一种求解化工动态优化问题的迭代自适应粒子群方法

智能优化方法因其简单、易实现且具有良好的全局搜索能力,在动态优化中的应用越来越广泛,但传统的智能方法收敛速度相对较慢。提出了一种迭代自适应粒子群优化方法（IAPSO）来求解一般的化工动态优化问题。首先通过控制变量参数化将原动态优化问题转化为非线性规划问题,再利用所提出的迭代自适应粒子群优化方法进行求解。相比传统的粒子群优化方法,该种迭代自适应粒子群优化方法具有收敛速度更快的优点,主要原因是：该算法根据粒子种群分布特性自适应调整参数;该算法通过缩减搜索空间并迭代使用粒子群算法搜索最优解。将提出的迭代自适应粒子群方法应用到多个经典动态优化问题中,测试结果表明,该方法简单、有效,精度高,且收敛速度比传统粒子群算法有显著提升。     

Inferential Control of Reactive Destillation Columns – An Algorithmic Approach

Decentralized control system design comprises the selection of a suitable control structure and controller parameters. Here, mixed integer optimization is used to determine the optimal control structure and the optimal controller parameters simultaneously. The process dynamics is included explicitly into the constraints using a rigorous nonlinear dynamic process model. Depending on the objective function, which is used for the evaluation of competing control systems, two different formulations are proposed which lead to mixed‐integer dynamic optimization (MIDO) problems. A MIDO solution strategy based on the sequential approach is adopted in the present paper. Here, the MIDO problem is decomposed into a series of nonlinear programming (NLP) subproblems (dynamic optimization) where the binary variables are fixed, and mixed‐integer linear programming (MILP) master problems which determine a new binary configuration for the next NLP subproblem. The proposed methodology is applied to inferential control of reactive distillation columns as a challenging benchmark problem for chemical process control.     

A bilevel NLP sensitivity‐based decomposition for dynamic optimization with moving finite elements

Optimal control has guided numerous applications in chemical engineering, and exact determination of optimal profiles is essential for operation of separation and reactive processes, and operating strategies and recipe generation for batch processes. Here, a simultaneous collocation formulation based on moving finite elements is developed for the solution of a class of optimal control problems. Novel features of the algorithm include the direct location of breakpoints for control profiles and a termination criterion based on a constant Hamiltonian profile. The algorithm is stabilized and performance is significantly improved by decomposing the overall nonlinear programming (NLP) formulation into an inner problem, which solves a fixed element simultaneous collocation problem, and an outer problem, which adjusts the finite elements based on several error criteria. This bilevel formulation is aided by a NLP solver (the interior point optimizer) for both problems as well as an NLP sensitivity component, which provides derivative information from the inner problem to the outer problem. This approach is demonstrated on 11 dynamic optimization problems drawn from the optimal control and chemical engineering literature. © 2014 American Institute of Chemical Engineers AIChE J, 60: 966–979, 2014     

Control Parameterization‐Based Adaptive Particle Swarm Approach for Solving Chemical Dynamic Optimization Problems

A control parameterization‐based particle swarm optimization (CP‐PSO) approach is presented which combines control parameterization with particle swarm optimization to solve dynamic optimization problems in chemical engineering. To improve search efficiency and convergence rate, a control parameterization‐based adaptive particle swarm optimization (CP‐APSO) approach is proposed, in which inertia weight and acceleration coefficients are updated according to population distribution characteristics. Three benchmark chemical dynamic optimization problems are explored as illustration. The results demonstrate that CP‐APSO is efficient for solving a general class of chemical dynamic optimization problems and CP‐APSO largely outperforms CP‐PSO on the convergence rate.     

基于CSTR的反应器网络综合双层优化算法

反应器网络综合问题一般都是复杂的非线性规划问题,在分析基于全混流反应器的反应器网络模型特点的基础上,提出了求解该模型的双层优化算法. 通过将反应器网络综合非线性规划问题分解为物流流量和反应器体积空间的线性优化和浓度空间的优化搜索问题,降低了所求解问题的规模和难度,同时利用全局优化算法进行浓度空间的优化搜索,提高了求得全局最优解的概率. 实例研究表明,双层优化算法可以更准确地给出最优的反应器网络结构以及网络中反应器的类型和大小.     

基于差分进化算法的控制变量参数化方法及其在化工过程动态优化中的应用(英文)

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.     

A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles

A three-stage computation framework for solving parameter estimation problems for dynamic systems with multiple data profiles is developed. The dynamic parameter estimation problem is transformed into a nonlinear programming (NLP) problem by using collocation on finite elements. The model parameters to be estimated are treated in the upper stage by solving an NLP problem. The middle stage consists of multiple NLP problems nested in the upper stage, representing the data reconciliation step for each data profile. We use the quasi-sequential dynamic optimization approach to solve these problems. In the lower stage, the state variables and their gradients are evaluated through integrating the model equations. Since the second-order derivatives are not required in the computation framework this proposed method will be efficient for solving nonlinear dynamic parameter estimation problems. The computational results obtained on a parameter estimation problem for two CSTR models demonstrate the effectiveness of the proposed approach.     

A trust region filter method for glass box/black box optimization

Modern nonlinear programming solvers can be utilized to solve very large scale problems in chemical engineering. However, these methods require fully open models with accurate derivatives. In this article, we address the hybrid glass box/black box optimization problem, in which part of a system is modeled with open, equation based models and part is black box. When equation based reduced models are used in place of the black box, NLP solvers may be applied directly but an accurate solution is not guaranteed. In this work, a trust region filter algorithm for glass box/black box optimization is presented. By combining concepts from trust region filter methods and derivative free optimization, the method guarantees convergence to first‐order critical points of the original glass box/black box problem. The algorithm is demonstrated on three comprehensive examples in chemical process optimization. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3124–3136, 2016     

Solving mixed integer nonlinear programming problems with line-up competition algorithm

Line-up competition algorithm (LCA), a global optimization algorithm proposed recently, is applied to the solution of mixed integer nonlinear programming (MINLP) problems. Through using alternative schemes to handle integer variables, the algorithm reported previously for solving NLP problems can be extended expediently to the solution of MINLP problems. The performance of the LCA is tested with several non-convex MINLP problems published in the literature, including the optimal design of multi-product batch chemical processes and the location-allocation problem. Testing shows that the LCA algorithm is efficient and robust in the solution of MINLP problems.     

Global optimization of stiff dynamical systems

We present a deterministic global optimization method for nonlinear programming formulations constrained by stiff systems of ordinary differential equation (ODE) initial value problems (IVPs). The examples arise from dynamic optimization problems exhibiting both fast and slow transient phenomena commonly encountered in model-based systems engineering applications. The proposed approach utilizes unconditionally stable implicit integration methods to reformulate the ODE-constrained problem into a nonconvex nonlinear program (NLP) with implicit functions embedded. This problem is then solved to global optimality in finite time using a spatial branch-and-bound framework utilizing convex/concave relaxations of implicit functions constructed by a method which fully exploits problem sparsity. The algorithms were implemented in the Julia programming language within the EAGO.jl package and demonstrated on five illustrative examples with varying complexity relevant in process systems engineering. The developed methods enable the guaranteed global solution of dynamic optimization problems with stiff ODE–IVPs embedded.     

ASTRO‐FOLD 2.0: An enhanced framework for protein structure prediction

The three‐dimensional (3‐D) structure prediction of proteins, given their amino acid sequence, is addressed using the first principles–based approach ASTRO‐FOLD 2.0. The key features presented are: (1) Secondary structure prediction using a novel optimization‐based consensus approach, (2) β‐sheet topology prediction using mixed‐integer linear optimization (MILP), (3) Residue‐to‐residue contact prediction using a high‐resolution distance‐dependent force field and MILP formulation, (4) Tight dihedral angle and distance bound generation for loop residues using dihedral angle clustering and non‐linear optimization (NLP), (5) 3‐D structure prediction using deterministic global optimization, stochastic conformational space annealing, and the full‐atomistic ECEPP/3 potential, (6) Near‐native structure selection using a traveling salesman problem‐based clustering approach, ICON, and (7) Improved bound generation using chemical shifts of subsets of heavy atoms, generated by SPARTA and CS23D. Computational results of ASTRO‐FOLD 2.0 on 47 blind targets of the recently concluded CASP9 experiment are presented. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Dynamic optimization of the methylmethacrylate cell‐cast process for plastic sheet production

Traditionally, the methylmethacrylate (MMA) polymerization reaction process for plastic sheet production has been carried out using warming baths. However, it has been observed that the manufactured polymer tends to feature poor homogeneity characteristics measured in terms of properties like molecular weight distribution. Nonhomogeneous polymer properties should be avoided because they give rise to a product with undesired wide quality characteristics. To improve homogeneity properties force‐circulated warm air reactors have been proposed, such reactors are normally operated under isothermal air temperature conditions. However, we demonstrate that dynamic optimal warming temperature profiles lead to a polymer sheet with better homogeneity characteristics, especially when compared against simple isothermal operating policies. In this work, the dynamic optimization of a heating and polymerization reaction process for plastic sheet production in a force‐circulated warm air reactor is addressed. The optimization formulation is based on the dynamic representation of the two‐directional heating and reaction process taking place within the system, and includes kinetic equations for the bulk free radical polymerization reactions of MMA. The mathematical model is cast as a time dependent partial differential equation (PDE) system, the optimal heating profile calculation turns out to be a dynamic optimization problem embedded in a distributed parameter system. A simultaneous optimization approach is selected to solve the dynamic optimization problem. Trough full discretization of all decision variables, a nonlinear programming (NLP) model is obtained and solved by using the IPOPT optimization solver. The results are presented about the dynamic optimization for two plastic sheets of different thickness and compared them against simple operating policies. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

PTFE间歇聚合反应过程变周期动态经济优化控制

聚四氟乙烯(PTFE)间歇聚合生产模式可满足小批量、多用途以及高质量产品的市场需求。针对PTFE聚合过程存在强非线性和大时滞特性,提出了一种基于自由终端的动态经济优化控制方法。首先,将生产周期作为一个自由度纳入优化变量建立动态经济优化问题,采用改进控制变量参数化方法,控制输入被离散为可变长度的片状序列,便可将动态经济优化问题转换为非线性规划(NLP)问题;然后,采用基于梯度下降的内点罚函数法求解NLP问题,通过变周期预测时域的滚动优化控制方法优化控制输入和终端时间;最后将提出的变周期动态经济优化控制与传统PI控制、非线性模型预测控制进行对比测试分析,仿真结果表明本方法单位经济效益更高,生产周期更短,突显了间歇生产的灵活性。     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

迭代遗传算法及其用于生物反应器补料优化

针对化工动态优化的数值求解问题,提出将迭代思想与遗传操作相结合,构建迭代遗传算法.算法首先对时间区间和控制搜索域实施离散化,进而应用遗传操作搜索离散问题的最优控制策略.逐步收缩搜索域并迭代以消减离散化带来的偏差,不断改善寻优结果,增强算法的稳健性.实例测试表明该算法简便、可行、高效,已成功地应用于Lee-Ramirez生物反应器补料流率的优化,运算结果优于文献值,显示了迭代遗传算法的优越性.迭代遗传算法尤其适用于系统的梯度信息不可得的情况.     

Experimental evaluation of an approach to online redesign of experiments for parameter determination

The online redesign of experiments for parameter determination of nonlinear dynamic systems has been studied recently by different research groups. In this article, this technique is assessed in a real case study for the first time. The presented algorithm adopts well‐known concepts from model‐based control. Compared to previous studies, special attention is given to the efficient treatment of the underlying nonlinear and possibly ill‐conditioned parameter estimation and experiment design problems. These problems are solved with single shooting and gradient‐based nonlinear programming (NLP) solvers. We use an initial value solver, which generates first‐ and second‐order sensitivities to compute exact derivatives of the problem functions. As a special feature, we propose the integration of a local parameter identifiability analysis and a corresponding algorithm that generates well‐conditioned problems. The practical applicability is demonstrated by experimental application to a chromatography column system where A, D, and E optimal experiments are performed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1981–1995, 2013     

含滞后及不确定参数动态过程系统的定量优化方法与应用

许多动态化工系统含有不确定参数。当含不确定参数的过程系统又带有滞后环节时,系统的优化问题就变得非常复杂。对含不确定参数的化工系统的动态过程进行优化,若未考虑滞后环节对动态优化结果的影响,不能保证系统实际操作的优化及安全运行。本文采用改进的有限元正交配置优化算法,较好地解决了含有滞后、不确定参数的化工过程的动态优化问题。最后将一个具有循环返料的反应-分离器系统以及一个绝热反应釜作为案例对该优化方法的应用进行分析,根据案例的研究验证了该优化方法的有效性,从而为含有滞后、不确定参数的动态系统的设计和操作性能优化提供一种有效的定量分析方法和理论依据。     

序贯优化化工动态问题的蚁群算法

针对化工动态优化问题,分析现有数值解法的不足,提出序贯执行蚁群寻优操作,逐步寻找最佳解的策略,构建序贯蚁群算法.算法首先对时间区间和控制变量搜索域实施离散化,以一组整数编码的蚁群路径表示可行控制策略,进而应用蚁群寻优操作寻找离散问题的最优控制策略.逐步收缩控制搜索域并反复上述步骤,不断改善寻优结果.序贯蚁群算法简便快捷,用于化工动态优化问题效果良好,计算结果体现了算法的稳健性.     

非线性动态优化问题的改进控制矢量迭代法(Ⅰ)无路径约束问题(英文)

This study proposes an efficient indirect approach for general nonlinear dynamic optimization problems without path constraints. The approach incorporates the virtues both from indirect and direct methods: it solves the optimality conditions like the traditional indirect methods do, but uses a discretization technique inspired from direct methods. Compared with other indirect approaches, the proposed approach has two main advantages: (1) the discretized optimization problem only employs unconstrained nonlinear programming (NLP) algorithms such as BFGS (Broyden-Fletcher-Goldfarb-Shanno), rather than constrained NLP algorithms, therefore the computational efficiency is increased; (2) the relationship between the number of the discretized time intervals and the integration error of the four-step Adams predictor-corrector algorithm is established, thus the minimal number of time intervals that under desired integration tolerance can be estimated. The classic batch reactor problem is tested and compared in detail with literature reports, and the results reveal the effectiveness of the proposed approach. Dealing with path constraints requires extra techniques, and will be studied in the second paper.