Multi-objective optimization of seeded batch crystallization processes

The optimization of a batch cooling crystallizer has been traditionally sought with respect to the cooling profile and seeding characteristics that keep supersaturation at an optimum level throughout the operation. Crystallization processes typically have multiple performance objectives and optimization using different objective functions leads to significantly different optimal operating conditions. Thus different temperature profiles and seeding characteristics impose a complex interplay on the crystallizer behavior and there is a trade-off between the performance objectives. Therefore, a multi-objective approach should be adopted for optimization of a batch crystallizer for best process operation. This study presents the solution of various optimal control problems for a seeded batch crystallizer within a multi-objective framework. A well known multi-objective evolutionary algorithm, the elitist Nondominated Sorting Genetic Algorithm, has been adapted here to illustrate the potential for the multi-objective optimization approach.     

Optimized species growth in epoxy polymerization with real-coded NSGA-II

Satisfaction of twin objectives of maximization of M_n along with minimization of PDI do not necessarily guarantee the maximization of concentration of desired species in a semibatch epoxy polymerization process. As the final product consists of a number of polymer species, a need is felt to perform an advanced optimization study to come up with such process conditions for which the selective growth of a particular polymer species is maximized in minimum possible processing time and the population of other species should be at their lowest values. These above-mentioned conflicting objectives frame the platform for a multi-objective optimization problem, which is solved here using a real-coded non-dominated sorting genetic algorithm or NSGA II and Pareto optimal solutions are obtained. The decision variables are discrete addition rates of various ingredients, e.g. the amount of addition of bisphenol-A (a monomer), sodium hydroxide and epichlorohydrin at different time steps. All species balance equations, bounds on M_n, PDI and addition amounts are treated as constraints. Results are very promising in terms of optimized operations for selective enhancement of desired polymer species for the epoxy polymerization process. Total additions are kept very close to available experimental conditions to minimize probable extrapolation errors. It has been observed that preferential oligomer production is extremely difficult for epoxy polymerization. Lower chain polymers are the only choice for a good quality, stable polymer product.     

非线性污水处理过程的多目标优化

研究了复杂非线性污水处理过程的多目标优化。针对污水处理过程的非线性动力系统,建立了使污水处理过程运行成本和描述实际输出与期望输出偏差的平方可积误差设计指标同时达到最优的多目标优化模型。采用间接优化方法,首先将描述污水处理过程优化的多目标非线性问题转化为多目标线性规划问题,然后利用遗传算法对其进行求解。本文方法不仅获得了多目标优化问题的近似Pareto前沿,而且由于采用的是多目标线性规划方法,所以具有计算成本低的优点。     

基于非支配排序遗传算法的乙苯脱氢工艺条件优化

为提高现有乙苯脱氢制苯乙烯生产装置的生产率和节能水平,优化技术是一种有效的技术手段。基于改进的非支配排序遗传算法(NSGA-Ⅱ)研究了乙苯脱氢工艺条件的优化问题。把乙苯脱氢反应过程的转化率、选择性作为优化目标,动力学模型以及实际生产状况作为约束条件,构造乙苯脱氢过程的多目标优化问题。基于NSGA-Ⅱ算法求解得到的优化问题的Pareto最优集,分析了各个操作条件对乙苯脱氢生产过程转化率和选择性的影响,最后利用模糊综合评价法,为合理决策提供了有效的依据。结果表明NSGA-Ⅱ具有良好的全局优化性能,运用该算法可在不同的操作约束条件下,求解得到相应的满意解。     

Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor

In this paper, a novel algorithm is proposed for solving multiobjective optimization problems. The proposed algorithm, multiobjective differential evolution (MODE), is applied to optimize industrial adiabatic styrene reactor considering productivity, selectivity and yield as the main objectives. Five combinations of the objectives are considered. Pareto set (a set of equally good solutions) obtained for all the cases is compared with results reported using non-dominated sorting genetic algorithm (NSGA). The results show that all objectives besides profit can be improved compared to those reported using NSGA and current operating conditions. The Pareto optimal front provides wide-ranging optimal operating conditions and an appropriate operating point can be selected based on the requirements of the user.     

基于改进粒子群算法的乙苯脱氢过程多目标优化

设计了一种基于支配关系构造非支配解集的多目标粒子群算法(MOPSO),将当前找到的非支配解保存到一个外部集——最优解集,利用支配更新其最优解集,多次迭代后得到Pareto最优解集。把乙苯脱氢反应过程的收率和选择性作为优化目标,动力学模型和实际生产状况作为约束条件构造乙苯脱氢过程的多目标优化问题,利用改进的多目标粒子群算法进行优化求解。基于求得的Pareto最优解集研究了各个操作条件对乙苯脱氢生产过程收率和选择性的影响,为后续乙苯催化脱氢系统实施先进控制奠定了基础。     

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usual y run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non-linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables (MDNSGA-I ) is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta-tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.     

Multi-objective operation optimization of olefin separation process for MTO plant

In modern coal processing industries, methanol-to-olefins (MTO) is an important equipment. Its olefin separation process is facing with problems such as the change of raw materials, the loss of olefin products and the high consumption of utilities. Operation optimization is required to achieve maximum benefits under the circumstance of quality assurance and requirements. This article takes the pre-depropanized olefin separation process of Lummus as the research object. And the optimization objectives are the total yield of ethylene and propylene as well as the total energy consumption. Modeling, simulation and multi-objective optimization of the process are conducted. Non-dominated sorting genetic algorithm (NSGA-II) is used to solve multi-objective optimization problem. The simultaneous optimization of 15 operational variables is achieved. Under the current yield, the optimal operation point is found by reducing the reflux ratio of low pressure depropanizer, deethanizer and 1^# propylene tower and so on. The results show that the optimal operating point can reduce energy consumption by 20 MW compared with the existing operating point. The optimization interval of each operation variable corresponding to different trade-off points is determined by the comprehensive analysis of decision variables. It is also found that distillation equipment can operate in different optimal operation intervals.     

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.     

MTO烯烃分离过程的多目标操作优化

现代煤化工中,甲醇制烯烃 （MTO） 是一个非常重要的装置。其烯烃分离过程面临着原料变动大、烯烃产品损失以及较高的公用工程消耗等问题。这就需要在满足产品规格和需求的情况下,优化操作条件以实现最大效益。以Lummus前脱丙烷的烯烃分离工艺为研究对象,以增加乙烯与丙烯的总收率和降低总能耗为优化目标,对该工艺流程进行建模模拟与多目标优化。采用非支配排序遗传算法（NSGA-II）进行多目标优化的求解,实现了15个操作变量的同时优化。在维持产品收率不变的前提下,可通过降低脱丙烷塔、脱乙烷塔和1^#丙烯精馏塔的回流比等优化措施找到了当前最优操作点。结果表明,该最优操作点与现有操作点相比可降低20 MW能耗。通过对决策变量的综合分析,确定了不同目标权衡下对应的各个操作变量的优化区间,发现精馏塔可以在多个最佳操作区间内运行。     

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。     

基于动态优化的催化裂化装置再生器裕量分析与控制设计(Ⅱ) 求解方法与结果分析

用动态优化的方法求解催化裂化装置再生器的工艺裕量与控制设计。对于该多目标混合整数动态优化问题,通过ε-约束法处理多目标优化问题,将控制性能目标函数转化为控制性能约束;通过将0-1变量松弛化、引入附加等式约束求解混合整数动态优化问题。求解得到非劣解集,绘制关于控制性能指标和工艺指标的关系曲线,发现系统对控制器性能的要求愈高,所需要的裕量应愈大。由此进行折中处理,从而找到兼顾工艺要求和控制性能的催化裂化装置再生器优化设计方案。     

不确定性条件下对固体氧化物燃料电池-质子交换膜燃料电池联合系统的综合/设计优化(英文)

Solid oxide fuel cell–proton exchange membrane (SOFC–PEM) hybrid system is being foreseen as a valuable alternative for power generation. As this hybrid system is a conceptual design, many uncertainties involving input values should be considered at the early stage of process optimization. We present in this paper a general-ized framework of multi-objective optimization under uncertainty for the synthesis/design optimization of the SOFC–PEM hybrid system. The framework is based on geometric, economic and electrochemical models and focuses on evaluating the effect of uncertainty in operating parameters on three conflicting objectives:electricity efficiency, SOFC current density and capital cost of system. The multi-objective optimization provides solutions in the form of a Pareto surface, with a range of possible synthesis/design solutions and a logical procedure for searching the global optimum solution for decision maker. Comparing the stochastic and deterministic Pareto surfaces of different objectives, we conclude that the objectives are considerably influenced by uncertainties because the two trade-off surfaces are different.     

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.     

Pareto-optimal solutions for multi-objective optimization of fed-batch bioreactors using nondominated sorting genetic algorithm

Many optimal control problems are characterized by their multiple performance measures that are often noncommensurable and competing with each other. The presence of multiple objectives in a problem usually give rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Evolutionary algorithms have been recognized to be well suited for multi-objective optimization because of their capability to evolve a set of nondominated solutions distributed along the Pareto front. This has led to the development of many evolutionary multi-objective optimization algorithms among which Nondominated Sorting Genetic Algorithm (NSGA and its enhanced version NSGA-II) has been found effective in solving a wide variety of problems. Recently, we reported a genetic algorithm based technique for solving dynamic single-objective optimization problems, with single as well as multiple control variables, that appear in fed-batch bioreactor applications. The purpose of this study is to extend this methodology for solution of multi-objective optimal control problems under the framework of NSGA-II. The applicability of the technique is illustrated by solving two optimal control problems, taken from literature, which have usually been solved by several methods as single-objective dynamic optimization problems.     

Synthesis/design optimization of SOFC-PEM hybrid system under uncertainty

Solid oxide fuel cell–proton exchange membrane (SOFC–PEM) hybrid system is being foreseen as a valuable alternative for power generation. As this hybrid system is a conceptual design, many uncertaintie...     

A multi-objective invasive weeds optimization algorithm for solving multi-skill multi-mode resource constrained project scheduling problem

A new multi-skill multi-mode resource constrained project scheduling problem with three objectives is studied in this paper. The objectives are: (1) minimizing project's makespan, (2) minimizing total cost of allocating workers to skills, and (3) maximizing total quality of processing activities. A meta-heuristic algorithm called multi-objective invasive weeds optimization algorithm (MOIWO) with a new chromosome structure guaranteeing feasibility of solutions is developed to solve the proposed problem. Two other meta-heuristic algorithms called non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO) are used to validate the solutions obtained by the developed MOIWO. The parameters of the developed algorithms are calibrated using Taguchi method. The results of the experiments show that the MOIWO algorithm has better performance in terms of diversification metric, the MOPSO algorithm has better performance regarding mean ideal distance, while NSGA-II algorithm has better performance in terms of spread of non-dominance solution and spacing metrics.     

面向产品分布协调的两段提升管催化裂解多目标优化

根据两段提升管重油催化裂解过程工艺特点和经济运行要求，基于过程机理模型，考虑多种约束条件，构造了同时最大化丙烯、汽油产量以及最小化干气产量的多目标操作优化问题，并采用标准化法向约束方法求解获得了完整、均匀分布的Pareto最优解。仿真结果表明，多目标优化结果可以定量地描述出丙烯、汽油和干气收率间的最优折中，以及操作变量、约束条件对产品分布的影响，可以为过程优化操作提供指导。     

基于NSGA-Ⅱ的模拟移动床色谱分离过程多目标操作优化

多目标优化策略被应用于模拟移动床过程的操作优化中，采用一种基于Pareto最优解的多目标优化算法——NSGA-Ⅱ算法，以分离联萘酚对映体的模拟移动床色谱分离过程作为研究对象，利用模拟移动床TMB数学模型，以分离性能指标作为目标函数进行了多目标操作优化设计。优化结果表明，NSGA-Ⅱ算法得到的非劣解在目标空间分布均匀，算法收敛性和鲁棒性好。基于NSGA-Ⅱ算法的面向分离性能多目标优化设计方法为模拟移动床分离过程的工艺设计和操作指导提供了有效的工具。