No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Multiobjective differential evolution (MODE) for optimization of adiabatic styrene reactor
Abstract
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.
... DE has been successfully used by several researchers such as Babu et al. [30][31][32] and Khademi et al. [33][34][35][36] in various elds. After that, MODE algorithm, as an extended DE method, proposed by Babu et al. [37] has been successfully used to handle multi-objective optimization problems. ...
... This technique has been presented as an e cient, fast, robust, and simple method for stochastic global optimization. The main algorithm of DE can be found in the literature [37,45], and it consists of a four-step procedure: (1) random choice of an initial population vector, (2) mutation/perturbation (3) crossover/recombination, and (4) selection. ...
... The termination criterion of this procedure is an assigned number of generations. A detailed representation of MODE algorithm using DE approach and the general pseudo-code for MODE can be found in the literature [37,48]. ...
... Chaves González e Vega-Rodriguez [78] abordaram o projeto e geração de sequências de DNA confiáveis para computação biomolecular. No contexto multiobjetivo, destacam-se trabalhos como a otimização estrutural de vigas [218], a determinação do perfil ótimo de alimentação de substrato e dos eventos em um problema de controle ótimo com índice flutuante [216], a otimização das condições operacionais de um reator industrial utilizado para a produção de estireno [22] e o uso de técnicas de metamodelagem associada ao enfoque multiobjetivo para o tratamento de um problema de interação fluido-estrutura [211]. Várias outras aplicações do algoritmo de DE podem ser encontradas nas Refs. ...
... As principais vantagens do algoritmo de DE são: sua simplicidade conceitual, facilidade de implementação, robustez e tempo de processamento satisfatório [21,22,295,405]. Neste sentido, alguns autores [21,405] acreditam que o desenvolvimento e o aprimoramento do algoritmo de DE logo permitirão superar os atuais GAs em termos de convergência, no número de avaliações da função objetivo e no tempo de processamento. ...
... Com relação à escolha dos parâmetros do algoritmo de DE, Storn e Price [295] aconselham o uso dos seguintes valores: número de indivíduos da população como sendo um valor entre 5 e 10 vezes o número de variáveis de projeto, taxa de perturbação F entre 0, 2 e 2, 0 e probabilidade de cruzamento Cr entre 0, 1 e 1, 0. Sobre a escolha da estratégia DE/x/y/z, Angira e Babu [18], Babu e Anbarasu [21] e Babu et al. [22] constataram em seus trabalhos que os melhores resultados, em termos de convergência e diversidade para os problemas estudados por esses autores, foram obtidos quando se utilizou a estratégia DE/rand/1/bin (opção 7 na Tabela 13.1). Em contrapartida, Oliveira [275] verificou em seu trabalho que a escolha da estratégia pouco influenciou os resultados dos casos analisados. ...
The use of computational methods from the second half of the last century led to a major breakthrough in modeling problems encountered in nature and industry. Use of these models has facilitated the practice of engineering in all its dimensions. In this work, solutions based on computational intelligence techniques to inverse problems in radiative transfer are addressed comprehensively. Suitable for researchers and students interested in heuristic optimization and their applications.
... Most real problems are subject to multiple and conflicting objectives, which can be related to each other, as pointed out by Babu et al. 8 The modeling of complex problems using only one objective can be an impractical approach, causing eventual errors to be introduced in the mathematical modeling when certain simplifications are imposed to meet the chosen modeling paradigm. In contrast, multiobjective optimization models have additional degrees of freedom concerning those with a single objective, in such a way that there is not a single optimal solution, but a set of Pareto optimal solutions, 9 any of which is a fair choice. ...
... Multiobjective optimization consists of finding a set of points that represents the best balance in relation to optimizing all objectives simultaneously, that is, a collection of solutions that relates to the objectives, which conflict with each other in most cases. 8 L e t ⊂ P n d e n o t e a h y p e r -r e c t a n g l e o f a l l = ∈ x x x ( , ..., ) n n 1 T , such that x inf ≤ x ≤ x sup , where these inequalities are taken coordinate by coordinate, that is, ...
... Although the foregoing model is for an empty tubular reactor, the pseudo-homogeneous model case implies that the same model can be applied to a packed-bed reactor where there are no fluid-tocatalyst particle mass and/or heat transfer resistances or they are considered small. Pseudohomogeneous tubular reactor models are widely employed in the literature to simulate, design/optimize and control catalytic fixed bed reactors [29][30][31][32][33][34][35][36][37][38][39][40]. This is because pseudohomogeneous models are much simpler to use for simulation, optimization or control design since the inter-and intra-particle resistances are neglected. ...
... This is expected because using the latter method requires the solution of a set of linear algebraic equations, while the former method involves only simple function evaluations. e-ISSN: 2289-7771 847 Using the initial steady-state solution, , = 1, 2, , j x j n ; the set of nonlinear ODEs given by Eq. (36) are integrated numerically using the 3rd-order semi-implicit Runge-Kutta method routines [13] to determine the transient response of xj(t) to the input, u(t). When required, the eigenvalues of the linear (or linearized) lumped orthogonal models are computed using the QR routine [13]. ...
In this paper, the modelling, numerical lumping and simulation of the dynamics of one-dimensional, isothermal axial dispersion tubular reactors for single, irreversible reactions with Power Law (PL) and Langmuir-Hinshelwood-Hougen-Watson (LHHW)-type kinetics are presented. For the PL-type kinetics, first-order and second-order reactions are considered, while Michaelis-Menten and ethylene hydrogenation or enzyme substrate-inhibited reactions are considered for the LHHW-type kinetics. The partial differential equations (PDEs) developed for the one-dimensional, isothermal axial dispersion tubular reactors with both the PL and LHHW-type kinetics are lumped to ordinary differential equations (ODEs) using the global orthogonal collocation technique. For the nominal design/operating parameters considered, using only 3 or 4 collocation points, are found to adequately simulate the dynamic response of the systems. On the other hand, simulations over a range of the design/operating parameters require between 5 to 7 collocations points for better results, especially as the Peclet number for mass transfer is increased from the nominal value to 100. The orthogonal collocation models are used to carry out parametric studies of the dynamic response behaviours of the one-dimensional, isothermal axial dispersion tubular reactors for the four reaction kinetics. For each of the four types of reaction kinetics considered, graphical plots are presented to show the effects of the inlet feed concentration, Peclet number for mass transfer and the Damköhler number on the reactor exit concentration dynamics to step-change in the inlet feed concentration. The internal dynamics of the linear (or linearized) systems are examined by computing the eigenvalues of the linear (or linearized) lumped orthogonal collocation models. The relatively small order of the lumped orthogonal collocation dynamic models make them attractive and useful for dynamic resilience analysis and control system analysis/design studies.
... Most real problems are subject to multiple objectives, which can be related to each other, as pointed out by Babu et al. [5]. The modeling of complex problems using only one objective can be an impractical task, causing eventual errors to be introduced to the proposed model, when certain simplifications are imposed to meet the chosen modeling paradigm. ...
... An optimal Pareto solution dominates any other feasible point in the search space and, therefore, all of these solutions are considered better than any other. Therefore, multi-objective optimization consists of finding a set of points that represents the best balance in relation to minimizing all objectives simultaneously, that is, a collection of solutions that relates the objectives, which are in conflict with each other, in most cases [5]. ...
Mathematical models simulate various events under different conditions, enabling an early overview of the system to be implemented in practice, reducing the waste of resources and in less time. In project optimization, these models play a fundamental role, allowing to obtain parameters and attributes capable of enhancing product performance, reducing costs and operating time. These enhancements depend on several factors, including an accurate computational modeling of the inherent characteristics of the system. In general, such models include uncertainties in their mathematical formulations, which affect the feasibility of the results and their practical implementation. In this work, two different approaches capable of quantifying uncertainties during the optimization of mathematical models are considered. In the first, robust optimization, the sensitivity of decision variables in relation to deviations caused by external factors is evaluated. Robust solutions tend to reduce deviations due to possible system changes. The second approach, reliability-based optimization, measures the probability of system failure and obtains model parameters that ensures an established level of reliability. Overall, the fundamental objective is to formulate a multi-objective optimization problem capable of handling robust and reliability-based optimizations, to obtain solutions that are least sensitive to external noise and that satisfy prescribed reliability levels. The proposed formulation is analyzed by solving benchmark and chemical engineering problems. The results show the influence of both methodologies for the analysis of uncertainties, the multi-objective approach provides a variety of feasible optimizers, and the formulation proves to be flexible, so that the uncertainties can be incorporated into the problem considering the needs of each project.
... The features of the stochastic optimization algorithms have gained a lot of attention and they have been used in many different optimization problems, such as dynamic optimization, multiobjective optimization, parameter estimation, nonlinear dynamic analysis of chemical processes, clustering analysis, constrained and global optimizations (Durand et al, 2009;Babu et al, 2005;Schwaab et al ,2008;Ourique et al, 2002;Karaboga e Ozturk, 2011;Karaboga e Akay, 2011). ...
... Among stochastic algorithms available in literature, four algorithms were used in this work and their characteristic are briefly described below. These algorithms were chosen since they are commonly used for solving optimization problems in the engineering field (Babu et al, 2005;Ourique et al, 2002;Li et al, 2000). Particle Swarm Optimization, Differential Evolution and Artificial Bee Colony are population-based algorithms where a solution set is interacted in order to find the global optimum. ...
Este trabalho compara algoritmos estocásticos diferentes aplicados a problemas de minimização de funções teste, para as quais técnicas matemáticas tradicionais costumam falhar. Os algoritmos estocásticos avaliados neste trabalho foram Colônia Artificial de Abelhas (CAB), Evolução Diferencial (ED), Enxame de Partículas (EP) e Recozimento Simulado (RS). Os parâmetros internos de cada algoritmo foram alterados e seus efeitos na performance do algoritmo foram avaliados e comparados na minimização de seis funções teste (Ackley, Griewank, Parabolic, Rastrigin, Rosenbrock and Scheffers). Os resultados permitiram concluir sobre a importância de uma definição adequada dos parâmetros internos. Além disso, a minimização da função de Rosenbrock com alta dimensão foi realizada com a melhor configuração de cada algoritmo. Os resultados mostraram que a maioria dos algoritmos conseguiu encontrar o mínimo global das funções multimodais. Entretanto, os algoritmos ED e CAB apresentaram os melhores resultados em termos de convergência e qualidade de resultados.
... Babu et al. [8] also used multiobjective differential evaluation (MODE) algorithm to optimize the styrene reactor, and the results are compared with those obtained from the non-dominated sorting genetic algorithm (NSAG).The parato set based on the new algorithm was found to be much better than that obtained by the NSGA. ...
... Salim Fettaka [12] used the dual population evolutionary algorithm (DPEA) to circumscribe the pareto domain of two and three objective optimization case studies for three different configurations of the reactor: adiabatic, steam-injected and isothermal reactor model in styrene production. He found that the DPEA led to pareto domains for which the spread of each objective covers a wider range of values of non-dominated solutions compared to those reported by Yee et al. [7] and Babu et al. [8] (Mousavi, et al., 2012) [13] proposed a A pseudohomogeneous model with artificial neural network model to achieve the prof iles of ethyl benzene conversion, styrene yield and selectivity through the length of catalytic bed reactor. Good agreement was found between model results and industrial data Also, mathematical models for predicting the fractional conversion of ethyl benzene and yields of products in a catalytic membrane reactor for the dehydrogenation of ethyl benzene were developed by Akpa, [4]. ...
–
Dehydrogenation of ethyl benzene and hydrogenation of nitrobenzene are coupled in the catalytic shell and tube membrane reactor to enhance the conversion and yield of the dehydrogenation reaction. The reactor system needs to be optimized to achieve the maximum
benefit. Six process variables are selected as decision variables, which are; ethyl and nitrobenzene molar flow rate, pressure and temperature on shell and tube side. The flow rate of ethyl benzene can be considered as the effective variable on the nitrobenzene conversion and styrene yield.
Optimization technique is the powerful tool to generate several new designs and sets of operating conditions. This reduces the risk of experimental runs and the consumed cost for design and
operation. The optimal operating conditions could enhance the yield of styrene within the range of (51 to 99.6%) and conversion of nitrobenzene within range of (35.7 to 79.6%) compared to the
previous works which were within range of (49 to 98%) for styrene yield and (21 to 79%) for nitrobenzene conversion at the same range of operating conditions. For highly nonlinear membrane reactor, the global stochastic genetic optimization algorithm has been found more
reliable than the deterministic methods. The accuracy of optimization search can be increased by adaption of the genetic operators.
... Com relaçãoà escolha dos parâmetros do algoritmo de ED, Storn e Price (1995) aconselham o uso dos seguintes valores: número de indivíduos da população como sendo igual a um valor entre 5 e 10 vezes o número de variáveis de projeto, taxa de perturbação F entre 0,2 e 2,0, probabilidade de cruzamento CR entre 0,1 e 1,0, e estratégia DE/RAND/1/BIN (Babu et al., 2005).É importante ressaltar que outros valores para esses parâmetros podem ser atribuídos de acordo com uma aplicação particular. ...
... Na literatura especializada, inúmeras aplicações usando o algoritmo de ED podem ser encontradas, dentre as quais pode-se citar a determinação do perfilótimo de alimentação de substrato em fermentadores (Kapadi e Gudi, 2004); a determinação das condições operacionais de um reator industrial utilizado para a produção de estireno (Babu et al., 2005); a otimização multi-objetivo de vigas (Lobato e Steffen Jr, 2007), a determinação do perfilótimo de alimentação de substrato em um problema de controleótimo comíndice flutuante , a estimação de parâmetros cinéticos em um secador rotatório ; o uso de técnicas de meta-modelagem associada ao enfoque multi-objetivo para o tratamento de um problema de interação fluido-estrutura (Lobato, 2008), o uso de técnicas de meta-modelagem aplicado ao processo de usinagem (Lobato et al., 2012a), estimação de propriedades em problemas de transferência de calor por radiação (Lobato et al., 2012b), estimação de parâmetros em pirólise (Santos et al., 2012), projeto de hidrociclones (Silva et al., 2012), entre outras aplicações. ...
... To solve the overall kinetic equation (Eq. 14) [43,44], the Runge-Kutta 4th-order procedure was employed. Figure 5 presents a comparison between the simulated and experimental thermal valorization processes (in the form of dα/dt) in relation to temperature. ...
Seaweeds are essential autotrophs in the marine environment, resembling submerged forests near shorelines that provide habitats for various organisms. They have now become a significant source of numerous bio-products and are cultivated and harvested in various regions worldwide, contributing to the burgeoning blue economy. Environmentally friendly utilization of marine resources is one solution to meet the increasing demand for bioenergy and bio-products in the advancing blue economy. In this study, we investigated the bioenergy potential of the brown macroalgae Dictyota dichotoma using the slow pyrolysis technique. The pyrolysis process was conducted at three different heating rates (5, 10, and 20 °C min⁻¹) in an inert nitrogen gas atmosphere, starting from room temperature and reaching 800 °C. Four valorization stages were identified, and the data obtained were fitted to various model-free iso-conversional methods, namely Friedman, Flynn-Wall-Ozawa, Kissinger-Akahira-Sunose, and Starink. The calculated activation energies ranged from 157.32 to 185.71 kJmol⁻¹. The pre-exponential factor, determined from the kinetic compensation effect for the valorization processes, fell within the range of 4.8 × 10⁸ to 6.5 × 10¹⁷ min⁻¹. This range demonstrated the thermal conversion of both bioorganic and inorganic molecules, encompassing the relevant reactions throughout the entire process. Analysis using a master plot indicated that the pyrolysis of brown macroalgae primarily follows a diffusion-based process. The reproducibility of the data was further confirmed by fitting the experimental parameters obtained during the simulation process. The thermodynamic analysis revealed values of enthalpy (ΔH) ranging from 146.85 to 179.72 kJmol⁻¹ and values of Gibbs free energy (ΔG) ranging from 143.91 to 288.19 kJmol⁻¹. These findings demonstrate the endothermic and non-spontaneous behavior of seaweed biomass pyrolysis reactions. The entropic values indicated the formation of more ordered molecules during the latter three-pyrolysis stages. Overall, the results highlight the suitability of Dictyota seaweed biomass as a promising feedstock for bioenergy generation, contributing to the development of the blue economy.
... The differential evolution approach is presented for multi-objective optimization problems in optimization of adiabatic styrene reactors. The proposed algorithm is applied to determine the optimal operating condition for the manufacture of styrene [28]. In case of optimal design of a gas transmission network, an evolutionary computation technique has been successfully applied for the optimal design of gas transmission network. ...
Differential Evolution (DE) is optimization technique inspired by nature based non-conventional evolution. DE's exceptional accuracy at numerical optimization, faster convergence & its independence on initial and final constraints defines its value for providing an excellent solution set. The DE algorithm includes four stages-generation, mutation, crossover and population. It provides solutions for a wide set of optimization problems with equality or inequality constraints regardless of stability and dimension of problem. This work systematically implemented DE Algorithm for solving two benchmark problems from literature and frequently used by researchers in this field. The solution by DE and conventional method have been compared to check the effectiveness of DE. It is found that DE is simple to implement and converges faster towards global optima than other methods.
... The DE approach is presented for multiobjective optimization problems in optimization of adiabatic styrene reactors. The proposed algorithm is applied to determine the optimal operating condition for the manufacture of styrene [28]. In the case of optimal design of gas transmission network, an evolutionary computation technique has been successfully applied for the optimal design of gas transmission network. ...
Differential Evolution (DE) is an evolutionary optimization technique that is very simple, fast, and
robust at numerical optimization. It has mainly three advantages; finding the true global minimum regardless of
the initial parameter values, fast convergence, and using few control parameters. The main advantage of the DE
over other methods is its stability. DE algorithm is a population based algorithm like genetic algorithms using
similar operators; crossover, mutation and selection. DE becomes impressive because of the parameters;
crossover ratio (CR) and mutation factor (F) do not require the same tuning which is necessary in many other
Evolutionary Algorithms.
In the present study, DE has been used to solve the two chemical engineering problems from the literature. The
comparison is made with some other well-known conventional and non-conventional optimization methods. From
the results, it was observed that the convergence speed of DE is significantly better than the other techniques.
Therefore, DE algorithm seems to be a promising approach for engineering optimization problems.
... The differential evolution approach is presented for multi-objective optimization problems in optimization of adiabatic styrene reactor. The proposed algorithm is applied to determine the optimal operating condition for the manufacture of styrene [24]. In case of optimal design of gas transmission network, an evolutionary computation technique has been successfully applied for the optimal design of gas transmission network. ...
Differential Evolution (DE) algorithm is a new heuristic approach mainly having three advantages; finding the true global minimum regardless of the initial parameter values, fast convergence, and using few control parameters. The biggest advantage of the differential evolution approach over other non-traditional method approach is its stability. DE algorithm is a population based algorithm like genetic algorithms using similar operators; crossover, mutation and selection. Differential evolution algorithm can be easily applied to a wide variety of real valued problems despite noisy, multimodal, multidimensional spaces which usually makes the problems very difficult for optimization. Differential evolution becomes impressive because of the parameters crossover ratio (CR) and mutation factor (F) do not require the same tuning which is necessary in many other Evolutionary Algorithms. In the present study, DE has been used to solve the various chemical engineering problems from the literature. We have compared the performance of DE algorithm to that of some other well-known versions conventional and non-conventional optimization methods. From the simulation results, it was observed that the convergence speed of DE is significantly better than the other techniques. Therefore, DE algorithm seems to be a promising approach for engineering optimization problems.
... To solve bi-objective problems, two multi-objective DE variants were used against COVID-19, but without much success. MODE (Babu et al. 2005) algorithm was said to be used and compared against an unspecified variants of PSO and GA by Singh et al. (2020b), but the results were not clearly discussed. DECMOSA (Zamuda et al. 2009) was used to solve bi-objective problem of balancing costs and disease spread when allocating resources to hospitals (Zheng et al. 2020b), but was generally outperformed by other algorithms. ...
COVID-19 disease, which highly affected global life in 2020, led to a rapid scientific response. Versatile optimization methods found their application in scientific studies related to COVID-19 pandemic. Differential Evolution (DE) and Particle Swarm Optimization (PSO) are two metaheuristics that for over two decades have been widely researched and used in various fields of science. In this paper a survey of DE and PSO applications for problems related with COVID-19 pandemic that were rapidly published in 2020 is presented from two different points of view: 1. practitioners seeking the appropriate method to solve particular problem, 2. experts in metaheuristics that are interested in methodological details, inter comparisons between different methods, and the ways for improvement. The effectiveness and popularity of DE and PSO is analyzed in the context of other metaheuristics used against COVID-19. It is found that in COVID-19 related studies: 1. DE and PSO are most frequently used for calibration of epidemiological models and image-based classification of patients or symptoms, but applications are versatile, even interconnecting the pandemic and humanities; 2. reporting on DE or PSO methodological details is often scarce, and the choices made are not necessarily appropriate for the particular algorithm or problem; 3. mainly the basic variants of DE and PSO that were proposed in the late XX century are applied, and research performed in recent two decades is rather ignored; 4. the number of citations and the availability of codes in various programming languages seems to be the main factors for choosing metaheuristics that are finally used.
... Par exemple, pour l'optimisation avec une seule fonction objectif, on pourrait utiliser l'algorithme d'évolution différentielle (DE) (Storn et al. 1997) ou Particle Swarm Optimization (PSO) (Kennedy et al. 1995). Il y a aussi des algorithmes de type multi-objectif, tels que l'algorithme d'évolution différentielle multi-objectif (MODE) (Babu et al. 2005) ou l'algorithme Multi-objectif particle swarm optimization (MOPSO) (Coello et al. 2002). ...
Les modèles génotype-phénotype, permettant de tester les performances de génotypes sous différents climats, sont considérés comme des outils d’avenir pour concevoir de nouvelles variétés. Cependant, des progrès sont encore nécessaires pour inclure le contrôle génétique complexe dans les modèles basés sur les processus et réaliser l’intégration de l’information (métabolisme, contrôle enzymatique, génétique quantitative) du gène à la plante. Dans ce sens, un modèle cinétique du métabolisme des sucres a été développé par Desnoues et al. (2018) pour simuler les concentrations de différents sucres au cours du développement du fruit de la pêche. Les objectifs de mes travaux de thèse sont (a) d’estimer la variabilité inter-génotype des valeurs des paramètres du modèle et (b) d’étudier l’architecture du contrôle génétique des paramètres génotype-dépendants. Pour atteindre ces objectifs, il est nécessaire d’estimer les paramètres influents du modèle pour l’ensemble des 106 génotypes dont certains n’ont que peu de données observées. Le nombre de paramètres et la non linéarité du modèle rendent la calibration du modèle peu fiable (notamment du fait du grand nombre de paramètres comparé au nombre de données disponibles et des corrélations entre eux) et coûteuse en terme de temps de calcul. Aussi, nous avons développé une stratégie de réduction du modèle initial visant à diminuer le nombre de paramètres et simplifier la structure du modèle tout en maintenant la structure du réseau et l’identité des variables, afin de faciliter leur interprétation biologique. L’estimation des paramètres du modèle réduit ainsi obtenu a été réalisée à l’échelle de la population en utilisant une approche non linéaire du modèle mixte (Baey et al.2018), qui permet d’estimer simultanément les paramètres individuels pour tous les génotypes, et comparée aux méthodes plus conventionnelles qui procèdent à l’estimation des paramètres individuellement, génotype par génotype. Nous montrons que la fiabilité des estimations est largement améliorée et que les corrélations entre les paramètres estimés sont réduites. La dernière étape a consisté à estimer les liaisons entre les marqueurs du génome et les paramètres génotype-dépendants. Nous avons comparé les résultats d’une analyse dite indépendante (estimation de paramètres puis détection des régions génomiques impliquées) à une méthode d’analyse conjointe(Onogi 2020). Ces travaux de thèse constituent une étape essentielle au développement d’un outil qui prenne en compte un contrôle génétique complexe des caractères pour concevoir des idéotypes.
... Yee et al. (2003) performed multiobjective optimization of a styrene reactor with multiobjective functions of maximizing total styrene production, selectivity, and yield, using Non-dominated Sorting Genetic Algorithm (NSGA). Babu, et al. (2005) compared results obtained using NSGA to those obtained using multiobjective differential evolution (MODE), verifying better results using MODE. Gujarathi & Babu (2010) have also employed MODE in the optimization of two different reactor configurations: a single bed adiabatic reactor to a reactor with intermediate steam injection. ...
In this study, steady-state axial-flow and radial-flow multibed catalyst reactors for dehydrogenation of ethylbenzene into styrene were simulated based on an intrinsic heterogeneous kinetic model. The reactors were then optimized using nonlinear programming with the multiobjective function of maximizing styrene selectivity and conversion. The simulations were consistent and versatile. Comparing the two optimized reactor configurations, radial-flow has proved to be a better alternative than axial-flow because of operating at lower pressures. The benefits of operating at lower pressures are also evident at optimized inlet temperature schemes, as the inlet temperatures of catalyst beds are greater along reactor pressure drop. The obtained set of optimal results can be used to perform an integrated process analysis and define suitable operational conditions. Weighing objective functions with respectively 0.3 and 0.7, styrene selectivity and conversion were respectively 85.3% and 72.5% for the axial-flow reactor and 87.0% and 76.5% for the radial-flow reactor.
... To evaluate the effectiveness of the proposed IMBA, the algorithm will be compared with several well-known multiobjective algorithms, i.e., MOPSO (Reyes-Sierra and Coello 2006), MOABC (Saad et al. 2018), MODE (Babu et al. 2005), MOBA (Yang 2011), NSGA-II (Macedo et al. 2017), and SPEA2 (Macedo et al. 2017). In our experiments, each algorithm was independently run approximately 20 times for each instance. ...
This paper deals with a multiperiod multiobjective fuzzy portfolio selectiossn problem based on credibility theory. A credibilistic multiobjective mean-VaR model is formulated for the multiperiod portfolio selection problem, whereby the return is quantified by the credibilistic mean and the risk is measured by the credibilistic VaR. We also consider liquidity, cardinality, and upper and lower bound constraints to obtain a more realistic model. Furthermore, to solve the proposed model efficiently, an improved multiobjective bat algorithm termed IMBA is designed, in which three new strategies, i.e., the global best solution selection strategy, candidate solution generation strategy, and competitive learning strategy, are proposed to increase the convergence speed and improve the solution quality. Finally, comparative experiments are presented to show the applicability and superiority of the proposed approaches from two aspects. First, the designed IMBA is compared with seven typical algorithms, i.e., multiobjective particle swarm optimization, multiobjective artificial bee colony, multiobjective firefly algorithm, multiobjective differential evolution, multiobjective bat, the non-dominated sorting genetic algorithm (NSGA-II) and strength pareto evolutionary algorithm 2 (SPEA2), on a number of benchmark test problems. Second, the applicability of the proposed model to practical applications of portfolio selection is given under different circumstances.
... However, existing studies are designed to deal with optimization under uncertainty, such as the refinery planning [75] and integrated oil supply chain [76,77]. There are other real-world applications using MOP in Chemical Engineering [78]: modeling of chemical processes, polymer extrusion and other applications [79][80][81][82][83][84]. Moreover, it is believed that many-objectives optimization problems with their applications in petroleum and refinery processes are still of great interest from the academic and industrial point-of-views. ...
Multiobjective optimization (MOO) techniques are of much interest with their applications to petroleum refinery catalytic processes for finding optimal solutions in the midst of conflicting objectives. The rationale behind using MOO is that if objectives are in conflict, a set of trade-off optimal modeling solutions must be obtained to help management select the most-preferred operational solution for a refinery process. Using MOO does not involve hyperparameters thereby reducing the expensive parameter tuning tasks. A true MOO method allows numerous Pareto-based optimal solutions to be identified so that management and decision-makers' preference information can be used to finally select a single preferred solution. This review discusses MOO algorithms and their applications in petroleum and refinery processes. The survey provides insights into the fundamentals, metrics, and relevant algorithms conceived for MOO in petroleum and refinery fields. Also, it provides a deeper discussion of state-of-the-art research conducted to optimize conflicting objectives simultaneously for three main refinery processes, namely hydrotreating, desulfurization, and cracking. Finally, several research and application directions specific to refinery processes are discussed.
... The fusion factor and entropy metrics are used as the fitness function to select the optimal features. A multi-objective differential evolution can solve many computationally complex problems (Babu et al. 2005). It can significantly balance the fast convergence and population diversity. ...
The advancements in automated diagnostic tools allow researchers to obtain more and more information from medical images. Recently, to obtain more informative medical images, multi-modality images have been used. These images have significantly more information as compared to traditional medical images. However, the construction of multi-modality images is not an easy task. The proposed approach, initially, decomposes the image into sub-bands using a non-subsampled contourlet transform (NSCT) domain. Thereafter, an extreme version of the Inception (Xception) is used for feature extraction of the source images. The multi-objective differential evolution is used to select the optimal features. Thereafter, the coefficient of determination and the energy loss based fusion functions are used to obtain the fused coefficients. Finally, the fused image is computed by applying the inverse NSCT. Extensive experimental results show that the proposed approach outperforms the competitive multi-modality image fusion approaches.
... A otimização multi-objetivo consiste em encontrar um conjunto de pontos que formam a curva de Pareto, isto é, um conjunto de pontos que relacionam os objetivos, geralmente, confl itantes (Babu et al., 2005). Isso signifi ca que a melhoria de um objetivo pode levar à deterioração de outro, e vice versa. ...
... That study investigated the internal performance parameters such as turbine inlet temperature, turbine inlet and back pressures, and LNG pressure as the variables of the multiobjective optimization study. Beside the LNG fired systems, multiobjective optimization was also applied in the other process engineering applications such as a reactor (Babu et al., 2005), manufacturing processes (Tarafder et al., 2005), industrial grinding (Mitra and Gopinath, 2004), gas separation systems (Chang and Hou, 2006), petrochemical industry (Al-Sharrah et al., 2010), waste management systems (Chang and Hwang, 1996), and industrial hydrogen plants (Rajesh et al., 2001). Although the aforementioned studies performed reliable multiobjective functions in the thermoeconomic optimization, they prefer two multiobjectives in the Pareto frontier plots. ...
Liquefied natural gas (LNG), a clean fuel type mainly containing methane, has been becoming more popular amongst the other fuels for the power generation systems. Although there are a lot of thermodynamic and thermoeconomic assessments about the LNG fired power generation systems, the environmental and sustainability aspects have still lack investigation, especially on the optimization step. To minimize this gap, a multiobjective optimization study is performed for the LNG fired micro-cogeneration system. The current study considers various objective functions from thermodynamic, environmental, thermoeconomic, and sustainability aspects. A newly developed sustainability index is used as one of the objective functions in the study. The approach is defined as the complex multiobjective optimization procedure that constitutes different multiobjective optimization groups to better understand and evaluate the different objective functions together. The controllable air temperature and relative humidity are selected as the external decision variables. The best trade-off regions are identified between 300.00 K and 313.15 K at the relative humidity of 90% while they are found between 310.15 K and 313.15 K at the relative humidity of 50%. The high relative humidity and ambient air temperature present the best climatic conditions for the optimal operation of the small-scale system during the indoor operations.
... Various optimization strategies based on DE algorithm to solve multi-objective problems can be found in the literature [22][23][24]. In order to solve the RBO problem in the multi-objective context, the multi-objective optimization differential evolution (MODE [14]) is used. ...
In this contribution, a new methodology based on a double-loop iteration process is proposed for the treatment of uncertainties in engineering system design. The inner optimization loop is used to find the solution associated with the highest probability value (inverse reliability analysis), and the outer loop is the regular optimization loop used to solve the considered reliability problem through differential evolution and multi-objective optimization differential evolution algorithms. The proposed methodology is applied to mathematical functions and to the design of classical engineering systems according to both mono- and multi-objective contexts. The obtained results are compared with those obtained by classical approaches and demonstrate that the proposed strategy represents an interesting alternative to reliability design of engineering systems.
... Genetic Algorithms (GA) is popular for efficient optimization and robustness motivated by Darwin's principle of natural selection and survival using fitness function. Differential Evolution, an improved version of GA, and its various strategies have been successfully applied to many engineering, management, scientific, finance & economics related problems [13][14][15][16][17][18][19][20][21][22][23][24]. ...
The basic aim of this paper is to present a broad picture of Big Data and to show how information can be retrieved using different methodologies and especially using evolutionary computation techniques that help in the information retrieval process in a better way compared to traditional retrieval techniques. Big data is considered as a collection of large data which are heterogeneous in nature and cannot be handled by traditional computing techniques and require more advanced statistical procedures to extract relevant information from a voluminous pool of data. This paper also covers some of the basic information retrieval models which are used and present a basic outline of evolutionary computation techniques.
... The main differences are: (i) the F parameter is generated from a random generator between 0 and 1; (ii) only the nondominated solutions are retained for recombination; (iii) the generated offspring is placed into the population if it dominates the first selected parent; and (iv) the constraints are handled using a penalty function approach. Babu et al. (2005) to optimize the operation of an adiabatic styrene reactor. This work concerns a comparative study between the performance of MODE and the results of NSGA reported in a previous paper (Yee et al., 2003). ...
... Their model is defined by six equations from material balance, one equation of energy balance, and one of pressure drop. All kinetic data and model equation are taken from Elnashaie and Elshishini (1994) [9] , Yee et al. (2002) [11] , and Babu et al. (2005) [16] . The results showed that the objective functions such as styrene flow rate, yield, and selectivity can be improved by adapting optimal operating conditions. ...
In this research, two models were developed to simulate a steady state fixed bed reactor used for styrene production by ethylbenzene dehydrogenation. The first is one-dimensional model while the second is two-dimensional model. One-dimensional model considered axial gradient only while the two-dimensional model considered axial and radial gradients for same taken variables.
The developed mathematical models consisted of nonlinear simultaneous equations in multiple dependent variables. A complete description of the reactor bed involves partial, ordinary differential and algebric equations (PDEs, DEs and AEs) describing the temperatures, concentrations and pressure drop across the reactor was given. The model equations are solved by finite differences method. The reactor models were coded with Matlab 6.5 program and various numerical techniques were used to obtain the desired solution.
The simulation data for both models were validated with industrial reactor results with a very good concordance.
... The advantage of DE over other evolutionary algorithms is that it is simple, easy to use, speedy and greater probability of finding the global optima for function optimization [2] [3]. DE has been successfully used in various real life fields like Electrical power systems [4], electromagnetism [5], control systems [6], Bioinformatics [7], chemical engineering [8], image processing [9], artificial neural networks [10], signal processing [11] etc. ...
Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.
... The evolution algorithm decides how to perform those operations and generate a new offspring of pulses [48] Once a generation and its offspring has been generated, the selection must be performed to choose the survivors, in order to proceed with the algorihm. We have adopted a two-fold selection strategy [40,41]: First, on the individual level, a trial pulse with more desirable values of ionization and laser duration than its direct predecessor substitutes it. Second, on a global level, the principle of dominance is applied: Dominated lasers are excluded from the pool of successful lasers and consequently re-initialized before being allowed to spawn again. ...
How fast can a laser pulse ionize an atom? We address this question by considering pulses that carry a fixed time-integrated energy per-area, and finding those that achieve the double requirement of maximizing the ionization that they induce, while having the shortest duration. We formulate this double-objective quantum optimal control problem by making use of the Pareto approach to multi-objetive optimization, and the differential evolution genetic algorithm. The goal is to find out how much a precise time-profiling of ultra-fast, large-bandwidth pulses may speed up the ionization process with respect to simple-shape pulses. We work on a simple one-dimensional model of hydrogen-like atoms (the P\"oschl-Teller potential), that allows to tune the number of bound states that play a role in the ionization dynamics. We show how the detailed shape of the pulse accelerates the ionization process, and how the presence or absence of bound states influences the velocity of the process.
... Technical approaches for the development of these dynamic models to adequately describe the treatment processes and biogas production vary from one method to another. The integration of different parameters and linear and nonlinear equations with single and multiobjective functions under different constraints in large-scale engineering problems is one of the challenges of using anaerobic models (Babu et al. 2005, Iqbal and Guria 2009, Abu Qdais et al. 2010. ...
Anaerobic digestion (AD) technology has become popular and is widely used due to its ability to produce renewable energy from wastes. The bioenergy produced in anaerobic digesters could be directly used as fuel, thereby reducing the release of biogas to the atmosphere. Due to the limited knowledge on the different process disturbances and microbial composition that are vital for the efficient operation of AD systems, models and control strategies with respect to external influences are needed without wasting time and resources. Different simple and complex mechanistic and data-driven modeling approaches have been developed to describe the processes taking place in the AD system. Microbial activities have been incorporated in some of these models to serve as a predictive tool in biological processes. The flexibility and power of computational intelligence of evolutionary algorithms (EAs) as direct search algorithms to solve multiobjective problems and generate Pareto-optimal solutions have also been exploited. Thus, this paper reviews state-of-the-art models based on the computational optimization methods for renewable and sustainable energy optimization. This paper discusses the different types of model approaches to enhance AD processes for bioenergy generation. The optimization and control strategies using EAs for advanced reactor performance and biogas production are highlighted. This information would be of interest to a dynamic group of researchers, including microbiologists and process engineers, thereby offering the latest research advances and importance of AD technology in the production of renewable energy.
... DE is a stochastic population based algorithm and has different strategies. The most used and successful strategy is the DE/rand/1/bin [10]. This strategy consists in randomly selecting an individual to be mutated, one difference vectors to perturb the selected individual and a binomial crossover. ...
... O algoritmo ED é uma versão melhorada dos atuais algoritmos genéticos para a resolução de problemas de otimização (Babu et al., 2005). A principal ideia por trás desta técnica heurística é o esquema proposto para atualização do vetor de variáveis de projeto que constitui uma população de candidatos em potencial. ...
In this chapter, the method called Differential Evolution (DE) is described, including a brief history, the algorithm, and its application to the inverse radiative transfer problem, for the determination of the single scattering albedo, optical thickness, and external isotropic radiation intensities incident on the boundary surfaces of one-dimensional homogeneous participating media. The results from the DE method are compared with those obtained with the Simulated Annealing (SA) method. It is also presented how to obtain estimates for the scattering and absorption coefficients in two-layer one-dimensional heterogeneous participating media. For comparison purposes, the results obtained with the Levenberg-Marquardt deterministic method (LM), as well as with a combination of the SA and LM methods, are presented.
The three-dimensional (3D) fluid flow and heat transfer analysis and geometric optimization of two rows circular and elliptic wavy fin and tube heat exchanger (FTHE) are numerically examined for staggered arrangement. Numerical optimization studies are carried out with modeFRONTIER 2021R3 commercial software and computational fluid dynamics (CFD) analysis are conducted with help of the ANSYS Fluent R2021a which is based on the finite volume method under the assumptions of incompressible, steady and turbulent flows, and conjugate heat transfer. The circular wavy FTHE is validated with the experimental data that is conducted in the literature. In the present work, two optimization cases are solved: (1) unconstrained optimization of circular wavy FTHE (2) constrained optimization of elliptic wavy FTHE. The optimization problems have more objectives, so they are treated as multi-objective design problems. The objectives of unconstrained optimization of circular wavy FTHE case are to obtain maximum heat transfer, minimum pumping power and minimum volume. The objectives of constrained optimization of elliptic wavy FTHE case are the maximization of heat transfer and minimization of pumping power, where the constraints are given using the optimum design values of circular case to get better designs. The performance of the circular and elliptic wavy FTHE is compared in tabular and graphical forms in terms of Colburn factor j, friction factor f, heat transfer, pumping power, fin efficiency, volume, and thermal-hydraulic performance (THP) parameter. The pumping power is seen to be reduced when elliptic geometries are used in FTHEs. This is due to the streamlined shape of tubes, which causes delays in the separation point and reduction of vortices in the wake region. For the optimum design chosen from Pareto designs, elliptic wavy FTHE outperforms circular wavy FTHE in terms of THP and fin efficiency by 111.9% and 3.2%, respectively.
In this study, industrial styrene reactors were optimized using the multi-objective algorithm Generalized Differential Evolution 3 (GDE3) to maximize their conversion and selectivity. When modeling the reactors, an intrinsic heterogeneous reaction model was adopted to produce realistic results, which would adequately encompass the complex influence of the decision variables in the system. Several optimal scenarios were obtained using two- and three-objective approaches, which can be used in integrated process analysis to define suitable operational conditions. These scenarios were studied from a fundamental perspective to explore the impact of the steam-to-ethylbenzene molar feed ratio, the number of catalyst beds, catalyst loading, operating pressure, and inlet temperatures on reactor performance. Furthermore, our GDE3 implementation has been made available in a public code repository and a Python package.
Chemical reactors are employed to produce several materials, which are utilized in numerous applications. The wide use of these chemical engineering units shows their importance as their performance vastly affects the production process. Thus, improving these units will develop the process and/or the manufactured material. Multi-objective optimization (MOO) with evolutionary algorithms (EA’s) has been used to solve several real world complex problems for improving the performance of chemical reactors with conflicting objectives. These objectives are of different nature as they could be economy, environment, safety, energy, exergy and/or process related. In this review, a brief description for MOO and EA’s and their several types and applications is given. Then, MOO studies, which are related to the materials’ production via chemical reactors, those were conducted with EA’s are classified into different classes and discussed. The studies were classified according to the produced material to hydrogen and synthesis gas, petrochemicals and hydrocarbons, biochemical, polymerization and other general processes. Finally, some guidelines are given to help in deciding on future research.
It is challenging to forecast foreign exchange rates due to the non-linear characters of the data. This paper applied a wavelet-based Elman neural network with the modified differential evolution algorithm to forecast foreign exchange rates. Elman neural network has dynamic characters because of the context layer in the structure. It makes Elman neural network suit for time series problems. The main factors, which affect the accuracy of the Elman neural network, included the transfer functions of the hidden layer and the parameters of the neural network. We applied the wavelet function to replace the sigmoid function in the hidden layer of the Elman neural network, and we found there was a “disruption problem” caused by the non-linear performance of the wavelet function. It didn’t improve the performance of the Elman neural network, but made it get worse in reverse. Then, the modified differential evolution algorithm was applied to train the parameters of the Elman neural network. To improve the optimizing performance of the differential evolution algorithm, the crossover probability and crossover factor were modified with adaptive strategies, and the local enhanced operator was added to the algorithm. According to the experiment, the modified algorithm improved the performance of the Elman neural network, and it solved the “disruption problem” of applying the wavelet function. These results show that the performance of the Elman neural network would be improved if both of the wavelet function and the modified differential evolution algorithm were applied integratedly.
Multi-objective differential evolution (MODE) algorithm has been widely used in solving multi-objective optimization problems. In this paper, a hybridization technique is proposed to improve the performance of MODE algorithm in terms of speed and convergence. The proposed hybrid MODE-dynamic-random local search (HMODE-DLS) algorithm combines MODE and dynamic-random local search (DLS) algorithm. To evaluate the proposed algorithm and validate its performance, benchmark test problems (both constrained and non-constrained) are considered to be solved using MODE and the proposed HMODE-DLS algorithms. To compare between the two algorithms, five performance metrices are calculated, which are convergence, spread, generational distance, spacing and hypervolume ratio. Mean and standard deviation values for the performance metrics are reported, and the best in each category is highlighted. The Conv metric results of the new hybrid MODE are compared with other reported ones. Additionally, the effect of local search probability is studied for selected problems. In general, HMODE-DLS performance outshines, in terms of convergence and robustness, compared with other tested algorithms. HMODE-DLS is, generally, faster, and its results are of improved quality compared to MODE algorithm.
There are limited coronavirus disease 2019 (COVID-19) testing kits, therefore, development of other diagnosis approaches is desirable. The doctors generally utilize chest X-rays and Computed Tomography (CT) scans to diagnose pneumonia, lung inflammation, abscesses, and/or enlarged lymph nodes. Since COVID-19 attacks the epithelial cells that line our respiratory tract, therefore, X-ray images are utilized in this paper, to classify the patients with infected (COVID-19 [Formula: see text]ve) and uninfected (COVID-19 [Formula: see text]ve) lungs. Almost all hospitals have X-ray imaging machines, therefore, the chest X-ray images can be used to test for COVID-19 without utilizing any kind of dedicated test kits. However, the chest X-ray-based COVID-19 classification requires a radiology expert and significant time, which is precious when COVID-19 infection is increasing at a rapid rate. Therefore, the development of an automated analysis approach is desirable to save the medical professionals’ valuable time. In this paper, a deep convolutional neural network (CNN) approach is designed and implemented. Besides, the hyper-parameters of CNN are tuned using Multi-objective Adaptive Differential Evolution (MADE). Extensive experiments are performed by considering the benchmark COVID-19 dataset. Comparative analysis reveals that the proposed technique outperforms the competitive machine learning models in terms of various performance metrics.
In the literature, a large number of works about the hydrocyclones geometry optimization to obtain high performance separators can be found. However, in these works, during the optimization process, no uncertainties in model, design variables and/or parameters are considered. In these cases, a small variation in the design variable vector can result in a meaningful change on the theoretical optimal design as represented by the minimization of the corresponding vector of objective functions. In this contribution, the Effective Mean Concept is associated with the Multi-Objective Optimization Differential Evolution to obtain solutions less sensitive to perturbations in the design variables during the thickener hydrocyclones design. For this purpose, the proposed multi-objective optimization problem considers the determination of geometric variables to maximize hydrocyclone's total efficiency (η), to minimize the underflow-to-throughput ratio (RL) and to minimize the Euler number (Eu). The robust results are compared with those obtained considering nominal context (without robustness). The results showed that the tested hydrocyclones present good thickener equipment and that the robust Pareto's curve presents less diversity in comparison with the nominal solution.
Networked systems, such as telecommunications, transportation, and power transmission, are critical for the economic development and social well‐being of a society and are required to keep the prescribed demand continuously satisfied. Therefore, when planning maintenance actions for such a system, the adverse influence on its reliability caused by the unavailability of the components in the process of being maintained needs to be taken into account. To deal with this problem, we propose a new bi‐objective optimization approach to determine the Pareto optimal maintenance plans for a networked system, simultaneously maximizing its reliability within the concerned planning horizon and minimizing the total maintenance cost. Both perfect and imperfect maintenance actions are considered. The proposed approach can well balance the influence of maintenance actions on a networked system's reliability during their implementation and after being completed and, thus, can help ensure its reliability of continuously satisfying the prescribed demand.
Computer Aided Design of Chemical Process is now a well established eld in the design of new process as well as in the optimization, revamp and retrot of existing ones. The use of powerful process simulators available today allows the process engineer to simulate even an entire process, but the majority of process simulators have only classical unit operations. So, if the process has a non-classical unit operation it needs to be simulated using a suitable computer language and further to be linked to the simulator. In this paper we addressed the problem of including a new unit operation in a process simulator and how to use the virtual plant to optimize and to evaluate the environmental impact of a chemical process. We used the free chemical process simulator COCO to simulate two styrene process production plant. The firrst one uses as a reactor a conventional PFR that is available in the simulator. The second plant uses a membrane reactor that was simulated using the software Scilab that was embedded in COCO simulator by using the CAPE-OPEN protocol. Then, we used both virtual plants to develop meta-models of the processes by using experimental design and surface responses. These empirical models were used after to optimize the plants and the results shown that it is possible to increase the styrene productivity up to 27.32 kmol/h using a PFR reactor and up to 30.56 kmol/h using a membrane reactor. Finally, we calculated the Potential of Environmental Impact (PEI) for each process using the WAR algorithm and we shown that both processes have PEI very similar. Therefore, the route that uses membrane reactor has an advantage over the route that uses PFR reactor since it allows to obtain higher styrene productivities.
Evolutionary algorithms (EAs) have witnessed a radically divergent perspective regarding their potential to optimize complex real-world non-differentiable numerical functions. Since its foundation in 1973, researchers have taken a keen interest in ameliorating the optimization performance of the basic EA, leading to many variants of the basic algorithm with enhanced performance. This chapter presents a gentle introduction to the basic concepts of EA with its application to single and multi-objective, constrained optimization problems. It begins with formal definitions of optimization and elaborately discusses the traditional calculus-based optimization policies highlighting their limitations to handle non-differentiable multimodal optimization problems. Gradually, the chapter explores the scope of EAs to solve such non-differentiable real-world dynamic optimization problems using the population-based meta-heuristic search strategy. The chapter next focuses on three major variants of EA, including genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO). In addition, it provides an overview of the multifaceted literature on engineering applications of EA.
The design of engineering systems is configured as a multiobjective problem. This in
turn is inherently conflicting, that is, the improvement in one of the objectives results in
worsening the other. Among the numerous applications that can be found in the literature,
the design of three-phase induction motor, basis functions whose alternating currents
are induced in the rotor circuit, rotating magnetic field produced by the stator coils,
appears as an interesting research topic, since it is directly related to manufacturing costs
of motors. In this context, this thesis aims the multiobjective optimization of electrical
machines via finite elements considering, for example, as objectives minimizing the volume
of the machine and maximizing energy efficiency via determining the vector of geometric
variables that characterize the mathematical model presented. For this purpose are used
multiobjective differential evolution algorithm and the results obtained are compared with
those obtained by multiobjective genetic algorithm. The results preliminary indicate
that the proposed methodology configures as an interesting alternative for the purpose
described above.
In this chapter, the treatment of multi-objective optimization problems considering Classical Aggregation Methods and both Deterministic and Non-Deterministic Methods is presented. In addition, a brief review about the treatment of constraints and heuristic approaches associated with dominance concept are also discussed.
This chapter presents the development of the Self-adaptive Multi-objective Optimization Differential Evolution algorithm, as proposed to solve problems with multiple objectives. In this context, a brief review about the Differential Evolution algorithm both for the mono- and for the multi-objective contexts is presented. In addition, the strategies considered to update the DE parameters are discussed. Finally, to illustrate the performance of this new multi-objective optimization algorithm, a mathematical test case is evaluated.
The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p-xylene (PX) to TPA is regarded as a critical and efficient chemical process in industry PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simultaneously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization problems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm (SADE) to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm (ISADE). Optimization results indicate that application of ISADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.
Traditionally, the parameters used in heuristic optimization algorithms areconsidered constant during the evolutionary process. Although this characteristic simplifies the computational codes and despite the good quality of results presented in the literature, the use of constant parameters does not avoid the occurrence of premature convergence and other difficulties related to parameters sensitivity. In this context, this study aims at developing a self-adaptive heuristic algorithm based on rate of convergence and population diversity concepts, which are used by the Differential Evolution algorithm. The methodology proposed is applied to the minimization of mathematical functions and to the determination of a protocol for drug administration in patients with cancer, through the formulation and solution of a multi-objective optimal control problem. In the present study the minimization of the number of cancerous cells and the minimization of the concentration of drugs that are administered to the patient represent the considered objective functions. The Pareto's Curve provides a set of optimized protocols, among which an efficient solution for drug administration can be chosen through a given criterion, aiming at practical applications.
This paper presents the application of Differential Evolution (DE) for the optimal design of shell-and-tube heat exchangers. A primary objective in the heat exchanger (HE) design is the estimation of the minimum heat transfer area required for a given heat duty, as it governs the overall cost of the heat exchanger. However, many number of discrete combinations of the design variables are possible. Hence the design engineer needs an efficient strategy in searching for the global minimum heat exchanger cost. In the present study, for the first time DE, an improved version of Genetic Algorithms (GA), has been successfully applied with 1,61,280 design configurations obtained by varying the design variables: tube outer diameter, tube pitch, tube length, number of tube passes, baffle spacing and baffle cut. Bell's method is used to find the heat transfer area for a given design configuration. For a case study taken up, it is observed that DE, an exceptionally simple evolution strategy, is significantly faster compared to GA and is also much more likely to find a function's true global optimum.
In the present study, the Differential Evolution (DE), an evolutionary computation technique, is applied to the optimal design of an auto-thermal ammonia synthesis reactor. This paper also presents the new concept of "Nested DE" (DE is also used to find out the best combination of key parameters of DE itself). The main objective in the optimal design of an auto-thermal ammonia synthesis reactor is the estimation of the optimal length of reactor for different top temperatures with the constraints of energy and mass balance of reaction and feed gas temperature & mass flow rate of nitrogen for ammonia production. Thousands of combinations of feed gas temperature, nitrogen mass flow rate, reacting gas temperature and reactor length are possible. This paper presents the application of two methods, viz., Runge-Kutta variable step size method, and Gear's method in combination with DE, and verify the contradictory results reported using simple GA in earlier literature. Apart from determining the optimal reactor length, the comparison of results obtained from different methods is presented. DE is found to be a robust, fast and simple evolutionary computation technique for optimization problems.
In this preliminary investigation two approaches are used to obtain intrinsic kinetics for the catalytic dehydrogenation of ethylbenzene to styrene on different promoted iron oxide catalysts: (1) A rigorous heterogeneous model based on the dusty gas model for the catalyst pellets is used to extract intrinsic kinetics from the data of an industrial reactor. (2) A pseudohomogeneous model is used to extract intrinsic kinetics from the results of a laboratory fixed bed reactor packed with in-house prepared powder catalysts with negligible diffusional resistances. The extracted intrinsic kinetics were used in the heterogeneous model to simulate the industrial reactor and the results for the three in-house prepared catalysts are compared with those of the industrial reactor.
Despite the industrial importance of the catalytic dehydrogenation of ethylbenzene to styrene, no studies are reported in the literature regarding the development of a kinetic model for the intrinsic rate of this multiple reaction system. Most of the kinetic models available in the literature are extracted from industrial reactor data using pseudohomogeneous reactor models. In the present paper a rigorous heterogeneous model is developed for the reactor based on the dusty gas model (Stefan-Maxwell equations) for diffusion and reaction in the catalyst pellets. This model is used to extract intrinsic kinetic constants from industrial reactor data through a simple iteration technique.
The detection of gross errors in the reconciliation of process measurement data is an important step in removing their distorting effects on the corrected data. Tests of maximum power (MP), based on the normal distribution, are known for the detection of gross errors in the measurements and for the constraints, but only for those remaining after the removal of unmeasured flows. Here, the MP tests are derived for the original constraints, which allows the direct detection of gross errors in species balances around individual process units. It is shown that the square of the MP test statistic is precisely equal to the reduction in the weighted sum of squares of the adjustments which results from the deletion of that constraint. The test is illustrated with two examples.
La détection des erreurs importantes dans le rapprochement des données de mesure de precédés est une étape majeure lorsqu'on veut supprimer les effets de distorsion sur les données corrigées. Les tests de puissance maximale (MP) basés sur une distribution normale permettent la detection des erreurs importantes dans les mesures et pour les contraintes, mais uniquement pour les erreurs qui subsistent après l'élimination des écoulements non mesurés. Dans ce travail. on établit les tests MP pour les contraintes originates, ce qui permet la détection directe des erreurs importantes dans les bilans d'espèces pour chaque unité de procédés. On montre que le carré de la statistique du test MP est exactement égal à la réduction dans la somme pondérée des carrés des ajustements qui résultent de la suppression de cette contrainte. L'essai est illustré par deux exemples.
The global optimization of mixed integer non-linear programming (MINLP) problems is an active research area in many engineering fields. In this work, Differential Evolution (DE), a hybrid Evolutionary Computation method, is used for the optimization of nonconvex MINLP problems and a comparison is made among the algorithms based on hybrid of Simplex & Simulated Annealing (M-SIMPSA), Genetic Algorithms (GA), and DE. It is found that DE, an exceptionally simple evolutionary computation method, is significantly faster and yields the global optimum for a wide range of the key parameters. Results indicate that DE is more reliable, efficient and hence a better approach to the optimization of nonconvex non-linear problems. DE found to be the best evolutionary computation method in all the problems studied.
In recent years, evolutionary algorithms (EAs) have been applied to the solution of non-convex problems in many engineering applications. EAs differ from the conventional algorithms since, in general, only the information regarding the objective function is required. In the present work, a test problem on 'optimization of extraction process' is solved using Differential Evolution (DE) and two new DE strategies. The objective of the present study is to maximize the total extraction rate at constant disk rotation speed subject to the inequality constraints. In 1980, scientist used a modified gradient-projection technique and in 1989 GRG (generalized reduced gradient method) was used to solve this problem. Apart from the well known seventh strategy (DE-7) i.e., DE/rand/1/bin, the two new strategies (NS-1 & NS-2) have been applied. A comparison of DE-7 with the proposed two new DE strategies is presented. Experimental Simulations are carried out by running the code for all possible combination of the DE key parameters F & CR (0.0<F<=1; and 0.0<CR<=1.0), where F is scaling factor & CR is crossover constant. The proposed two new DE strategies found to be better and robust ensuring 100% convergence to the global optimum.
Two test problems on multiobjective optimization (one simple general problem and the second one on an engineering application of cantilever design problem) are solved using differential evolution (DE). DE is a population based search algorithm, which is an improved version of genetic algorithm (GA), Simulations carried out involved solving (1) both the problems using Penalty function method, and (2) first problem using Weighing factor method and finding Pareto optimum set for the chosen problem, DE found to be robust and faster in optimization. To consolidate the power of DE, the classical Himmelblau function, with bounds on variables, is also solved using both DE and GA. DE found to give the exact optimum value within less generations compared to simple GA.
The use of evolutionary algorithms (EAs) to solve problems with
multiple objectives (known as multi-objective optimization problems
(MOPs)) has attracted much attention. Being population based approaches,
EAs offer a means to find a group of Pareto-optimal solutions in a
single run. Differential evolution (DE) is an EA that was developed to
handle optimization problems over continuous domains. The objective of
this paper is to introduce a novel Pareto-frontier differential
evolution (PDE) algorithm to solve MOPs. The solutions provided by the
proposed algorithm for two standard test problems, outperform the
Strength Pareto Evolutionary Algorithm, one of the state-of-the-art
evolutionary algorithms for solving MOPs
The task of designing an 18 parameter IIR-filter which has to meet tight specifications for both magnitude response and group delay is investigated. This problem must usually be tackeled by specialized design methods and requires an expert in digital signal processing for its solution. The usage of the general purpose minimization method Differential Evolution (DE), however, allows to perform the filter design with a minimum knowledge about digital filter design. ________________________________________ 1) International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, Suite 600, Fax: 510-643-7684. E-mail: storn@icsi.berkeley.edu. On leave from Siemens AG, ZFE T SN 2, OttoHahn -Ring 6, D-81739 Muenchen, Germany. Fax: 01149-636-44577, Email: rainer.storn@zfe.siemens.de, WWW: http://http.icsi.berkeley.edu/~storn/. 1 1. Introduction IIR filters are generally applied in cases where tight requirements for the magnitude response are imposed upon the filter while p...
This book adopts a generalized approach to modelling various engineering systems in such a way that the underlying principles can be applied to any new system. There is exhaustive coverage of all topics related to plant simulation; it covers process modelling, analysis, simulation, as well as optimization. A section is devoted to non-traditional optimization techniques, which would be useful not only for students, but also for researchers, professionals, consultants, and industrialists. Babu discusses case studies on specific-purpose simulation and dynamic simulation, and also includes an overview of professional software packages used in plant simulation like HYSIS.
A new non-sequential technique is proposed for the estimation of effective heat transfer parameters using radial temperature profile measurements in a gas–liquid co-current downflow through packed bed reactors (often referred to as trickle bed reactors). Orthogonal collocation method combined with a new optimization technique, differential evolution (DE) is employed for estimation. DE is an exceptionally simple, fast and robust, population based search algorithm that is able to locate near-optimal solutions to difficult problems. The results obtained from this new technique are compared with that of radial temperature profile (RTP) method. Results indicate that orthogonal collocation augmented with DE offer a powerful alternative to other methods reported in the literature. The proposed technique takes less computational time to converge when compared to the existing techniques without compromising with the accuracy of the parameter estimates. This new technique takes on an average 10 s on a 90 MHz Pentium processor as compared to 30 s by the RTP method. This new technique also assures of convergence from any starting point and requires less number of function evaluations.
An existing side-fired stream reformer is simulated using a rigorous model with proven reaction kinetics, incorporating aspects of heat transfer in the furnace and diffusion in the catalyst pellet. Thereafter, optimal conditions, which could lead to an improvement in its performance, are obtained. An adaptation of the nondominated sorting genetic algorithm is employed to perform a multiobjective optimization. For a fixed production rate of hydrogen from the unit, the simultaneous minimization of the methane feed rate and the maximization of the flow rate of carbon monoxide in the syngas are chosen as the two objective functions, keeping in mind the processing requirements, heat integration, and economics. For the design configuration considered in this study, sets of Pareto-optimal operating conditions are obtained. The results are expected to enable the engineer to gain useful insights into the process and guide him/her in operating the reformer to minimize processing costs and to maximize profits.
In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands that the user have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms (GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Schaffer and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias toward some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to find multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Schaffer and others suggest that the proposed method can be extended to higher dimensional and more difficult multiobjective problems. A number of suggestions for extension and application of the algorithm are also discussed.
In the last two decades impressive advances have been made toward the understanding and quantitative description of the kinetics, diffusion and overall performance of catalytic reactors. Despite these advances, however, the use of mathematical modeling of gas-solid catalytic reactors in industry is still limited. By consolidating this progress in the understanding of catalytic processes, this book applies these fundamental advances to the development of models for design, simulation and optimization of industrial reactors. With particular attention being paid to the verification of the developed models against industrial data, these models are used to optimize the performance of many practical reactor cases. Using a system approach for the development of the different components and the resulting overall models, the book gives an insight into the behavior of these complex industrial systems. In addition, the practical relevance of bifurcation, instability and chaos to industrial reactors is briefly discussed. This book will be invaluable to all academics, industrial researchers and designers involved with gas-solid catalytic reactors in the petrochemical and petroleum refining industries. Topics include: systems theory and principles for developing mathematical models of industrial fixed bed catalytic reactors; chemisorption and catalysis; intrinsic kinetics of gas-solid catalytic reactions; practical relevance of bifurcation, instability and chaos in catalytic reactions; effect of diffusional resistances: the single pellet problem; the overall reactor models; the catalyst deactivation problem; physico-chemical parameters for industrial steam reformers; numerical techniques for the solution of equations arising in the modeling of industrial fixed bed catalytic reactors; application of the collocation method to the catalyst deactivation problem; and maximum principle or the heterogeneous model.
A model of an industrial catalytic dehydrogenation reactor was developed. Several kinetic models were calibrated by using catalyst manufacturers' data. The calibrated Langmuir-Hinshelwood models did not represent the data well, so an empirical model was selected and a comparison was made between simulated and actual industrial operations for two different plants. The optimum operating conditions were explored for one- and two-bed reactor configurations by using two industrial catalyst systems.
The dehydrogenation of ethylbenzene to styrene in an ideal, adiabatic reactor has been modelled using side reactions in addition to the main one. The differential equations describing the process were integrated on an IBM 7040 digital computer.
A profit function ($ gained/hour) was chosen and for various combinations of process variables, which were subject to constraints, the single bed reactor was optimized by the method of Rosenbrock(1,2). Studies of a proposed two-bed reactor were also carried out. Catalyst deactivation during the reaction was not considered because of a lack of data.
The results showed that the existing reactor could be operated more efficiently if the present plant constraints were removed. Two beds in series gave still better results.
On a modelé la déshydrogénation de l'éthylbenzène en styrène dans un réacteur adiabatique et idéal, en utilisant les réactions secondaires en plus de la réaction principale. On a intégré sur un calculateur numérique IBM 7040 les équations différentielles qui décrivent le procédé.
On a choisi une fonction de bénéfice (dollars gagnés à l'heure) et optimisé, au moyen de la méthode Rosen-bock (1,2), le réacteur à lit simple pour différentes com-binaisons de variables de procédé, lesquelles étaient sujettes à des contraintes. On a aussi fait l'étude d'un réacteur propose à deux lits. On n'a pas tenu compte de la désactivation du catalyseur durant la réaction par suite du manque de données.
Les résultats ont démontré qu'on pourrait faire fonctionner le réacteur existant d'une manière plus efficace si l'on éliminait les contraintes actuelles. On a obtenu plus de succès avec deux lits en série.
A mathematical model is developed for a styrene pilot plant reactor. The steady state version of this model was used to optimize the location of a steam injection port part way along the catalytic bed. Significant improvement in reactor performance was predicted by splitting the steam feed between the reactor inlet and the injection port. Performance was measured in terms of market value of products minus a utility cost for the steam. Studies were also carried out via computer simulation to determine optimal operating conditions. An important result was the relationship of optimal steam-to-ethylbenzene feed ratio to the kinetic parameters which describe the main dehydrogenation reaction. A pilot plant was constructed and operated in order to investigate experimentally the predictions of the mathematical model. Instrumentation was designed and installed so that an on-line digital computer could acquire process measurements directly and establish operating conditions. The experimental program confirmed the improved performance by operation of the reactor with a steam injection port and the existence of an optimum of the steam-to-ethylbenzene feed ratio as indicated by simulation.
Since the measurements of concentrations and flow rates in a process at steady state are subject to random error, they do not, in general, obey the laws of conservation and other appropriate constraints. The reconciliation of these measurements with the set of constraints is an important step, both in monitoring process performance, and in modeling. A.C. Tamhane derived a measurement test of maximum power (MP) in the sense that the test has a greater probability of correctly finding a single gross error in a particular measurement than would any other test based on a linear combination of the measurements. It is the aim of this study to extend the concept of maximum power to the constraint test. The MP test on constraints can be developed for any m-dimensional, normally distributed vector, e, with nonsingular variance-covariance matrix, V. The null hypothesis, H0, is that the expected value of e is the zero vector, and the task is to define a unit normal variate which has the highest probability of detecting a true nonzero value. Two examples are presented, to compare the conventional and the MP constraint tests.
Chen, Shiou‐Shan (Raytheon Engineers & Constructors). Styrene, the simplest and most important member of a series of aromatic monomers, is produced in large quantities for polymerization. Its versatility has resulted in the manufacture of plastics, including polystyrene, ABS, SAN, styrene–butadiene latex, SBR, and unsaturated polyester resins. Polystyrene accounts for 65% of total styrene demand. Rapid growth in styrene production has been seen worldwide since 1970, including, since the 1980s, in the Pacific Rim. Many factors contribute to its growth. Chief among these are that it can be polymerized and copolymerized under a variety of conditions by common methods and that the raw materials, benzene and ethylene, are produced in large quantities in refineries and can be supplied through pipelines. The two process routes used commercially for manufacture of styrene, dehydrogenation, and coproduction with propylene oxide, are covered. Both routes use ethylbenzene as the intermediate.
The commodity nature of the product and easy access to licensed processes have enabled new producers in developing countries to enter the global styrene market. Timing is important as price fluctuates broadly and rapidly. A large number of styrene derivatives have been reported, and several have been used for manufacturing small‐volume specialty polymers, including vinyltoluene, para ‐methylstyrene, α‐methylstyrene, and divinylbenzene.
In this study, a simultaneous chemical kinetics and heat transfer model is used to predict the eeects of the most important physical and thermal properties (thermal conductivity, heat transfer coeecient, emissivity, reactor temperature and heat of reaction number) of the feedstock on the convective-radiant pyrolysis of biomass fuels for diierent geometries such as slab, cylinder and sphere. The pyrolysis rate is simulated by a kinetic scheme involving two parallel primary reactions and a third secondary reaction between volatile and gaseous products and the char. Finite diierence pure implicit scheme utilizing the Tri-Diagonal Matrix Algorithm (TDMA) is employed for solving heat transfer model equation. Runge–Kutta fourth order method is used for solving the chemical kinetics model equations. Simulations are carried out for diierent geometries considering the equivalent radius ranging from 0:0000125 m to 0:011 m, and the temperature ranging from 303 K to 2100 K. For conversion in the thermally thick regime (intra-particle heat transfer control), it is found that variations in the properties mainly aaect the activity of primary reactions. The highest sensitivity is associated with reactor temperature and emissivity. Applications of these ÿndings in reactor design and operation are discussed. The results obtained using the model used in the present study are in excellent agreement with many reported experimental studies, much better than the agreement with earlier models reported in the literature.
The impact of shrinkage on pyrolysis of biomass particles is studied employing a kinetic model coupled with heat transfer model using a practically signiÿcant kinetic scheme consisting of physically measurable parameters. The numerical model is used to examine the impact of shrinkage on particle size, pyrolysis time, product yields, speciÿc heat capacity and Biot number considering cylindrical geometry. Finite diierence pure implicit scheme utilizing tri-diagonal matrix algorithm (TDMA) is employed for solving heat transfer model equation. Runge–Kutta fourth-order method is used for chemical kinetics model equations. Simulations are carried out for radius ranging from 0.0000125 to 0:05 m, temperature ranging from 303 to 900 K and shrinkage factors ranging from 0.0 to 1.0. The results obtained using the model used in the present study are in excellent agreement with many experimental studies, much better than the agreement with the earlier models reported in the literature. Shrinkage aaects both the pyrolysis time and the product yield in thermally thick regime. However, it is found that shrinkage has negligible aaect on pyrolysis in the thermally thin regime. The impact of shrinkage reeects on pyrolysis in several ways. It includes reduction of the residence time of gases within the particle, cooling of the char layer due to higher mass ux rates of pyrolysis products and thinning the pyrolysis reaction region.
Differential Evolution (DE) is an evolutionary optimization technique, which is exceptionally simple, significantly faster & robust at numerical optimization and is more likely to find a function's true global optimum. Pyrolysis of biomass is an important and promising chemical process in the area of renewable energy sources. In the present study, the modeling and simulation of the above process is coupled with the optimization of a non-linear function using Differential Evolution. The objective in this problem is to estimate optimal time of pyrolysis and heating rate under the restriction on concentration of biomass. It serves as the input to the coupled ordinary differential equations to find the optimum values of volatiles and char using Runge-Kutta fourth order method.
Multiobjective optimization of a third-stage, wiped-film polyester reactor was carried out using a model that describes an industrial poly(ethylene terephthalate) reactor quite well. The two objective functions minimized are the the acid and vinyl end group concentrations in the product. These are two of the undesirable side products produced in the reactor. The optimization problem incorporates an endpoint constraint to produce a polymer with a desired value of the degree of polymerization. In addition, the concentration of the di-ethylene glycol end group in the product is constrained to lie within a certain range of values. Adaptations of the nondominated sorting genetic algorithm have been developed to obtain optimal values of the five decision variables: reactor pressure, temperature, catalyst concentration, residence time of the polymer inside the reactor, and the speed of the agitator. The optimal solution was a unique point (no Pareto set obtained). Problems of multiplicity and premature convergence were encountered. A “smoothening” procedure is suggested to generate near-optimal operating conditions. The optimal solution corresponds simultaneously to minimum values of the residence time of the polymeric reaction mass in the reactor.
A hybrid algorithm of evolutionary optimization, called hybrid differential evolution (HDE), is developed in this study. The acceleration phase and migration phase are embedded into the original algorithm of differential evolution (DE). These two phases are used to improve the convergence speed without decreasing the diversity among individuals. With some assumptions, this hybrid method is shown as a method using Np parallel processors of the two member evolution strategy, where Np is the number of individuals in the solution space. The multiplier updating method is introduced in the proposed method to solve the constrained optimization problems. The topology of the augmented Lagrange function and the necessary conditions for the approach are also inspected. The method is then extended to solve the optimal control and optimal parameter selection problems. A fed-batch fermentation example is used to investigate the effectiveness of the proposed method. For comparison, several alternate methods are also employed to solve this process.
Operating hydrogen plants efficiently is a critical issue, central to any energy conservation exercise in petroleum refining and fertilizer industries. To achieve this goal, “optimal” operating conditions for improved unit performance need to be identified. In this work, an entire industrial hydrogen plant is simulated using rigorous process models for the steam reformer and shift converters. An adaptation of the nondominated sorting genetic algorithm (NSGA) is then employed to perform a multi-objective optimization on the unit performance. Simultaneous maximization of product hydrogen and export steam flow rates is considered as the two objective functions for a fixed feed rate of methane to the existing unit. For the specified plant configuration, Pareto-optimal sets of operating conditions are successfully obtained by NSGA for different process conditions. The results serve as a target for the operator to aim at, in order to achieve cost effective operation of hydrogen plants.
The paper describes a multiobjective optimization study for industrial styrene reactors using non-dominated sorting genetic algorithm (NSGA). Several two- and three- objective functions, namely, production, yield and selectivity of styrene, are considered for adiabatic as well as steam-injected styrene reactors. Pareto optimal (a set of equally good) solutions are obtained due to conflicting effect of either ethyl benzene feed temperature or flow rate. The results provide extensive range of optimal operating conditions, from which a suitable operating point can be selected based on the specific requirements in the plant. # 2002 Elsevier Science Ltd. All rights reserved.
. This paper presents a critical review of the most important evolutionary-based multiobjective optimization techniques developed over the years, emphasizing the importance of analyzing their Operations Research roots as a way to motivate the development of new approaches that exploit the search capabilities of evolutionary algorithms. Each technique is briefly described mentioning its advantages and disadvantages, their degree of applicability and some of their known applications. Finally, the future trends in this discipline and some of the open areas of research are also addressed. Keywords: multiobjective optimization, multicriteria optimization, vector optimization, genetic algorithms, evolutionary algorithms, artificial intelligence. 1 Introduction Since the pioneer work of Rosenberg in the late 60s regarding the possibility of using genetic-based search to deal with multiple objectives, this new area of research (now called evolutionary multiobjective optimization) has grown c...
Process Plant Simulation Optimization of thermal cracker operation using differential evolution A differential evolution approach for global optimization of MINLP problems
- Babu
- B V India
- B V Babu
- R Angira
* Babu, B.V., 2004. Process Plant Simulation. Oxford University Press, India. * Babu, B.V., Angira, R., 2001. Optimization of thermal cracker operation using differential evolution. Proceedings of International Symposium & 54th Annual Session of IIChE (CHEMCON-2001), CLRI, Chennai, December 19–22, 2001. * Babu, B.V., Angira, R., 2002. A differential evolution approach for global optimization of MINLP problems. Proceedings of 4th Asia-Pacific Conference on Simulated Evolution And Learning (SEAL'02), Singapore, November 18–22, 2002, Paper No. 1033, vol. 2, pp. 880–884.
Introduction to Chemical Engineering Thermodynamics Multi-objective function optimization using non-dominated sorting genetic algorithms
- J M Smith
- H C Vanness
Smith, J.M., Vanness, H.C., 1975. Introduction to Chemical Engineering Thermodynamics. third ed. McGraw-Hill, Tokyo. Srinivas, N., Deb, K., 1995. Multi-objective function optimization using non-dominated sorting genetic algorithms. Evolutionary Computation 2, 221–248.
Evolutionary computation strategy for optimization of an alkylation reaction Differential evolution for multi-objective optimization
- Babu
- B V Gaurav
- C Babu
- B V Jehan
* Babu, B.V., Gaurav, C., 2000. Evolutionary computation strategy for optimization of an alkylation reaction. Proceedings of International Symposium & 53rd Annual Session of IIChE (CHEMCON-2000), Science City, Calcutta, December 18–21, 2000. * Babu, B.V., Jehan, M.M.L., 2003. Differential evolution for multi-objective optimization. Proceedings of 2003 Congress on Evolutionary Computation (CEC-2003), Canberra, Australia, December 8–12, 2003, pp. 2696–2703.
New Optimization Techniques in Engineering Differential evolution—a simple evolution strategy for fast optimization. Dr. Dobb's optimization of steam reformer using genetic algorithm
- Onwubolu
- G C Babu
- B V Heidelberg
- Germany
- K Price
- R Storn
* Onwubolu, G.C., Babu, B.V., 2004. New Optimization Techniques in Engineering. Springer, Heidelberg, Germany. Price, K., Storn, R., 1997. Differential evolution—a simple evolution strategy for fast optimization. Dr. Dobb's Journal 22, 18–24,78. optimization of steam reformer using genetic algorithm. Industrial and Engineering Chemistry Research 39, 706–717.
Multiobjective optimization of wet film PET reactor using population based search techniques
- Syed Mubeen
Syed Mubeen, J.H., 2004. Multiobjective optimization of wet film PET reactor using population based search techniques. ME Dissertation Report (2002H101006). Birla Institute of Technology and Science, Pilani, India.
Multi-objective optimization of an industrial wiped-film PET reactor
- Bhaskar