Dynamic Process Optimization Research Articles

Integration of Scheduling and Dynamic Optimization of Batch Processes under Uncertainty: Two-Stage Stochastic Programming Approach and Enhanced Generalized Benders Decomposition Algorithm

Integration of scheduling and dynamic optimization significantly improves the overall performance of a production process compared to the traditional sequential method. However, most integrated methods focus on solving deterministic problems without explicitly taking process uncertainty into account. We propose a novel integrated method for sequential batch processes under uncertainty. The integrated problem is formulated into a two-stage stochastic program. The first-stage decisions are modeled with binary variables for assignment and sequencing while the second-stage decisions are the remaining ones. To solve the resulting complicated integrated problem, we develop two efficient algorithms based on the framework of generalized Benders decomposition. The first algorithm decomposes the integrated problem according to the scenarios so that the subproblems can be optimized independently over each scenario. Besides the scenario decomposition, the second algorithm further decomposes dynamic models from the sc...

Economic model predictive control with time‐varying objective function for nonlinear process systems

Economic model predictive control (EMPC) is a control scheme that combines real‐time dynamic economic process optimization with the feedback properties of model predictive control (MPC) by replacing the quadratic cost function with a general economic cost function. Almost all the recent work on EMPC involves cost functions that are time invariant (do not explicitly account for time‐varying process economics). In the present work, we focus on the development of a Lyapunov‐based EMPC (LEMPC) scheme that is formulated with an explicitly time‐varying economic cost function. First, the formulation of the proposed two‐mode LEMPC is given. Second, closed‐loop stability is proven through a theoretical treatment. Last, we demonstrate through extensive closed‐loop simulations of a chemical process that the proposed LEMPC can achieve stability with time‐varying economic cost as well as improve economic performance of the process over a conventional MPC scheme. © 2013 American Institute of Chemical Engineers AIChE J 60: 507–519, 2014

Chemical process dynamic optimization based on the differential evolution algorithm with an adaptive scheduling mutation strategy

To solve chemical process dynamic optimization problems, a differential evolution algorithm integrated with adaptive scheduling mutation strategy (ASDE) is proposed. According to the evolution feedback information, ASDE, with adaptive control parameters, adopts the round-robin scheduling algorithm to adaptively schedule different mutation strategies. By employing an adaptive mutation strategy and control parameters, the real-time optimal control parameters and mutation strategy are obtained to improve the optimization performance. The performance of ASDE is evaluated using a suite of 14 benchmark functions. The results demonstrate that ASDE performs better than four conventional differential evolution (DE) algorithm variants with different mutation strategies, and that the whole performance of ASDE is equivalent to a self-adaptive DE algorithm variant and better than five conventional DE algorithm variants. Furthermore, ASDE was applied to solve a typical dynamic optimization problem of a chemical process. The obtained results indicate that ASDE is a feasible and competitive optimizer for this kind of problem.

Integrating process dynamics within batch process scheduling via mixed-integer dynamic optimization

During batch process scheduling, products' batch size, processing conditions as well as operating times are usually established offline and considered out of the scope of the decision making stage. In practice, process dynamics may vary from the ones forecasted, in such a manner that the predicted optimal conditions will not be the best in practice. As a result of this mismatch, the plant usually operates under sub-optimal conditions, but if the process is flexible, its processing conditions can still be adapted to the actual plant needs in order to improve the overall performance. Given this situation, there is a strong motivation for developing models and optimization tools to fully integrate process dynamics into batch scheduling. In this work, the potential of directly including control variables with time varying values and variable batch sizes in the scheduling of batch plants is explored. The optimization of process dynamics, which is time varying, along with scheduling tasks is accomplished using rigorous mixed-integer dynamic optimization techniques. Through several examples, we show that integrating both decision-making levels can lead to significant economic savings.

Integrated Scheduling and Dynamic Optimization of Complex Batch Processes with General Network Structure Using a Generalized Benders Decomposition Approach

We address the integration of scheduling and dynamic optimization for batch chemical processes. The processes can have complex network structures, allowing material splitting and mixing. The integrated problem is formulated as a mixed-integer dynamic optimization problem where a continuous-time scheduling model is linked to the dynamic models via processing times, processing costs, and batch sizes. To reduce the computational complexity, we develop a tailored and efficient decomposition method based on the framework of generalized Benders decomposition by exploiting the special structure of the integrated problem. The decomposed master problem is a scheduling problem with variable processing times and processing costs, as well as the Benders cuts. The primal problem comprises a set of separable dynamic optimization problems for the processing units. By collaboratively optimizing the process scheduling and the process dynamics, the proposed method substantially improve the overall economic performance of the batch production compared with the conventional sequential method which solves the scheduling problem and the dynamic optimization problems separately. In comparison with the simultaneous method which solves the integrated problem by a general-purpose MINLP solver directly, the proposed method can reduce computational times by orders of magnitude.

Chemical process dynamic optimization based on hybrid differential evolution algorithm integrated with Alopex

To solve dynamic optimization problem of chemical process (CPDOP), a hybrid differential evolution algorithm, which is integrated with Alopex and named as Alopex-DE, was proposed. In Alopex-DE, each original individual has its own symbiotic individual, which consists of control parameters. Differential evolution operator is applied for the original individuals to search the global optimization solution. Alopex algorithm is used to co-evolve the symbiotic individuals during the original individual evolution and enhance the fitness of the original individuals. Thus, control parameters are self-adaptively adjusted by Alopex to obtain the real-time optimum values for the original population. To illustrate the whole performance of Alopex-DE, several varietal DEs were applied to optimize 13 benchmark functions. The results show that the whole performance of Alopex-DE is the best. Further, Alopex-DE was applied to solve 4 typical CPDOPs, and the effect of the discrete time degree on the optimization solution was analyzed. The satisfactory result is obtained.

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013

Chaotic Differential Evolution Algorithm Based On Competitive Coevolution And Its Application To Dynamic Optimization Of Chemical Processes

A chaotic differential evolution algorithm based on competition coevolution is proposed to improve the performance of the differential evolution (DE) algorithm. In the proposed algorithm (named CO-CDE), at first the population is divided into several sub-populations, each sub-population evolves individually, using different differential schemes. At the end of the evolution each sub-population will have one individual with best fitness. After that all the individuals with best fitness compete with each other, at this time the fitness of one individual is defined as the number of times one individual is superior to others. Therefore one individual with best fitness is picked out and its information is shared by the whole population. To avoid premature convergence and raise the probability of escaping from local optima, a chaotic evolutionary operation based on chaotic variables is introduced into the algorithm and implemented to the whole population. The simulation experiment shows that the CO-CDE algorithm...

Mathematical modeling, design and optimization of conceptual configuration of soil-like substrate bioreactor based on system dynamics and digital simulation

It will be absolutely necessary to establish a Bioregenerative Life Support System (BLSS) for both manned exploration of deep space and subsequent founding of extraterrestrial colonies, a goal to which our species not only aspires but to which it likely must attain in order to insure its own future survival. Currently constraining the transport and transformation rates of substances in BLSS is the treatment of inedible plant biomass. To overcome this problem, a Soil-like Substrate (SLS) has been employed, rendering sustainable wheat cultivation from an otherwise inedible wheat biomass. The SLS bioreactor which is a specific artificial ecosystem consisting of wheat, earthworms, bacterial microflora, inedible wheat biomass and the artificial environment has theoretically been built in order to investigate the SLS formation process as well as the system's effective design and optimization. A valid mathematical model of the SLS bioreactor was developed and a performance index function (PIF) was put forward for sufficient description and comprehensive evaluation of the SLS bioreactor operation state, respectively. The closed-loop SLS bioreactor with a Linear-Quadratic Gaussian (LQG) servo controller was also designed through dynamic process optimization. The digital simulation on closed-loop SLS bioreactor indicated PIF could robustly stabilize at the desired level with desire dynamic performance specification under the action of artificial environment factors. Therefore, the closed-loop SLS bioreactor which might be built from the mathematical model and digital simulation has the potential to substantially increase both the closure degree and reliability of BLSS.

Novel Control Vector Parameterization Method with Differential Evolution Algorithm and Its Application in Dynamic Optimization of Chemical Processes

Two general approaches are adopted in solving dynamic optimization problems in chemical processes, namely, the analytical and numerical methods. The numerical method, which is based on heuristic algorithms, has been widely used. An approach that combines differential evolution (DE) algorithm and control vector parameterization (CVP) is proposed in this paper. In the proposed CVP, control variables are approximated with polynomials based on state variables and time in the entire time interval. Region reduction strategy is used in DE to reduce the width of the search region, which improves the computing efficiency. The results of the case studies demonstrate the feasibility and efficiency of the proposed methods.

Study on optimization method of dynamic extraction process

To establish a new optimized extraction process based on dynamic changes in extract concentration during the extraction process. Sanqi was taken as an example to compare the concentration of marker components, total solids yield and similarity evaluation of the fingerprint images of extracts by orthogonal design optimization process and dynamic optimization process to assess the feasibility of dynamic process optimization method. The concentration of marker components and total solids yield vary less than 5%, with a 100% of similarity in fingerprints, indicating basic coincidence between extracts by the two optimized processes. The dynamic process optimization process could save 79% of the extraction time. In the extraction time, the dynamic optimization process is superior to the orthogonal design optimization process in that it can significantly reduce the extraction time and lower production costs.

Newton-conjugate gradient (CG) augmented Lagrangian method for path constrained dynamic process optimization

In this paper, a Newton-conjugate gradient (CG) augmented Lagrangian method is proposed for solving the path constrained dynamic process optimization problems. The path constraints are simplified as a single final time constraint by using a novel constraint aggregation function. Then, a control vector parameterization (CVP) approach is applied to convert the constraints simplified dynamic optimization problem into a nonlinear programming (NLP) problem with inequality constraints. By constructing an augmented Lagrangian function, the inequality constraints are introduced into the augmented objective function, and a box constrained NLP problem is generated. Then, a linear search Newton-CG approach, also known as truncated Newton (TN) approach, is applied to solve the problem. By constructing the Hamiltonian functions of objective and constraint functions, two adjoint systems are generated to calculate the gradients which are needed in the process of NLP solution. Simulation examples demonstrate the effectiveness of the algorithm.

Integrated scheduling and dynamic optimization of batch processes using state equipment networks

AbstractA systematic framework for the integration of short‐term scheduling and dynamic optimization (DO) of batch processes is described. The state equipment network (SEN) is used to represent a process system, where it decomposes the process into two basic kinds of entities: process materials and process units. Mathematical modeling based on the SEN framework invokes both logical disjunctions and operational dynamics; thus the integrated formulation leads to a mixed‐logic dynamic optimization (MLDO) problem. The integrated approach seeks to benefit the overall process performance by incorporating process dynamics into scheduling considerations. The solution procedure of an MLDO problem is also addressed in this article, where MLDO problems are translated into mixed‐integer nonlinear programs using the Big M reformulation and the simultaneous collocation method. Finally, through two case studies, we show advantages of the integrated approach over the conventional recipe‐based scheduling method. © 2012 American Institute of Chemical Engineers AIChE J, 2012

An investigation of Economics-Driven NMPC-Formulations for a Continuous Catalytic Distillation System

For continuously operated processes, even a small increase in the efficiency pays important dividends in terms of energy savings and profit. Therefore, tighter and more efficient control of chemical plants is becoming a strategic objective. In this work, we demonstrate the use of dynamic process optimization to improve the business performance of chemical processes. Model predictive control techniques are widely applied to coupled multivariable control problems. The reference values in these problems are usually adjusted by infrequent optimizations based upon a static rigorous nonlinear model of the plant. In between these optimizations, however, the process may undergo sub-optimality of operation due to the presence of disturbances. In this paper, nonlinear model-based optimization with different schemes is proposed to combine optimal operation and feedback control. The work demonstrates the feasibility and the potential of using optimizing as well as economics-oriented tracking control techniques for a challenging example, a catalytic distillation process. The performances of the proposed controllers are investigated and compared. This work points out that by using direct optimizing NMPC, the plant economics can be handled better while guaranteeing the product specifications.

Using fuzzy logic to tune an evolutionary algorithm for dynamic optimization of chemical processes

Dynamic optimization of chemical processes can be carried out with evolutionary algorithms that involve many parameters. These parameters need to be given appropriate values for the algorithms to perform efficiently. This paper proposes parameter setting methods based on factorial experimentation and fuzzy logic, aimed at balancing convergence speed, robustness (consistent performance for each problem) and versatility (applicability to many different problems). The methods were tested on an existing dynamic optimisation method with at least nine tuneable parameters. The test problem set turned out to be quite demanding due to one particular problem behaving in opposite direction to the rest with respect to the most influential factor, population size. It is probable that no single tuning would be possible that will satisfy all problems. However, for the other problems, the Fuzzy Logic tuning method proposed in this paper proves to be a very promising approach.

Using Sparse-Grid Methods To Improve Computation Efficiency in Solving Dynamic Nonlinear Chance-Constrained Optimization Problems

Chance-constrained programming is known as a suitable approach to optimization under uncertainty. However, a serious difficulty is the requirement of evaluating the probability of holding inequality constraints through the numerical computation of multidimensional integrals. If a nonlinear system with many uncertain variables is considered, the computational load will be prohibitive when using a full-grid integration method. Thus our aim is to investigate a method to decrease the computation expense in solving nonlinear chance-constrained optimization problems with many uncertain variables. In particular, we consider dynamic nonlinear process optimization under uncertainty, which will be transferred into a nonlinear chance-constrained optimization problem by a discretization scheme. To solve this problem, we propose to use sparse-grid methods for the evaluation of the objective function, the probability of constraint satisfaction, and their gradients. These components are implemented in a nonlinear progra...

Dynamic Water Network Topology Optimization of Batch Processes

A water network (WN) for a batch process could be seen as a dynamic structure which changes its topology at fixed time intervals delimited by events. During each time interval, the WN could be abst...

Dynamic simulation and optimization of an SC papermaking line – illustrated with case studies

Abstract Dynamic modeling and simulation software can be used to simulate the industrial processes such as papermaking in order to improve the efficiency of the process. A dynamic simulation model can be combined with an optimization method to maximize the advantages which simulation tools can offer. In this paper, we combine dynamic process simulation and optimization to see how it can benefit a papermaking process which was envisaged to consist of a TMP mill, stock preparation, short circulation, a paper machine, and a reel. The aim is to increase the efficiency and minimize the costs involved in papermaking.

Dynamic optimization of batch diafiltration processes

A comprehensive modeling approach is proposed for the dynamic simulation and operation optimization of batch diafiltration processes. We provide a unified technology for water utilization control that addresses generality versus special cases. A rigorous dynamical model of the diafiltration process with concentration-dependent rejections of solutes is developed. We determine the optimal time-dependent profile of the diluant flow for the entire process using dynamic optimization methods. The results show that optimal process operation needs not to be any of the conventional diafiltration concepts. The presented optimization technique is a useful tool for improving the performance of a membrane diafiltration process.

A Comparison of Arithmetic Operations for Dynamic Process Optimization Approach

A comparison of arithmetic operations of two dynamic process optimization approaches called quasi-sequential approach and reduced Sequential Quadratic Programming (rSQP) simultaneous approach with respect to equality constrained optimization problems is presented. Through the detail comparison of arithmetic operations, it is concluded that the average iteration number within differential algebraic equations (DAEs) integration of quasi-sequential approach could be regarded as a criterion. One formula is given to calculate the threshold value of average iteration number. If the average iteration number is less than the threshold value, quasi-sequential approach takes advantage of rSQP simultaneous approach which is more suitable contrarily. Two optimal control problems are given to demonstrate the usage of threshold value. For optimal control problems whose objective is to stay near desired operating point, the iteration number is usually small. Therefore, quasi-sequential approach seems more suitable for such problems.