Efficient constraint handling scheme for differential evolutionary algorithm in solving chemical engineering optimization problem

This paper introduces a new constraint handling scheme developed for the differential evolutionary algorithm to solve constrained optimization problems. The developed approach uses a repair algorithm based on the gradient information derived from the equality constraint set to correct infeasible solutions. A dominance-based selection scheme is also applied to incorporate constraints into the objective function. To illustrate the developed algorithm and to compare its efficiency with other tradition method, several test problems and chemical engineering optimization problems are used. A traditional constraint handling technique is compared; both in terms of solution quality and the number of function evaluations required. The performance of our developed scheme compares favorably with traditional penalty function method. Our developed algorithm can effectively handle constraints encountered in chemical engineering optimization problems.     

一种改进的差分进化算法及其在化工过程优化中的应用

Differential evolution （DE） is an evolutionary optimization method, which has been successfully used in many practical cases. However, DE involves large computation time, especially, when used to optimize the compurationally expensive objective function. To overcome this .difficulty, the concept of immunity based on vaccination is used to help proliferate excellent schemata and to restrain the degenerate phenomenon. To improve the effective- ness of vaccines, a new vaccine autonomous obtaining method, and a method of deciding the probability of vacci- nation are proposed. In addition, a method for modifying the search space dynamically is proposed to enhance the possibility of converging to the true global optimum. Experiments showed that the improved DE performs better than the classical DE significantly.     

A data-driven optimization algorithm for differential algebraic equations with numerical infeasibilities

Support vector machines (SVMs) based optimization framework is presented for the data-driven optimization of numerically infeasible differential algebraic equations (DAEs) without the full discretization of the underlying first-principles model. By formulating the stability constraint of the numerical integration of a DAE system as a supervised classification problem, we are able to demonstrate that SVMs can accurately map the boundary of numerical infeasibility. The necessity of this data-driven approach is demonstrated on a two-dimensional motivating example, where highly accurate SVM models are trained, validated, and tested using the data collected from the numerical integration of DAEs. Furthermore, this methodology is extended and tested for a multidimensional case study from reaction engineering (i.e., thermal cracking of natural gas liquids). The data-driven optimization of this complex case study is explored through integrating the SVM models with a constrained global grey-box optimization algorithm, namely the ARGONAUT framework.     

An efficient method for optimal design of large-scale integrated chemical production sites with endogenous uncertainty

Integrated sites are tightly interconnected networks of large-scale chemical processes. Given the large-scale network structure of these sites, disruptions in any of its nodes, or individual chemical processes, can propagate and disrupt the operation of the whole network. Random process failures that reduce or shut down production capacity are among the most common disruptions. The impact of such disruptive events can be mitigated by adding parallel units and/or intermediate storage. In this paper, we address the design of large-scale, integrated sites considering random process failures. In a previous work (Terrazas-Moreno et al., 2010), we proposed a novel mixed-integer linear programming (MILP) model to maximize the average production capacity of an integrated site while minimizing the required capital investment. The present work deals with the solution of large-scale problem instances for which a strategy is proposed that consists of two elements. On one hand, we use Benders decomposition to overcome the combinatorial complexity of the MILP model. On the other hand, we exploit discrete-rate simulation tools to obtain a relevant reduced sample of failure scenarios or states. We first illustrate this strategy in a small example. Next, we address an industrial case study where we use a detailed simulation model to assess the quality of the design obtained from the MILP model.     

An inexact interior point method for optimization of differential algebraic systems

This paper presents an inexact factorization technique in the context of an interior point method for optimal control of systems described by Differential Algebraic Equations (DAEs). The proposed method is based on a numerically banded structure arising in the normal equations. The structure implies that banded factorization techniques can be used to calculate inexact Newton directions at a low computational cost. Numerical experiments show that a narrow band in the normal equations can be selected without impeding the convergence of the method.     

快速界面法制备FeOOH@CoNi-LDH@NF用于高效析氧

以六水合硝酸钴、六水合硝酸镍、尿素和氟化铵为原料,采用水热法在镍网上原位构筑层状双金属氢氧化物(LDH)(CoNi-LDH@NF),然后采用快速界面法在硝酸钠和六水合氯化铁的100℃溶液中对其进行刻蚀制备了FeOOH@CoNi-LDH@NF.利用XRD、SEM、XPS和TEM对FeOOH@CoNi-LDH@NF进行了形...     

An integrated framework for on-line supervised optimization

In this paper, an integrated supervisory framework is envisaged for more robust on-line optimization and exception handling. This system takes advantage of the capabilities of real time evolution algorithm [Sequeira, S., Graells, M., Puigjaner, L. (2002). Real time evolution for Online Optimization of Continuous Processes. Industrial & Engineering Chemistry Research 41, 1815–1825] plus a fault diagnosis system (FDS) for managing abnormal situations. Both systems are part of a supervisory module which is responsible for handling plant incidences (faults and disturbances) by taking the appropriate corrective actions. Thus, a more satisfactory on-line performance is achieved, while reaction to incidence is enhanced by providing combined cause-effect information to plant managers. The implementation of the supervised real time evolution scheme has been performed using Matlab and the commercial simulation package HYSYS.Plant, taking advantage of their communication capabilities (COM technology). The developed fault diagnosis system comprises a detection module based on multivariate statistical techniques and an isolation module that uses an artificial neural network as a pattern classifier. The benefits of this framework are illustrated through a case study consisting in a debutanizer distillation column. The handling of various plant incidences, involving different sources and types of disturbances are considered. Finally, results of the supervised real time evolution (SRTE) are compared with those obtained using the standard real time optimization approach (RTO), showing superior performance in most of the cases.     

An efficient method for a numerical description of virgin olive oil color with only two absorbance measurements

Four polynomial expressions are obtained that provide a good approximation and an easy, rapid calculation of the chromatic coordinates and the chroma—L ^*, a ^*, b ^*, and C—for the illuminant C and the standard observer, for a virgin or extra virgin olive oil; absorbance is measured at only 480 and 670 nm. These are as follows: L ^*=0.556458(A₄₈₀)²−2.51145A₄₈₀+0.55504(A₆₇₀)²−8.53016A₆₇₀+98.4089; a ^*=0.177372(A₄₈₀)²+2.1363A₄₈₀+1.43254(A₆₇₀)²−0.789231A₆₇₀−13.9246; b ^*=−16.0277(A₄₈₀)²+79.8932A₄₈₀−5.06558(A₆₇₀)²+3.36169A₆₇₀+31.9405; C=−15.8439(A₄₈₀)²+78.9312A₄₈₀−5.26784(A₆₇₀)²+3.56917A₆₇₀+33.3927. These give acceptable results, making the method a practical alternative to the extremely laborious Commission Internationale d’Eclairage (CIE) L ^* a ^* b ^* system, by which 391 absorbance values must be measured individually, nanometer by nanometer, before applying more complex equations. The validity of the proposed method has been confirmed by comparison, using a set of 20 sample oils different from the set of 25 oils used to generate the order of the equations. The variations between the values provided by the proposed and standard methods, respectively, had a mean of 0.00 for each of the chromatic variables—L ^* , a ^* , b ^* , and C; SD were moderate (0.71, 0.52, 1.22, and 1.22, respectively); the root mean square and the R ²-terms also confirmed the validity of the method.     

半间歇釜式反应器安全高效操作的数值优化策略

半间歇釜式反应器内物料积累过多且反应放热过快时,容易引发热失控风险,造成化工安全事故。设计较优的加料操作,既可以避免热失控风险,又可以缩短操作周期、提高生产效率。针对半间歇釜式反应器,以乙酸酐水解为模型反应,基于反应器数学模型,提出了一种安全高效加料操作的数值优化策略。在该策略中,首先确定不同加料方式（如一段、二段和三段加料）下的安全操作温度区间,然后在该温度区间内寻找最短操作周期对应的操作温度,该温度即为最佳的加料操作温度。优化结果表明三段加料的安全操作温度区间和最佳操作温度分别比一段加料宽60.9%和低1.9 K,六段加料已经基本可以实现操作周期最短,增加操作压力也有利于缩短操作周期。     

一种改进的差分进化算法及其在补料分批式生化反应器动态优化中的应用

动态优化是生物化工过程中的重要课题,求解动态优化问题通常有两种方法:解析法和数值法。基于智能进化算法的数值方法在动态优化中的应用越来越广泛,但是这些方法局部寻优能力不强,容易陷入局部最优,并且求解速度相对较慢。针对这些方法的不足,提出了一种改进的差分进化算法,设计了新的局部寻优算子来增强算法的局部寻优能力,并且采用一种新的控制策略表示方法来求解动态优化问题。通过求解补料分批式生化反应器的动态优化实例,证明了算法的有效性和鲁棒性。通过与其他几种方法进行对比,实验结果表明,所提出的方法在优化结果和计算代价方面都有优势。     

One-step approach for heat exchanger network retrofitting using integrated differential evolution

Heat exchanger network (HEN) retrofitting is more important and challenging than HEN synthesis since it involves modifying existing network for improved energy efficiency. Additional factors to be considered include spatial constraints, relocation and re-piping costs, reassignment and effective use of existing heat exchanger areas. The previous studies using stochastic global optimization algorithms are mainly focused on two-level approach: the first level uses a stochastic algorithm for optimizing structure, and the second level uses either a stochastic or a deterministic algorithm for optimizing continuous variables. In this study, we propose and test one-step approach where a stochastic global optimization method, namely, integrated differential evolution (IDE), handles both discrete and continuous variables together. Thus, HEN structure and retrofitting model parameters are simultaneously optimized by IDE, which avoids the algorithm trapping at a local optimum and also improves the computational efficiency. Results on HEN applications show that the proposed approach gives better solutions.     

An efficient chained-hash-table strategy for collision handling in hard-sphere discrete particle modeling

We develop an efficient algorithm for handling collision events that is suitable for Discrete Particle Modeling (DPM) of dense gas–solid fluidization systems. We improve on previous strategies that are discussed in this paper as a byproduct. The core idea is centered on the use of dynamic crosswise linked data structures. This type of data structures enables an efficient updating and managing of lists of collision events associated with particles. In addition, a chained-hash-table strategy is proposed to efficiently process particle collision sequences. For systems of N_p particles, this strategy allows a complexity O(1) time per collision regarding the event list handling operations.     

Multi-objective optimization of reverse osmosis networks by lexicographic optimization and augmented epsilon constraint method

This study proposes a multi-objective optimization (MOO) of reverse osmosis (RO) networks for seawater desalination. The membrane transport model takes into consideration of the longitudinal variation of the velocity, the pressure, and the concentration in the membrane modules. The RO network with three type energy recovery device options (pressure exchanger (PX), Hydraulic Turbocharger, and turbine) is introduced. Lexicographic optimization (for calculation of a more effective payoff table) and augmented ε-constraint method (to avoid inefficient Pareto solutions) are proposed to solve the MOO problem. A fuzzy decision maker is introduced to derive the most efficient solution among Pareto-optimal solutions. Firstly, different energy recovery option studies show that using PX is seen to be the most profitable option. Exergy analysis is used to evaluate the contribution of the equipments in energy degradation. Secondly, the proposed multi-objective framework simultaneously optimizes the total annualized cost (TAC) and energy consumption. With the increases of weighting for the main objective function: TAC, the most efficient solution moves to lower TAC direction. Finally, system recovery rate is added as the third objective function. It is reasonable to stay at the appropriate system recovery rather than to increase up to its limit and generating high energetic losses.     

An efficient preparation method for superabsorbent polymers

High water‐absorbent polyacrylates could be prepared by concentrated aqueous solution polymerization within a short time period, heating the monomer mixture by water bath. The influences of initiator content, bath temperature, crosslinker content (Cc), and degree of neutralization on water absorbency (Q) were investigated. The temperature changing of the monomer mixture during polymerization was thoroughly analyzed. The increase of initiator content as well as the increase of bath temperature results in the increase of water absorbency and reduces the crosslinking efficiency. The results are in conformity with Flory's network theory and also illustrate that lower crosslinking efficiency occurs when the polymerization rate is faster. An empirical relation of Q = 1.40 Cc^−0.665 is obtained and its exponent is very close to −0.6 in a derived relation. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 74: 119–124, 1999     

An efficient purification method for detonation nanodiamonds

This article reports the purification process of detonation soot to obtain pure nanodiamond powder. Nanodiamonds are synthesized by detonation using a high explosive mixture composed of trinitrotoluene and hexogen. The detonation of the charge leads to a powder containing nanodiamonds as well as metallic impurities and sp² carbon species. Further, to remove metallic particles, an unusual acidic treatment (hydrofluoric/nitric acids; i.e. fluorinated aqua regia) was set up. To eliminate sp² carbon species such as graphite and amorphous carbon, a thermal oxidation treatment was performed at 420 °C under air in a furnace during several hours. Transmission Electronic Microscopy, Raman spectroscopy, X-ray diffraction and Thermo-Gravimetric Analysis showed that this purification process is very efficient. From TGA measurements, a model of the carbon grain combustion was developed by considering graphitic shells surrounding the nanodiamond particles, and was used to demonstrate that the selective oxidation of graphite was experimentally realistic. Moreover, another model was set up from specific area measurements to evaluate the thickness of the functional groups surrounding the nanodiamonds after the oxidation of sp² carbonaceous species. The treatment described herein was achieved on several tens of grams of product and could be easily adapted to the industrial scale.     

An efficient numerical technique for solving one-dimensional batch crystallization models with size-dependent growth rates

In this work, an efficient numerical method is introduced for solving one-dimensional batch crystallization models with size-dependent growth rates. The proposed method consist of two parts. In the first part, a coupled system of ordinary differential equations (ODEs) for the moments and the solute concentration is numerically solved to obtain their discrete values in the time domain of interest. These discrete values are also used to get growth and nucleation rates in the same time domain. To overcome the issue of closure, a Gaussian quadrature method based on orthogonal polynomials is employed for approximating integrals appearing in the ODE system. In the second part, the discrete growth and nucleation rates along with the initial crystal size distribution (CSD) are used to construct the final CSD. The expression for CSD is obtained by applying the method of characteristics and Duhamel's principle on the given population balance model (PBM). The proposed method is efficient, accurate, and easy to implement in the computer. Several numerical test problems of batch crystallization processes are considered. For a validation, the results of the proposed technique are compared with those obtained using a high resolution finite volume scheme.     

An efficient latent variable optimization approach with stochastic constraints for complex industrial process

For complex chemical processes, process optimization is usually performed on causalmodels fromfirst principle models. When the mechanism models cannot be obtained easily, restricted model built by process data is used for dynamic process optimization. A new strategy is proposed for complex process optimization, in which latent variables are used as decision variables and statistics is used to describe constraints. As the constraint condition will be more complex by projecting the original variable to latent space, Hotelling T² statistics is introduced for constraint formulation in latent space. In this way, the constraint is simplified when the optimization is solved in low-dimensional space of latent variable. The validity of the methodology is illustrated in pH-level optimal control process and practical polypropylene grade transition process.     

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.