scholarly journals Toward a Comprehensive and Efficient Robust Optimization Framework for (Bio)chemical Processes

Processes ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 183 ◽  
Author(s):  
Xiangzhong Xie ◽  
René Schenkendorf ◽  
Ulrike Krewer
Keyword(s):  
Robust Optimization ◽  
Process Design ◽  
Optimization Problems ◽  
Equality Constraints ◽  
Uncertain Parameters ◽  
Approximation Accuracy ◽  
Model Based ◽  
Computational Expense ◽  
Robust Process ◽  
Point Estimation Method

Model-based design principles have received considerable attention in biotechnology and the chemical industry over the last two decades. However, parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies have been introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computational expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints for a robust process design. We also apply a global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies: (1) designing a heating/cooling profile for the essential part of a continuous production process; and (2) optimizing the feeding profile for a fed-batch reactor of the penicillin fermentation process. According to the derived results, the proposed framework of robust process design addresses uncertainties adequately and scales well with the number of uncertain parameters. Thus, the described robustification concept should be an ideal candidate for more complex (bio)chemical problems in model-based design.

scholarly journals Toward a Comprehensive and Efficient Robust Optimization Framework for (Bio)chemical Processes

2018 ◽  
Author(s):  
Xiangzhong Xie ◽  
René Schenkendorf ◽  
Ulrike Krewer
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Continuous Production ◽  
Equality Constraints ◽  
Parameter Uncertainties ◽  
Approximation Accuracy ◽  
Statistical Point ◽  
Model Based ◽  
Feeding Profile ◽  
Point Estimation Method

Model-based design has received considerable attention in biological and chemical industries over the last two decades. However, the parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies were introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computation expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints. We also suggest employing the information from global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies where one is to design a heating/cooling profile for the essential part of a continuous production process and the other is to optimize the feeding profile for a fed-batch reactor of the penicillin fermentation process. The results reveal that the proposed approach can be used successfully for complex (bio)chemical problems in model-based design.

Feasibility Robust Optimization via Scenario Generation and Reduction

2018 ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Solution

Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains without any known probability distributions. The proposed approach integrates a new sampling-based scenario generation scheme with a new scenario reduction approach in order to solve feasibility robust optimization problems. An analysis of the computational cost of the proposed approach was performed to provide worst case bounds on its computational cost. The new proposed approach was applied to three test problems and compared against other scenario-based robust optimization approaches. A test was conducted on one of the test problems to demonstrate that the computational cost of the proposed approach does not significantly increase as additional uncertain parameters are introduced. The results show that the proposed approach converges to a robust solution faster than conventional robust optimization approaches that discretize the uncertain parameters.

scholarly journals Robust Optimization Model with Shared Uncertain Parameters in Multi-Stage Logistics Production and Inventory Process

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 211
Author(s):  
Lijun Xu ◽  
Yijia Zhou ◽  
Bo Yu
Keyword(s):  
Robust Optimization ◽  
Optimization Model ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Uncertain Parameters ◽  
Worst Case ◽  
Robust Model ◽  
Multi Stage ◽  
Proposed Model ◽  
Dual Forms

In this paper, we focus on a class of robust optimization problems whose objectives and constraints share the same uncertain parameters. The existing approaches separately address the worst cases of each objective and each constraint, and then reformulate the model by their respective dual forms in their worst cases. These approaches may result in that the value of uncertain parameters in the optimal solution may not be the same one as in the worst case of each constraint, since it is highly improbable to reach their worst cases simultaneously. In terms of being too conservative for this kind of robust model, we propose a new robust optimization model with shared uncertain parameters involving only the worst case of objectives. The proposed model is evaluated for the multi-stage logistics production and inventory process problem. The numerical experiment shows that the proposed robust optimization model can give a valid and reasonable decision in practice.

scholarly journals Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Eliot Rudnick-Cohen ◽  
Jeffrey W. Herrmann ◽  
Shapour Azarm
Keyword(s):  
Robust Optimization ◽  
Optimization Problems ◽  
Computational Cost ◽  
Optimal Solution ◽  
Optimization Techniques ◽  
Scenario Generation ◽  
Test Problems ◽  
Optimization Approach ◽  
Uncertain Parameters ◽  
Worst Case

Abstract Feasibility robust optimization techniques solve optimization problems with uncertain parameters that appear only in their constraint functions. Solving such problems requires finding an optimal solution that is feasible for all realizations of the uncertain parameters. This paper presents a new feasibility robust optimization approach involving uncertain parameters defined on continuous domains. The proposed approach is based on an integration of two techniques: (i) a sampling-based scenario generation scheme and (ii) a local robust optimization approach. An analysis of the computational cost of this integrated approach is performed to provide worst-case bounds on its computational cost. The proposed approach is applied to several non-convex engineering test problems and compared against two existing robust optimization approaches. The results show that the proposed approach can efficiently find a robust optimal solution across the test problems, even when existing methods for non-convex robust optimization are unable to find a robust optimal solution. A scalable test problem is solved by the approach, demonstrating that its computational cost scales with problem size as predicted by an analysis of the worst-case computational cost bounds.

scholarly journals Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Processes ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 509 ◽  
Author(s):  
Xiangzhong Xie ◽  
René Schenkendorf
Keyword(s):  
Process Design ◽  
Measurement Data ◽  
Pharmaceutical Manufacturing ◽  
Chamber Pressure ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Model Based ◽  
Point Estimate Method ◽  
Robust Process

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.

Bayesian closed-loop robust process design considering model uncertainty and data quality

2019 ◽  
Vol 52 (3) ◽  
pp. 288-300 ◽  
Author(s):  
Linhan Ouyang ◽  
Jianxiong Chen ◽  
Yizhong Ma ◽  
Chanseok Park ◽  
Jionghua (Judy) Jin
Keyword(s):  
Data Quality ◽  
Process Design ◽  
Model Uncertainty ◽  
Closed Loop ◽  
Robust Process

scholarly journals Gasification of Biomass in Supercritical Water, Challenges for the Process Design—Lessons Learned from the Operation Experience of the First Dedicated Pilot Plant

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 455
Author(s):  
Nikolaos Boukis ◽  
I. Katharina Stoll
Keyword(s):  
Organic Matter ◽  
Supercritical Water ◽  
Process Design ◽  
Pilot Plant ◽  
Lessons Learned ◽  
Present Contribution ◽  
Flow Process ◽  
Combustible Gas ◽  
Supercritical Water Gasification ◽  
Robust Process

Gasification of organic matter under the conditions of supercritical water (T > 374 °C, p > 221 bar) is an allothermal, continuous flow process suitable to convert materials with high moisture content (<20 wt.% dry matter) into a combustible gas. The gasification of organic matter with water as a solvent offers several benefits, particularly the omission of an energy-intensive drying process. The reactions are fast, and mean residence times inside the reactor are consequently low (less than 5 min). However, there are still various challenges to be met. The combination of high temperature and pressure and the low concentration of organic matter require a robust process design. Additionally, the low value of the feed and the product predestinate the process for decentralized applications, which is a challenge for the economics of an application. The present contribution summarizes the experience gained during more than 10 years of operation of the first dedicated pilot plant for supercritical water gasification of biomass. The emphasis lies on highlighting the challenges in process design. In addition to some fundamental results gained from comparable laboratory plants, selected experimental results of the pilot plant “VERENA” (acronym for the German expression “experimental facility for the energetic exploitation of agricultural matter”) are presented.

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

scholarly journals Oracle-based algorithms for binary two-stage robust optimization

2020 ◽  
Vol 77 (2) ◽  
pp. 539-569
Author(s):  
Nicolas Kämmerling ◽  
Jannis Kurtz
Keyword(s):  
Robust Optimization ◽  
Branch And Bound ◽  
Optimization Problems ◽  
Capital Budgeting ◽  
Hub Location Problem ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Problem ◽  
Objective Uncertainty

Abstract In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying deterministic problem and an adversarial problem. For the deterministic problem any oracle can be used which returns an optimal solution for every possible scenario. We show that the latter lower bound can be implemented in a branch and bound procedure, where the branching is performed only over the first-stage decision variables. All results even hold for non-linear objective functions which are concave in the uncertain parameters. As an alternative solution method we apply a column-and-constraint generation algorithm to the binary two-stage robust problem with objective uncertainty. We test both algorithms on benchmark instances of the uncapacitated single-allocation hub-location problem and of the capital budgeting problem. Our results show that the branch and bound procedure outperforms the column-and-constraint generation algorithm.

Linearized Robust Counterparts of Two-Stage Robust Optimization Problems with Applications in Operations Management

2020 ◽  
Author(s):  
Amir Ardestani-Jaafari ◽  
Erick Delage
Keyword(s):  
Robust Optimization ◽  
Operations Management ◽  
Optimization Problems ◽  
Close Relation ◽  
Bilinear Programming ◽  
Two Stage ◽  
Bilinear Models ◽  
Robust Counterpart ◽  
Adjustable Robust Counterpart ◽  
Affinely Adjustable Robust Counterpart

In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method mainly relies on a linearization scheme employed in bilinear programming; therefore, we will say that it gives rise to the linearized robust counterpart models. We identify a close relation between this linearized robust counterpart model and the popular affinely adjustable robust counterpart model. We also describe methods of modifying both types of models to make these approximations less conservative. These methods are heavily inspired by the use of valid linear and conic inequalities in the linearization process for bilinear models. We finally demonstrate how to employ this new scheme in location-transportation and multi-item newsvendor problems to improve the numerical efficiency and performance guarantees of robust optimization.

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