airfoil shapes. Then, global search algorithm is used to optimize the model to obtain optimal airfoil fast. However, optimization results always depend on the approximation accuracy of the surrogate model. Actually, it is difficult to achieve a high accuracy of the model in the whole design space. Therefore, we introduce the idea of adaptive strategy to robust aerodynamic optimization and propose an adaptive stochastic optimization framework. The surrogate model is updated adaptively by increasing training airfoils according to historical optimization results to guarantee the accuracy near the optimal design point, which can greatly reduce the number of training airfoils. The proposed method is applied to a robust aerodynamic shape optimization for drag minimization considering uncertainty of Mach number in transonic region. It can be concluded that the proposed method can obtain better optimal results more efficiently than the traditional robust optimization method and global surrogate model method.

Fast robust optimization of ORC based on an artificial neural network for waste heat recovery