Multi‐Objective Optimization of a Batch Copoly(ethylene‐polyoxyethylene terephthalate) Reactor Using Different Adaptations of Nondominated Sorting Genetic Algorithm

Summary: A multi‐objective optimization is carried out for a copoly(ethylene‐polyoxyethylene terephthalate) (CEPT) batch reactor using different adaptations of the elitist nondominated sorting genetic algorithm (NSGA‐II). Several two objective function problems are formulated and solved. One objective is to minimize the total copolymerization time and other objective is to minimize the formation of total undesirable side products, namely, acid end group, vinyl ester end group, diethylene glycol ester end group of polyethylene terephthalate, and diethylene glycol. End‐point constraint is incorporated to obtain the specified number‐average degree of copolymerization. The operating temperature history of batch CEPT reactor is the only important decision variable for first optimization problem, whereas operating temperature history and molar ratio of feed to the reactor are taken as decision variables for the second optimization problem. Optimal Pareto frontiers are obtained for both the problems studied. In order to operate the polymerization reactor optimally, it is found that higher isothermal temperature history is needed for short copolymerization time, whereas lower nonisothermal temperature history is required for higher copolymerization time. The results of NSGA‐II technique are analyzed and compared with the jumping gene (JG) and adapted jumping gene (aJG) operator in NSGA‐II separately. It is found that NSGA‐II‐JG is superior to NSGA‐II and NSGA‐II‐aJG.

Optimization of a batch copoly(ethylene‐polyoxyethylene terephthalate) reactor.     

Multiobjective optimization of a free radical bulk polymerization reactor using genetic algorithm

A multiobjective optimization technique has been developed for free radical bulk polymerization reactors using genetic algorithm. The polymerization of methyl methacrylate in a batch reactor has been studied as an example. The two objective functions which are minimized are the total reaction time and the polydispersity index of the polymer product. Simultaneously, end‐point constraints are incorporated to attain desired values of the monomer conversion (x_m) and the number average chain length (μ_n). A nondominated sorting genetic algorithm (NSGA) has been adapted to obtain the optimal control variable (temperature) history. It has been shown that the optimal solution converges to a unique point and no Pareto set is obtained. It has been observed that the optimal solution obtained using the NSGA for multiobjective function optimization compares very well with the solution obtained using the simple genetic algorithm (SGA) for a single objective function optimization problem, in which only the total reaction time is minimized and the two end‐point constraints on x_m and μ_n are satisfied.     

New analysis of the optimization of electromagnetic shielding properties using conducting polymers and a multi‐objective approach

Recently, an approach was proposed to optimize multi‐layer shields of polyaniline–polyurethane (PAni/PU) conducting composites in the microwave band. Though by this method shields for different applications can be obtained which are light‐weight and offer a low percolation threshold, the full potential of the design process could not be tapped since the underlying optimization problem includes only one objective. In this work we go one step beyond and re‐formulate the design problem as a multi‐objective optimization problem (MOP). To be more precise, we involve simultaneously the shielding efficiency as well as the weight and the cost of the material—i.e. all the requirements for modern shielding materials—within the optimization process. After having stated the model we present two possible ways to approximate the solution set—the so‐called Pareto set—and address the related and important decision‐making problem. All steps are demonstrated on a particular three‐layered composite in order to show the applicability of the novel approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Effect of Caustic Addition in Epoxy Polymerization Process: A Single and Multi‐Objective Evolutionary Approach

Summary: An epoxy polymerization process is studied in semi‐batch mode. Caustic has a very critical influence on epoxy polymerization process, which is modeled as a set of highly nonlinear coupled ODE's (ordinary differential equations). Owing to the highly complicated, nonlinear domain of analysis, “Differential Evolution (DE)” and “Genetic Algorithm (GA)” are used as optimization tools to identify the ‐PDI Pareto set and study the best operating strategy with respect to NaOH addition. The moment of various oligomeric components during the semi‐batch polymerization is also presented for a better understanding of the process. This study demonstrates the potential of evolutionary optimization algorithm to identify various operating philosophies of a semi‐batch epoxy reactor for a targeted product quality.

Pareto plot for epoxy polymerization process with intermediate NaOH addition varying from 0.0 to 1.0 kmol · m⁻³.     

Multiresponse problems: desirability and other optimization approaches

A diversity of multiresponse optimization methods has been introduced in the literature; however, their performance has not been thoroughly explored, and only a classical desirability‐based criterion has been commonly used. With the aim of contributing to help practitioners in selecting an effective criterion for solving multiresponse optimization problems developed under the response surface methodology framework, and thus to find compromise solutions that are technically and economically more favorable, the working ability of several easy‐to‐use criteria is evaluated and compared with that of a theoretically sound method. Four case studies with different numbers and types of responses are considered. Less‐sophisticated criteria were able to generate solutions similar to those generated by sophisticated methods, even when the objective is to depict the Pareto frontier in problems with conflicting responses. Two easy‐to‐use criteria that require less‐subjective information from the user yielded solutions similar to those of a classical desirability‐based criterion. Preference parameters range and increment impact on optimal solutions were also evaluated.     

Multi‐objective optimization of heating channels for rapid heating cycle injection mold using Pareto‐based genetic algorithm

Rapid heating cycle molding (RHCM) technology is a novel polymer injection molding method developed in recent years. In this paper, the principle of RHCM technology was introduced and a RHCM mold for producing a large‐size LCD TV panel was presented. Aiming at achieving a uniform temperature distribution on the cavity surface as well as making sure of the heating efficiency, the factors that influence temperature distribution and heating efficiency were analyzed. The center coordinates of the heating channels were considered as the main design variables. Multi‐objective functions for optimizing the temperature distribution uniformity and heating efficiency were proposed. The layout of the heating channels for a 46‐inch LCD TV panel RHCM mold was optimized by using the finite element method and Pareto‐based genetic algorithm (GA). The temperature distribution uniformity on the stationary mold insert cavity surface was largely improved by using optimal design results and the heating efficiency was also guaranteed. Copyright © 2009 John Wiley & Sons, Ltd.     

Kinetic Analysis and Optimization for the Catalytic Esterification Step of PPT Polymerization

Summary: A well‐validated kinetic scheme has been studied for PPT, poly(propylene terephthalate) polymerization process in batch and semi‐batch mode with tetrabutoxytitanium (TBOT), a proven catalyst. Optimization study and analysis for PPT are rare, as the industrial relevance of PPT just became vibrant due to the commercial availability of one of its monomers in industrial scale in the recent past. Correctness of the analysis is checked by a new approach and parameters for the model are estimated from available experimental data. Solubility of terephthalic acid (TPA) is less in reaction medium and this effect is also considered along with the reaction scheme. Several simulations have been performed to see various process dynamics and this ultimately helps in formulating optimization problems. Using recently developed and well tested real‐coded non‐dominated sorting genetic algorithm‐II, a state‐of‐the art evolutionary optimization algorithm, a couple of three objective optimization problems have been solved and corresponding Pareto sets are presented. Results show remarkably promising aspects of productivity enhancement with an improvement in product quality. Sensitivity analysis for relatively uncertain solubility parameter is also performed to estimate its effect over the proposed optimal solutions.

Multiobjective Pareto front for 3 objectives: degree of polymerization, time and (bTPA + bPG).     

Estimation of rotation ambiguity in multivariate curve resolution with charged particle swarm optimization (cPSO‐MCR)

Rotation ambiguity (RA) in multivariate curve resolution (MCR) is an undesirable case, when the physicochemical constraints are not sufficiently strong to provide a unique resolution of the data matrix of the mixtures into spectra and concentration profiles of individual chemical components. RA is often met in MCR of overlapped chromatographic peaks, kinetic and equilibrium data, and fluorescence two‐dimensional spectra. In case of RA, a single candidate solution has little practical value. So, the whole set of feasible solutions should be characterized somehow. It is a quite intricate task in a general case. In the present paper, a method was proposed to estimate RA with charged particle swarm optimization (cPSO), a population‐based algorithm. The criteria for updating the particles were modified, so that the swarm converged to the steady state, which spanned the set of feasible solutions. The performance of cPSO‐MCR was demonstrated on test functions, simulated datasets, and real‐world data. Good accordance of the cPSO‐MCR results with the analytical solutions (Borgen plots) was observed. cPSO‐MCR was also shown to be capable of estimating the strength of the constraints and of revealing RA in noisy data. As compared with analytical methods, cPSO‐MCR is simpler to implement, expands to more than three chemical compounds, is immune to noise, and can be easily adapted to virtually all types of constraints and objective functions (constraint based or residue based). cPSO‐MCR also provides natural visual information about the level of RA in spectra and concentration profiles, similar to the methods of two extreme solutions (e.g., MCR‐BANDS). Copyright © 2014 John Wiley & Sons, Ltd.     

N‐vinylcaprolactam‐based microgels: Synthesis and characterization

Poly(N‐vinylcaprolactam) (PVCL) is well known for its thermoresponsive behavior in aqueous solutions. PVCL combines useful and important properties; it is biocompatible polymer with the phase transition in the region of physiological temperature (32–38 °C). This combination of properties allows consideration of PVCL as a material for design biomedical devices and use in drug delivery systems. In this work, PVCL based temperature‐sensitive crosslinked particles (microgels) were synthesized in a batch reactor to analyze the effect of the crosslinker, initiator, surfactant, temperature, and VCL concentration on polymerization process and final microgels characteristics. The mean particle diameters at different temperatures and the volume phase‐transition temperature of the final product were analyzed. To obtain information about the inner structure of microgel particles, semicontinuous polymerizations were carried out and the evolution of the hydrodynamic average particle diameters at different temperatures of the microgel synthesized was investigated. In the case of microgel particles obtained in a batch reactor the size and the swelling‐de‐swelling behavior as a function of the temperature of the medium can be tuned by modulating the reaction variables. When the microgel particles were synthesized in a semibatch reactor different swelling‐de‐swelling behaviors were observed depending on particles inner structure. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2510–2524, 2008     

A new method for the gradient‐based optimization of molecular complexes

We present a novel method for the local optimization of molecular complexes. This new approach is especially suited for usage in molecular docking. In molecular modeling, molecules are often described employing a compact representation to reduce the number of degrees of freedom. This compact representation is realized by fixing bond lengths and angles while permitting changes in translation, orientation, and selected dihedral angles. Gradient‐based energy minimization of molecular complexes using this representation suffers from well‐known singularities arising during the optimization process. We suggest an approach new in the field of structure optimization that allows to employ gradient‐based optimization algorithms for such a compact representation. We propose to use exponential mapping to define the molecular orientation which facilitates calculating the orientational gradient. To avoid singularities of this parametrization, the local minimization algorithm is modified to change efficiently the orientational parameters while preserving the molecular orientation, i.e. we perform well‐defined jumps on the objective function. Our approach is applicable to continuous, but not necessarily differentiable objective functions. We evaluated our new method by optimizing several ligands with an increasing number of internal degrees of freedom in the presence of large receptors. In comparison to the method of Solis and Wets in the challenging case of a non‐differentiable scoring function, our proposed method leads to substantially improved results in all test cases, i.e. we obtain better scores in fewer steps for all complexes. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009     

Pareto calibration with built-in wavelength selection

In multivariate regression, it is often reported that wavelength selection can improve results. Improvement is often solely based on bias measures such as the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV), R² for the calibration and validation, etc. In recent studies, it has been shown that when variance measures are included, Pareto optimal models can be determined. However, variance measures used to date do not provide the ability to choose wavelength subset models relative to full wavelength models when wavelength subset models may be the Pareto models. In this paper, simplex optimization is used with a more complete variance measure to generate Pareto optimal models. The standard basis set is used as well a basis set that includes the range and null space of the calibration spectra. Results show that it is possible to identify Pareto optimal models and if a wavelength subset is best, these are the models found. Regression coefficients for non-essential wavelengths are zero to near zero.     

Optimization of preparative chromatographic separation of multiple rare earth elements

This work presents a method to optimize multi-product chromatographic systems with multiple objective functions. The system studied is a neodymium, samarium, europium, gadolinium mixture separated in an ion exchange chromatography step. A homogeneous Langmuir Mobile Phase Modified model is calibrated to fit the experiments, and then used to perform the optimization task. For the optimization a multi-objective Differential Evolution algorithm was used, with weighting based on relative value of the components to find optimal operation points along the Pareto front. The objectives of the Pareto front are weighted productivity and weighted yield with purity as an equality constraint. A prioritizing scheme based on relative values is applied for determining the pooling order. A simple rule of thumb for pooling strategy selection is presented. The multi-objective optimization gives a Pareto front which shows the rule of thumb, as a gap in one of the objective functions.     

Self‐defining tree‐like classifiers for interpretation of Raman spectroscopic experiments

In this contribution, a technique is proposed to create a data‐driven interpretation of a given chemometric analysis of a Raman dataset. In real‐world applications, the chemometric analysis is fixed by some external measurement, for example, a legal standard, or a set of fixed goals. Thus, the exact chemometric work flow is fixed because of those goals. However, a further optimization, for example, of the measurement itself relies on an interpretation of the resulting chemometric analysis. For this purpose, a data‐driven analysis of the chemometric analysis itself has to be carried out. This contribution tries to achieve that goal by combining two methods. The first proposed technique is the calculation of the so‐called importance map, which allows the computation of the importance of every channel for a given model and a given dataset. This importance map is constructed after the complete result of an out‐of‐bag (OOB) validation and the decrease of accuracy by randomized channels. The second technique is the growing of the optimal decision tree based on the action of the model used for chemometric analysis. By this way, a clustering is achieved on which by binary classifiers, the optimal decision tree is grown. This tree can be interpreted as dividing the whole dataset into meta clusters. Combining these techniques, a new way of interpreting datasets based on the chosen model is proposed. This combination closes the gap between chemometric analysis and the need for interpretation. Copyright © 2016 John Wiley & Sons, Ltd.     

Industrial SBR Process: Computer Simulation Study for Online Estimation of Steady‐State Variables Using Neural Networks

This work investigates the industrial production of styrene‐butadiene rubber in a continuous reactor train, and proposes a soft sensor for online monitoring of several processes and polymer quality variables in each reactor. The soft sensor includes two independent artificial neural networks (ANN). The first ANN estimates monomer conversion, solid content, polymer production, average particle diameter, and average copolymer composition; the second ANN estimates average molecular weights and average branching degrees. The required ANN inputs are: (i) the reagent feed rates into the first reactor and (ii) the reaction heat rate in each reactor. The proposed ANN‐based soft sensor proved robust to several measurement errors, and is suitable for online estimation and closed‐loop control strategies.

     

Characterization of Mononuclear Non‐heme Iron(III)‐Superoxo Complex with a Five‐Azole Ligand Set

Reaction of O₂ with a high‐spin mononuclear iron(II) complex supported by a five‐azole donor set yields the corresponding mononuclear non‐heme iron(III)–superoxo species, which was characterized by UV/Vis spectroscopy and resonance Raman spectroscopy. ¹H NMR analysis reveals diamagnetic nature of the superoxo complex arising from antiferromagnetic coupling between the spins on the low‐spin iron(III) and superoxide. This superoxo species reacts with H‐atom donating reagents to give a low‐spin iron(III)–hydroperoxo species showing characteristic UV/Vis, resonance Raman, and EPR spectra.     

Optimization strategy based on genetic algorithms and neural networks applied to a polymerization process

The article presents a simple and general methodology, especially destined to the optimization of complex, strongly nonlinear systems, for which no extensive knowledge or precise models are available. The optimization problem is solved by means of a simple genetic algorithm, and the results are interpreted both from the mathematical point of view (the minimization of the objective function) and technological (the estimation of the achievement of individual objectives in multiobjective optimization). The use of a scalar objective function is supported by the fact that the genetic algorithm also computes the weights attached to the individual objectives along with the optimal values of the decision variables. The optimization strategy is accomplished in three stages: (1) the design and training of the neural model by a new method based on a genetic algorithm where information about the network is coded into the chromosomes; (2) the actual optimization based on genetic algorithms, which implies testing different values for parameters and different variants of the algorithm, computing the weights of the individual objectives and determining the optimal values for the decision variables; (3) the user's decision, who chooses a solution based on technological criteria. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Constrained optimization of a preparative ion-exchange step for antibody purification

Today, the optimization of chromatographic separation is usually based on experimental work and rule of thumb. The process and analytical technology (PAT) initiative, of the US Food and Drug Administration, has provided the opportunity of using model-based approach when designing downstream processing of pharmaceutical substances. A nonlinear chromatography model was used in this study to optimize a preparative ion-exchange separation step involving two components. Separation was simulated with the general rate model employing Langmuir kinetics. Optimization was performed with an indirect method allowing constraints on the purity, thus avoiding sub-optimization, which can lead to noisy objective functions. The six decision variables used in the optimizations were flow rate, loading volume, initial salt concentration in the elution, final salt concentration in the linear elution gradient and the two cut points. A graphical representation of the effect of the decision variables on the objective function was used to verify that the optimization had converged to the true optimum. The optimal operating points, using productivity and yield separately as objective functions, were found and compared with the product of productivity and yield as objective function. The optimum obtained with this objective function had a lower productivity, than the productivity function, but much higher yield, which makes it a good substitute for a cost function.     

Polyethylene Made with Combinations of Single‐Site‐Type Catalysts: Monte Carlo Simulation of Long‐Chain Branch Formation

The formation of long‐chain branches (LCBs) during ethylene polymerization with a combination of catalysts was studied by Monte Carlo simulation. The model describes polymerization with a non‐branching catalyst that produces linear macromonomers, and a branching catalyst that produces linear and branched macromonomers. The LCBs are formed when the branching catalyst incorporates a macromonomer. The discussion is based on the three types of chain topology obtained during the synthesis: linear, comb‐branched, or hyperbranched. Simulation results show how the chain length distribution and the number of LCBs change according to the ratio between the two catalysts present in the reactor. The ratio hyperbranched/comb‐branched is defined to evaluate the system composition and the contribution of each catalyst.