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The Use of Differential Evolution Algorithm for Solving Chemical Engineering Problems

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The Use of Differential Evolution Algorithm for Solving Chemical Engineering Problems Rev Chem Eng 2016; 32(2): 149–180 Elena Niculina Dragoi and Silvia Curteanu* The use of differential evolution algorithm for solving chemical engineering problems DOI 10.1515/revce-2015-0042 become more available, and the industry is on the lookout Received July 10, 2015; accepted December 11, 2015; previously for increased productivity and minimization of by-product published online February 8, 2016 formation (Gujarathi and Babu 2009). In addition, there are many problems that involve a simultaneous optimiza- Abstract: Differential evolution (DE), belonging to the tion of many competing specifications and constraints, evolutionary algorithm class, is a simple and power- which are difficult to solve without powerful optimization ful optimizer with great potential for solving different techniques (Tan et al. 2008). In this context, researchers types of synthetic and real-life problems. Optimization have focused on finding improved approaches for opti- is an important aspect in the chemical engineering area, mizing different aspects of real-world problems, includ- especially when striving to obtain the best results with ing the ones encountered in the chemical engineering a minimum of consumed resources and a minimum of area. Optimizing real-world problems supposes two steps: additional by-products. From the optimization point of (i) constructing the model and (ii) solving the optimiza- view, DE seems to be an attractive approach for many tion model (Levy et al. 2009). researchers who are trying to improve existing systems or The model (which is usually represented by a math- to design new ones. In this context, here, a review of the ematical description of the system under consideration) most important approaches applying different versions has three main components: (i) variables, (ii) constraints, of DE (simple, modified, or hybridized) for solving spe- and (iii) objective function (Levy et al. 2009). The scope cific chemical engineering problems is realized. Based on of optimization is to determine the values of the system the idea that optimization can be performed at different parameters (variables) for which the overall performance levels, two distinct cases were considered – process and is the best (measured using an objective function or a model optimization. In both cases, there are a multitude fitness function) under some given conditions (Das and of problems solved, from different points of view and with Suganthan 2011). The variables of the model correspond various parameters, this large area of successful applica- to the specific characteristics of the studied system, rep- tions indicating the flexibility and performance of DE. resenting components that can be changed to create Keywords: chemical engineering processes; differential different possibilities. The objective function and the evolution; modeling; neural networks; optimization. constraints values can be obtained from (i) analytically known formulae (phenomenological models), (ii) the outcome of a computational process (such as modeling 1 Introduction approaches) and (iii) measurements of the actual process (Snyman 2005). Optimization is an important aspect, the efficient explo- Concerning the problem of solving the optimization ration of systems workflow and reduction of consumed model, different approaches can be encountered. The resources being always desirable. As technology evolves, traditional optimization algorithms are based on gradi- highly sophisticated and well-controlled chemical plants ent methods. These methods have a high probability of getting trapped in local optima (especially in high nonlin- ear cases) and do not guarantee identification of optimum *Corresponding author: Silvia Curteanu, Faculty of Chemical Engineering and Environmental Protection, Department of Chemical (Angira and Babu 2006). As nonlinearity is an important Engineering/Applied Informatics, “Gheorghe Asachi” Technical aspect (as it is introduced by equipment design relations, University Iasi, Bd. Prof.dr.doc. Dimitrie Mangeron, No. 71A, equilibrium relations, or by combined heat and mass bal- 700050, Iasi, Romania, e-mail: [email protected] ances, among other things) (Angira and Babu 2006), new Elena Niculina Dragoi: Faculty of Chemical Engineering and techniques that can deal well with these problems have Environmental Protection, Department of Chemical Engineering/ Applied Informatics, “Gheorghe Asachi” Technical University Iasi, been proposed and tested (Bastos-Filho et al. 2011, Precup Bd. Prof.dr.doc. Dimitrie Mangeron, No. 71A, 700050, Iasi, Romania. et al. 2012, Mavrovouniotis and Yang 2013, Yacoub et al. http://orcid.org/0000-0001-5006-000X 2014). In recent years, population-based optimization 150 E.N. Dragoi and S. Curteanu: Differential evolution in chemical engineering procedures (with biological inspiration) have been dis- 5 refers to some practical aspects, being a short over- tinguished as powerful approaches that can be efficiently view that connects the DE algorithm (taking into account applied for solving different optimization problems from characteristics and possibilities of improvement) with various areas. This group includes algorithms like genetic its application for model and process optimization. The algorithm (GA), differential evolution (DE), ant colony opti- last section concludes the paper. The chemical engineer- mization, or particle swarm optimization (PSO). Among ing applications are selected to emphasize all the above these algorithms, DE is relatively new, being proposed in aspects. 1995 (Storn and Price 1995). It is a powerful approach, in many theoretical and practical situations outperforming its counterparts. It is a simple, new-generation evolution- ary algorithm (EA), developed for solving optimization 2 Differential evolution problems over continuous domains (Abbass 2002, Hu and Yan 2009a). Due to its characteristics – simplicity, few The DE inspiration source is represented by the Darwinian control parameters, and ability to handle nondifferenti- principle of evolution, in which only the fittest individuals able, nonlinear, and multimodal objective functions – it survive to the next generations. It was proposed in 1995, gradually became more popular, in the field of chemical and over the years, as its strong and weak points were engineering being used for a large area of applications identified, it underwent a series of improvements and (Pant et al. 2009b). hybridizations. However, the base elements remained the In this article, a review of the most relevant works same. applying classic or modified DE versions, in stand-alone As with every EA, DE starts with an initial pool of applications or in combination with other specific soft- potential solutions that are evolved (using principles like ware or algorithms, is performed. The applications dis- mutation, crossover, and selection) until a stop criterion is cussed in the next sections are dated after 2009, but DE reached. The mutation and selection steps (which are sto- has been used to solve chemical engineering problems chastic processes) are the main mechanism used for new from the early days. A few examples are given in Table 1. individual generation, while selection is (as its name sug- The paper is organized as follows: Section 2 presents gests) the step in which a competition for survival takes the main characteristics of the DE algorithm, its steps, the place (Greenwood and Tyrrell 2006). stop criteria usually employed, and the principal mecha- These DE operations have similar terminology with nisms for improving its performance. In Section 3, specific the ones from other EAs, but their application, role, and aspects related to the application of DE for the problem motivation are different. Another difference between DE of process optimization are discussed. A clear distinction and other EAs (such as GA) consists in the parameter between the use of simple variants (also known as classic encoding. DE encodes all the parameters using a floating approaches) and the hybrid versions is made. Section 4 point, while classic GA uses a binary encoding scheme. tackles the problem of model optimization, and Section This real value encoding and the fact that DE parameters Table 1: A few examples of DE applications in chemical engineering prior to 2009. Domain References Application Reactors and fermentation Chiou and Wang (2001) Estimation of Monod model parameters of a bioreactor Wang et al. (2001) Estimation of kinetic parameters of the ethanol fermentation process Chiou and Wang (1999) Feed batch fermentation Wang and Cheng (1999) Feed batch fermentation Kapadi and Gudi (2004) Feed batch fermentation Thermal engineering Babu et al. (2004) Optimal design of an ammonia synthesis reactor Babu et al. (2005) Optimization of adiabatic styrene reactor Babu and Sastry (1999) Estimation of heat transfer parameters in a trickle bed reactor Babu and Munawar (2001) Optimal design of shell and tube heat exchanger Babu and Angira (2006) Heat exchanger network design Fuel engineering Chen et al. (2002) True boiling point curve of crude oil; effect of pressure on entropy Babu and Chaurasia (2003) Estimation of optimal time of pyrolysis and heating rate Angira and Babu (2006) Alkylation process optimization Babu and Angira (2006) Alkylation process optimization E.N. Dragoi and S. Curteanu: Differential evolution in chemical engineering 151 are manipulated with arithmetic operators have several where bk,L and bk,U are the lower and upper limits of each advantages: efficient memory
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