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Processes
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Algorithms and Applications in Dynamic Optimization
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Algorithms and Applications in Dynamic Optimization

A special issue of Processes (ISSN 2227-9717). This special issue belongs to the section "Process Control and Monitoring".

Deadline for manuscript submissions: closed (29 February 2016) | Viewed by 45113

Special Issue Editor

Dr. Carl D. Laird

E-Mail Website
Guest Editor
FRNY G027C, School of Chemical Engineering, Purdue University, Forney Hall of Chemical Engineering, 480 Stadium Mall Drive, West Lafayette, IN 47907-2100, USA

Special Issue Information

Dear Colleagues,

Mathematical programming has proven to be a valuable tool in the process industries for improving both design and operations. However, operational challenges are driving the need for more rigorous models, including those considering system dynamics and distributed properties. As computational capabilities increase, there is continued opportunity to develop reliable problem formulations and efficient solution strategies for optimization of complex processes modeled by differential equations.

Several techniques are available for local optimization of differential-algebraic equations (DAEs). For indirect or optimize-then-discretize methods, optimality conditions are applied to the dynamic optimization problem, resulting in a set of differential equations typically solved numerically. For direct or discretize-then-optimize approaches, the DAE system is discretized prior to the application of optimality conditions. These techniques can be further categorized into sequential, simultaneous, or multiple-shooting techniques. Approaches differ in many aspects, including discretization strategies, optimization algorithms, and computation of gradient information.

Numerous problems in the process industries require optimization of differential-algebraic equations (DAEs), including optimal operation of batch processes, dynamic real-time optimization, optimal load transition, and nonlinear model predictive control (MPC). Furthermore, spatially distributed systems, particulate processes, and other models with internally and externally distributed properties, can be discretized along some dimensions, giving rise to a large set of DAEs. Efficient optimization of DAEs can be challenging for several reasons. Large systems of DAEs, like those arising from spatial discretization, can be computationally intensive, and may necessitate the use of advanced computing hardware. In addition, online applications like nonlinear MPC typically require solutions within a fixed, small time horizon. The challenges inherent in these problem classes illustrate the need for reliable and efficient methods to solve dynamic optimization problems.

The special issue, “Algorithms and Applications in Dynamic Optimization” of the journal Processes, aims to cover recent advances in optimization of complex DAE models. Appropriate contributions include novel solution strategies, and advanced modeling and problem formulations for dynamic optimization of complex process. Applications and solution strategies in global optimization of dynamic systems are also welcomed.

Dr. Carl D. Laird
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Processes is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


Keywords

  • mathematical programming
  • dynamic optimization
  • global optimization
  • ordinary differential equations
  • differential algebraic equations
  • algorithm complexity
  • algorithm efficiency
  • dynamic modeling
  • model predictive control
  • dynamic real-time optimization

Published Papers (6 papers)

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271 KiB  
Article
Parallel Solution of Robust Nonlinear Model Predictive Control Problems in Batch Crystallization
by Yankai Cao, Jia Kang, Zoltan K. Nagy and Carl D. Laird
Processes 2016, 4(3), 20; https://doi.org/10.3390/pr4030020 - 30 Jun 2016
Cited by 7 | Viewed by 4890
Abstract
Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC) strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves these optimization problems using the parallel Schur [...] Read more.
Representing the uncertainties with a set of scenarios, the optimization problem resulting from a robust nonlinear model predictive control (NMPC) strategy at each sampling instance can be viewed as a large-scale stochastic program. This paper solves these optimization problems using the parallel Schur complement method developed to solve stochastic programs on distributed and shared memory machines. The control strategy is illustrated with a case study of a multidimensional unseeded batch crystallization process. For this application, a robust NMPC based on min–max optimization guarantees satisfaction of all state and input constraints for a set of uncertainty realizations, and also provides better robust performance compared with open-loop optimal control, nominal NMPC, and robust NMPC minimizing the expected performance at each sampling instance. The performance of robust NMPC can be improved by generating optimization scenarios using Bayesian inference. With the efficient parallel solver, the solution time of one optimization problem is reduced from 6.7 min to 0.5 min, allowing for real-time application. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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4840 KiB  
Article
A Dynamic Optimization Model for Designing Open-Channel Raceway Ponds for Batch Production of Algal Biomass
by Soumya Yadala and Selen Cremaschi
Processes 2016, 4(2), 10; https://doi.org/10.3390/pr4020010 - 30 Mar 2016
Cited by 14 | Viewed by 7635
Abstract
This work focuses on designing the optimum raceway pond by considering the effects of sunlight availability, temperature fluctuations, and harvest time on algae growth, and introduces a dynamic programing model to do so. Culture properties such as biomass productivity, growth rate, and concentration, [...] Read more.
This work focuses on designing the optimum raceway pond by considering the effects of sunlight availability, temperature fluctuations, and harvest time on algae growth, and introduces a dynamic programing model to do so. Culture properties such as biomass productivity, growth rate, and concentration, and physical properties, such as average velocity, pond temperature, and rate of evaporation, were estimated daily depending on the dynamic behavior of solar zenith angle, diurnal pattern of solar irradiance, and temperature fluctuations at the location. Case studies consider two algae species (Phaeodactylum. tricornutum and Isochrysis. galbana) and four locations (Tulsa, USA; Hyderabad, India; Cape Town, South Africa; and Rio de Janeiro, Brazil). They investigate the influences of the type of algae strain and geographical location on algae biomass production costs. From our case studies, the combination of I. galbana species grown in Hyderabad, India, with a raceway pond geometry of 30 cm channel depth, about a meter channel width, and 300 m in length, and a harvest interval of every six days yielded the minimum algal biomass production costs. The results of the sensitivity analysis reveal that smaller channel depths and longer ponds (within the ranges considered) are recommended to minimize the net present cost of algae biomass production. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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3373 KiB  
Article
Hybrid Dynamic Optimization Methods for Systems Biology with Efficient Sensitivities
by Nicholas R. Lewis, John D. Hedengren and Eric L. Haseltine
Processes 2015, 3(3), 701-729; https://doi.org/10.3390/pr3030701 - 21 Sep 2015
Cited by 10 | Viewed by 9313
Abstract
In recent years, model optimization in the field of computational biology has become a prominent area for development of pharmaceutical drugs. The increased amount of experimental data leads to the increase in complexity of proposed models. With increased complexity comes a necessity for [...] Read more.
In recent years, model optimization in the field of computational biology has become a prominent area for development of pharmaceutical drugs. The increased amount of experimental data leads to the increase in complexity of proposed models. With increased complexity comes a necessity for computational algorithms that are able to handle the large datasets that are used to fit model parameters. In this study the ability of simultaneous, hybrid simultaneous, and sequential algorithms are tested on two models representative of computational systems biology. The first case models the cells affected by a virus in a population and serves as a benchmark model for the proposed hybrid algorithm. The second model is the ErbB model and shows the ability of the hybrid sequential and simultaneous method to solve large-scale biological models. Post-processing analysis reveals insights into the model formulation that are important for understanding the specific parameter optimization. A parameter sensitivity analysis reveals shortcomings and difficulties in the ErbB model parameter optimization due to the model formulation rather than the solver capacity. Suggested methods are model reformulation to improve input-to-output model linearity, sensitivity ranking, and choice of solver. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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3616 KiB  
Article
Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes
by Anders Holmqvist, Christian Andersson, Fredrik Magnusson and Johan Åkesson
Processes 2015, 3(3), 568-606; https://doi.org/10.3390/pr3030568 - 16 Jul 2015
Cited by 10 | Viewed by 9562
Abstract
This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate [...] Read more.
This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate optimal elution trajectories in the presence of uncertainty. Computational tractability is obtained by casting the robust counterpart problem in the framework of bilevel optimal control where the upper level concerns forward simulation of the Lyapunov differential equation, and the nominal open-loop optimal control problem augmented with the robustified target component purity inequality constraint margin is considered in the lower level. The lower-level open-loop optimal control problem, constrained by spatially discretized partial differential equations, is transcribed into a finite dimensional nonlinear program using direct collocation, which is then solved by a primal-dual interior point method. The advantages of the robustification strategy are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography system. The study shows that penalizing the changes in the zero-order hold control gives optimal solutions with low sensitivity to uncertainty. A key result is that the robustified general elution trajectories outperformed the conventional linear trajectories both in terms of recovery yield and robustness. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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739 KiB  
Article
Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty
by Ian D. Washington and Christopher L.E. Swartz
Processes 2015, 3(3), 541-567; https://doi.org/10.3390/pr3030541 - 14 Jul 2015
Cited by 1 | Viewed by 5280
Abstract
A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval [...] Read more.
A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval over all scenario/period realizations. Each independent integration task is able to be solved in parallel as part of the function evaluations within a gradient-based non-linear programming solver. The focus of this paper is on demonstrating potential computation performance improvement when the embedded differential-algebraic equation model solution of the multi-period discretization is implemented in parallel. We assess our parallel dynamic optimization approach on two case studies; the first is a benchmark literature problem, while the second is a large-scale air separation problem that considers a robust set-point transition under parametric uncertainty. Results indicate that focusing on the speed-up of the embedded model evaluation can significantly decrease the overall computation time; however, as the multi-period formulation grows with increased realizations, the computational burden quickly shifts to the internal computation performed within the non-linear programming algorithm. This highlights the need for further decomposition, structure exploitation and parallelization within the non-linear programming algorithm and is the subject for further investigation. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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443 KiB  
Article
Dynamic Optimization in JModelica.org
by Fredrik Magnusson and Johan Åkesson
Processes 2015, 3(2), 471-496; https://doi.org/10.3390/pr3020471 - 19 Jun 2015
Cited by 17 | Viewed by 7590
Abstract
We present the open-source software framework in JModelica.org for numerically solving large-scale dynamic optimization problems. The framework solves problems whose dynamic systems are described in Modelica, an open modeling language supported by several different tools. The framework implements a numerical method based on [...] Read more.
We present the open-source software framework in JModelica.org for numerically solving large-scale dynamic optimization problems. The framework solves problems whose dynamic systems are described in Modelica, an open modeling language supported by several different tools. The framework implements a numerical method based on direct local collocation, of which the details are presented. The implementation uses the open-source third-party software package CasADi to construct the nonlinear program in order to efficiently obtain derivative information using algorithmic differentiation. The framework is interfaced with the numerical optimizers IPOPT and WORHP for finding local optima of the optimization problem after discretization. We provide an illustrative example based on the Van der Pol oscillator of how the framework is used. We also present results for an industrially relevant problem regarding optimal control of a distillation column. Full article
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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