Towards a better understanding of the epoxy-polymerization process using multi-objective evolutionary computation

The epoxy-polymerization process can be better understood by investigating the underlying optimization problem involving a number of conflicting objectives and more than 20 decision parameters. A combination of minimization or maximization of objectives, such as the number average molecular weight, polydispersity index and reaction time, are considered in this paper. The first two objectives are related to the properties of a polymer, whereas the third objective is related to productivity of the polymerization process. The decision variables are addition quantities of various reactants, e.g. the amount of addition for bisphenol-A (a monomer), sodium hydroxide and epichlorohydrin at different time steps (modeled in a semi-batch operation), whereas the satisfaction of all species balance equations is treated as constraints. A multi-objective evolutionary algorithm (the elitist non-dominated sorting genetic algorithm or NSGA-II) is used to obtain a set of non-dominated solutions in a single simulation run. The results show a substantial improvement (with about 300% more productivity) over the benchmark condition (reported by performing a one-time addition of reactants in the beginning in a batch process). Importantly, this study brings out a salient aspect of using an evolutionary approach to multi-objective problem solving. The availability of multiple optimal trade-off solutions allows a process engineer to have salient information about the polymerization process. Changes in the distribution of various polymer species in the course of polymerization process as observed among various Pareto-optimal solutions are identified and explained for this purpose. Such information provide important information about optimal operating conditions corresponding to different trade-offs among objectives, which are otherwise difficult to obtain. The systematic approach of starting from the two-objective problems to capture the essential features of interesting optimal operating conditions to finally solving the three-objective problem associated with the epoxy-polymerization problem in discovering the optimal trade-off interactions should motivate further such studies on other chemical process optimization problems. Overall, this paper demonstrates how fundamental optimization principles can be used systematically and reliably to find optimum operating conditions for complex chemical process operations.     

Optimization of an operating domestic wastewater treatment plant using elitist non-dominated sorting genetic algorithm

Multi-objective optimization of an operating domestic wastewater treatment plant is carried out using binary coded elitist non-dominated sorting genetic algorithm. Activated sludge model with extended aeration is used for optimization. For optimal plant operation, two different optimization problems are formulated and solved. The first optimization problem involves single-objective function to estimate kinetic parameters in activated sludge model using available plant data by minimizing the weighted sum-of-square errors between computed and plant values. The second optimization problem involves single-, two- and three-objective functions for efficient plant monitoring. In second category problem, objective functions are based on plant performance criteria (i.e., maximizing the influent flow rate of wastewater and minimizing the exit effluent concentration) and economic criteria (i.e., minimizing the plant operating cost). The important decision variables are: mean cell-residence time, mixed liquor suspended solid concentration in the reactor and underflow sludge concentration. Unique solution is obtained for the single-objective function optimization problem whereas a set of non-dominated solutions are obtained for the multi-objective optimization problems. A set of optimal operating conditions are proposed based on the present optimization study, which enhances the plant performance without affecting the discharge effluent quality. Finally, sensitivity analyses of the model results to the kinetic parameters and the kinetic parameters to the GA parameters are carried out to know the sensitivity of the obtained results with changes in the input parameter space.     

基于元模型的过程系统优化

应用均匀实验设计和支持向量机方法构建复杂过程系统的经验模型(元模型),并将其作为适应度函数与遗传算法结合,建立了该系统的优化方法. 该方法只需采用少量仿真模型计算数据便可建立复杂过程系统的元模型,可显著降低复杂过程系统模型的计算过程,便于复杂过程系统的优化. 将该方法用于普光高含硫天然气净化装置全流程操作参数优化,在操作参数优化空间内均匀选取10个实验点,建立了净化装置全流程元模型,其预测值的相对误差小于4%. 优化结果表明,在优化操作点,净化装置有效能效率提高了6.6%.     

换热网络运行模拟优化

换热网络系统大多数是按给定工况,以投资费用和运行费用最优为目标设计的。但在实际运行过程中,确定和不确定性的影响因素往往导致换热网络的运行工况偏离设计值。偏离设计工况运行的换热网络性能变差,导致运行费用增加,甚至不能满足工艺物流换热要求。在换热网络结构给定条件下,将满足物流目标温度和运行费用最优作为目标函数,以单体模型和Yee et al.（1990）提出的多级超结构为基础,建立换热网络运行模拟优化模型,并进一步去除恒定膜传热系数假设使模型贴近实际问题。针对提出的非线性数学模型（NLP）问题,以标准粒子群算法为基础建立求解策略。在论文的最后,4个来源于已发表论文的实例研究证明了该优化方法的有效性。     

考虑环境影响的间歇过程多目标最优化设计

同时考虑费用和环境影响的间歇化工过程多目标最优化设计问题的求解,通常的做法是使用权重系数法,将其转变成单一目标来优化。但大多数情况下,这种权重系数很难确知。因此,有必要提供多个解以便于设计者作出合理的最终选择。采用多目标遗传算法和线性规划相结合的方法求解出间歇化工过程优化设计模型的非劣解集,并与不同权重系数下的单目标算例进行了比较。结果表明,用多目标遗传算法求解间歇化工过程是有效的。这为设计者在间歇化工过程最优化研究考虑环境因素的决策提供了更多的选择。     

Optimal design of liquid-solid circulating fluidized bed for continuous protein recovery

In recent years, liquid-solid circulating fluidized beds (LSCFBs) are being applied as a reactor system in a number of new applications. This study addresses optimal design of LSCFB system at the design stage for the continuous protein recovery. The operation of LSCFB system for continuous protein recovery is associated with several important objectives such as production rate and recovery of protein as well as the amount of ion exchange resin requirements, all of which need to be optimized simultaneously. In this study, an experimentally validated mathematical model was used to perform the multi-objective optimization of the LSCFB system at the design stage. In the optimization study, eight operating and design parameters were used as decision variables. These variables were chosen based on systematic sensitivity analysis of the system which showed complex interplay of the decision variables over the system performance indicators. Elitist non-dominated sorting genetic algorithm with its jumping gene adaptation (NSGA-II-aJG) was used to solve a number of two- and three-objective function optimization problems. The optimization resulted in Pareto optimal solutions, which provides a broad range of non-dominated solutions due to conflicting behavior of the decision variables on the system performance indicators. Compared to the optimization results obtained in the operating stage, the performance of the system was further improved at the design stage optimization as changes in physical dimensions of the LSCFB system can provide better performance than would have been possible by adjusting only the operating parameters.     

Integrated design of power- and resource-saving chemical processes and process control systems: Strategy,methods, and application

A strategy for the integrated design of power-and resource-saving chemical processes and the systems controlling their operating conditions with uncertain input data on physicochemical and process parameters is formulated. A multistep iterative procedure for solving integrated design problems is developed. The procedure includes the generation of alternative chemical processes meeting the “rigid” and/or “soft” flexibility constraints and the choice of operating (control) actions, the synthesis of alternative systems for the automatic control of the operating conditions of the chemical process and the choice of the best control system, the pairwise comparison of feasible automated integrated systems consisting of the chemical engineering process and its control system and the choice of the best integrated system using the criterion based on the power and resource savings and control quality by solving one-and/or two-stage stochastic optimization problems with rigid and/or soft constraints. An example integrated design of the flexible continuous synthesis of azo pigments with an automatic-control system for stabilizing the optimal static conditions is discussed.     

Design of reverse osmosis networks for multiple freshwater production

Reverse osmosis (RO) desalination, which produces multiple freshwater from seawater, has been studied in this work. An optimization method based on process synthesis has been applied to design the RO system. First, a simplified superstructure that contains all the feasible design for this desalination problem has been presented. In this structural representation, the stream split ratios and the logical expressions of stream mixing were employed, which can make the mathematical model easy to handle. Then, the membrane separation units employing the spiral wound reverse osmosis elements were described by using a pressure vessel model, which takes into account the pressure drop and the concentration changes in the membrane channel. The optimum design problem can be formulated as a mixedinteger non-linear programming (MINLP) problem, which minimizes the total annualized cost of the RO system. The cost equation relating the capital and operating cost to the design variables, as well as the structural variables, has been introduced in the objective function. The problem solution includes the optimal streams distribution, the optimal system structure and the operating conditions. The design method could also be used for the optimal selection of membrane element type in each stage and the optimal number of membrane elements in each pressure vessel. The effectiveness of this design methodology has been demonstrated by solving a desalination case. The comparisons with common industrial approach indicated that the integrative RO system proposed in this work is more economical, which can lead to significant capital cost and energy saving and provide an economically attractive desalination scheme.     

On the role of the necessary conditions of optimality in structuring dynamic real-time optimization schemes

In dynamic optimization problems, the optimal input profiles are typically obtained using models that predict the system behavior. In practice, however, process models are often inaccurate, and on-line model adaptation is required for appropriate prediction and re-optimization. In most dynamic real-time optimization schemes, the available measurements are used to update the plant model, with uncertainty being lumped into selected uncertain plant parameters; furthermore, a piecewise-constant parameterization is used for the input profiles. This paper argues that the knowledge of the necessary conditions of optimality (NCO) can help devise more efficient and more robust real-time optimization schemes. Ideally, the structuring decisions involve the NCO as follows: (i) one measures or estimates the plant NCO, (ii) a NCO-based input parameterization is used, and (iii) model adaptation is performed to meet the plant NCO. The benefit of using the NCO in dynamic real-time optimization is illustrated in simulation through the comparison of various schemes for solving a final-time optimal control problem in the presence of uncertainty.     

A generalized framework for solving dynamic optimization problems using the artificial chemical process paradigm: Applications to particulate processes and discrete dynamic systems

The solution of optimal control problems (OCPs) becomes a challenging task when the analyzed system includes non-convex, non-differentiable, or equation-free models in the set of constraints. To solve OCPs under such conditions, a new procedure, LARES-PR, is proposed. The procedure is based on integrating the LARES algorithm with a generalized representation of the control function. LARES is a global stochastic optimization algorithm based on the artificial chemical process paradigm. The generalized representation of the control function consists of variable-length segments, which permits the use of a combination of different types of finite elements (linear, quadratic, etc.) and/or specialized functions. The functional form and corresponding parameters are determined element-wise by solving a combinatorial optimization problem. The element size is also determined as part of the solution of the optimization problem, using a novel two-step encoding strategy. These building blocks result in an algorithm that is flexible and robust in solving optimal control problems. Furthermore, implementation is very simple.The algorithm's performance is studied with a challenging set of benchmark problems. Then LARES-PR is utilized to solve optimal control problems of systems described by population balance equations, including crystallization, nano-particle formation by nucleation/coalescence mechanism, and competitive reactions in a disperse system modeled by the Monte Carlo method. The algorithm is also applied to solving the DICE model of global warming, a complex discrete-time model.     

化工过程总体裕量与控制性能的权衡优化

化工过程的总体裕量可以用操作优化的经济效益进行评价,根据稳态优化和动态优化的经济效益可进一步划分为服务于操作控制的控制裕量和表征过程可实现经济效益的工艺裕量,二者都与化工过程的控制性能有关。针对具有一定裕量的化工过程进行多目标动态优化,优化目标分别为操作点的经济效益与动态过程中的控制性能指标,采用0-1变量描述控制结构,将控制结构和控制器参数也作为优化变量进行混合整数动态优化,采用Constrained NSGA-Ⅱ算法求解非劣解集,根据非劣解集分析总体工艺裕量、总体控制裕量与控制性能指标的关系。通过催化裂化装置的实例分析发现,对于具有一定裕量的化工过程,控制性能越高,所需的总体控制裕量越多,表征操作优化可实现经济效益的总体工艺裕量越少,只有通过对总体控制裕量和总体工艺裕量进行权衡,才能找到兼顾工艺要求和控制性能的工艺操作点和控制设计方案。     

Design of Chemical Engineering Systems with Chance Constraints

In the design of chemical process under uncertainty in initial information, an important problem is to determine a structure in which the control system will guarantee that all constraints are satisfied despite variations in internal and external factors at the operation stage. A method has been proposed for solving onestage optimization problems with chance constraints in the design of optimal flexible chemical processes. The developed approach makes it possible to avoid multidimensional integration in each of the iterations of problem solving, thus reducing the computational effort. The efficiency of the proposed approach is illustrated by model examples.     

Optimal robust optimization approximation for chance constrained optimization problem

Chance constraints are useful for modeling solution reliability in optimization under uncertainty. In general, solving chance constrained optimization problems is challenging and the existing methods for solving a chance constrained optimization problem largely rely on solving an approximation problem. Among the various approximation methods, robust optimization can provide safe and tractable analytical approximation. In this paper, we address the question of what is the optimal (least conservative) robust optimization approximation for the chance constrained optimization problems. A novel algorithm is proposed to find the smallest possible uncertainty set size that leads to the optimal robust optimization approximation. The proposed method first identifies the maximum set size that leads to feasible robust optimization problems and then identifies the best set size that leads to the desired probability of constraint satisfaction. Effectiveness of the proposed algorithm is demonstrated through a portfolio optimization problem, a production planning and a process scheduling problem.     

Drying in active hydrodynamic regimes

It is shown that the activation of hydrodynamic regimes is one way of solving the problem of increasing the efficiency of drying processes, which includes solving the problems of the process intensity and cost effectiveness, as well as the quality of the final product. A method for estimating the degree of the activity of a hydrodynamic regime is recommended. A strategy for choosing the optimal apparatus-technological design of the drying process is developed that includes the complex analysis of the materials to be dried and the classification of wet disperse materials according to sorption-structural characteristics taking into account adhesion-autohesion properties. Standard apparatuses for each class of materials are recommended. The problem of drying materials with increased adhesion-autohesion properties is chosen. Drying in vortex apparatuses with simultaneous size reduction is considered as an example.     

An integrated dimensionality reduction and surrogate optimization approach for plant-wide chemical process operation

With liquefied natural gas becoming increasingly prevalent as a flexible source of energy, the design and optimization of industrial refrigeration cycles becomes even more important. In this article, we propose an integrated surrogate modeling and optimization framework to model and optimize the complex CryoMan Cascade refrigeration cycle. Dimensionality reduction techniques are used to reduce the large number of process decision variables which are subsequently supplied to an array of Gaussian processes, modeling both the process objective as well as feasibility constraints. Through iterative resampling of the rigorous model, this data-driven surrogate is continually refined and subsequently optimized. This approach was not only able to improve on the results of directly optimizing the process flow sheet but also located the set of optimal operating conditions in only 2 h as opposed to the original 3 weeks, facilitating its use in the operational optimization and enhanced process design of large-scale industrial chemical systems.     

基于多目标教学优化算法在二甲苯吸附分离过程优化中的应用

以C8芳烃混合物的吸附分离过程作为研究对象, 应用多目标教学优化算法(multi-objective teaching-learning-based optimization algorithm, MOTLBO)对模拟移动床多目标优化问题进行求解。采用TMB方法, 建立了模拟移动床模型, 并对两个典型的模拟移动床多目标操作优化问题进行了优化设计。通过与NSGA-Ⅱ算法的比较, 证明了多目标教学优化算法在求解模拟移动床多目标优化问题上的有效性和优势。此外, 还分析了抽出液流量、抽余液流量以及步进时间等对多目标优化非劣解的影响, 优化结果为模拟移动床分离过程的工艺设计和操作提供了依据。     

模式识别法在化工调优中的应用

模式识别调优的基本出发点是,以工艺参数为特征变量构筑模式空间,按调优目标划分样本的类别.采用模式特征抽提方法压缩工艺参数,找出影响目标的主要因素.分别对两类调优问题,即最优指标问题和最优方向问题,提出了寻找最优工况的具体处理方法.对多目标调优也作了简单的讨论.     

Release mechanism analysis of design margin for slowly-time-varying chemical processes

Slowly-time-varying characteristics are common in chemical processes, and the changes of slowly-time-varying parameters in an operating cycle gradually decrease the performance of chemical process. So, enough margins must be added for design variables during the phase of process design according to the possible worst-case influence of slowly-time-varying parameters. The design margins will be released gradually compensating the worse influence of slowly-time-varying parameters in an operating cycle. It can be called as a perfect operation that the operating point is on the boundary of process constraints when an operating cycle is ending. In this paper, the margin release mechanism of slowly-time-varying chemical processes is analyzed. Based on the universal dynamic model containing slowly-time-varying parameters, the full cycle operation optimization is solved by minimum principle of optimal control. It is found that the optimal margin release trajectory is related to the curve of slowly-time-varying parameter, ensuring that the optimal margin release is only dependent on the operating cycle. This mechanism is verified by the example of acetylene hydrogenation reactor. For slowly-time-varying chemical processes, the shorter the operating cycle is set, the faster the design margin is released, the higher temporary economic benefit is obtained; otherwise, the longer the operating cycle is set, the more integrated economic benefit is accomplished.     

A multiobjective approach to design chemical plants with robust dynamic operability characteristics

In chemical plants, operability problems arise mainly due to poor process designs, inaccurate models and/or the control system designs that are unable to cope with process uncertainties. In this paper, a process design methodology is presented that addresses the issue of improving dynamic operability in the present of process uncertainty through appropriate design modifications. The multiobjective nature of the design problem is carefully exploited in the subsequent formulations and a nonlinear programming approach is taken for the simultaneous treatment of both steady-state and dynamic constraints.

Scope—Today, a chemical engineer faces the challenge of designing chemical plants that can operate safely, smoothly and profitably within a dynamic process environment. For a typical chemical plant, major contributions to such an environment originate from external disturbances such as variations in the feedstock quality, different product specifications and/or internal disturbances like catalyst poisoning and heat-exchanger fouling. To guarantee a flexible operation despite such upsets, traditionally, the procedure was either to oversize the equipment or to place large storage tanks between the processing units. Proposed design methods attempted to find optimal operating regimes for chemical plants while compensating for process uncertainty through empirical overdesign factors.

Studies concerned with the interplay between the process design and operation aspects have appeared recently [1, 2] and focused on achieving better controllability upon modifying the plant design, without explicitly considering process uncertainty. Nevertheless, maintaining satisfactory dynamic operability in an environment of uncertainty remained as a pressing issue and the need was raised quite frequently for a rigorous treatment of the topic [3].

The development of new analytical tools [4, 5] made it possible to consider dynamic operability at the process design stage and modify the plant design accordingly. In this paper, a methodology is presented, that systematically guides the designer towards process designs with better dynamic operability and economics, The problem is formulated within a multiobjective optimization framework and makes extensive use of singular-value decomposition and nonlinear semi-infinite programming techniques.

Conclusions and Significance—A multiobjective optimization problem is proposed for designing chemical processes with better dynamic operability characteristics. Robustness indices are used as the indicators of dynamic operability and placed as constraints within the optimization scheme. A semi-infinite nonlinear programming problem results due to the frequency-dependent nature of such constraints. A discretization procedure is suggested to handle the infinite number of constraints and an ellipsoid algorithm allows an interactive solution of the process design problem. A process consisting of three CSTRs is treated as an example, illustrating the potential of the methodology in solving design-related operability problems.     

慢时变化工过程裕量释放机制分析

化工过程普遍存在慢时变特性,在一个运行周期内慢时变参数的变化造成化工装置性能逐渐下降。为此,过程设计时需要按照慢时变参数可能的“最坏”影响对设计变量留出足够的设计裕量,在一个运行周期内通过操作逐渐释放,补偿慢时变参数的不利影响,且理想操作是保证到运行周期结束时化工装置性能恰好达到过程约束边界。本文对慢时变过程设计裕量的释放机制进行了分析,考虑含慢时变参数的全周期操作优化通用动态模型,通过最优控制的极小值原理求解该优化问题,建立了最优裕量释放轨迹和慢时变参数变化曲线之间的联系,从而证明最优裕量释放只与慢时变化工过程的运行周期有关。以乙炔加氢反应器为例验证了该裕量释放机制,对于慢时变化工过程,设定的运行周期越短,设计裕量释放越快,仅能获得较高的短期经济效益;反之,设定较长的运行周期,设计裕量缓慢释放,能获得更高的长期经济效益。