After this Introduction chapter in Part I Overview, the subsequent chapters in this book are organized in Parts II and III. Chapters 2 to 5 form Part II on DE developments, and Chapters 6 to 13 in Part III cover many chemical engineering applications of DE. An outline of these chapters is presented in this section. Many of the chapters contain exercises at the end for practice by the interested readers. Moreover, these exercises can also be adapted as projects for students in optimization courses.
In Chapter 2, Chen et al. describe DE, its parameters and their values.
They summarize the proposed modifications to various components of
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Fig. 1.7 Pareto-optimal front of Operating Cost and Investment in the top left plot, and the corresponding decision variable and dependent variables in other plots
3000
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0 200 400 600 800 1000 1200 100 150 200 250 300 350 400 Area of Heat Exchanger (m2) Area of Cooler (m2)
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Area of Heater (m2) 30 40 50 60 70 80 90 T2 (ºC)
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230 270 310 350 390
Min. Investment (k$) T1 (ºC)
430 40 55 70 85 100 115
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DE; these modifications have improved DE capabilities for tackling a variety of optimization problems. Further, Chen et al. provide an overview of chemical engineering applications of DE reported until the year 2009. In particular, DE has found many applications for parameter estimation and modeling in addition to process design and operation.
Recently, Dragoi and Curteanu (2016) reviewed DE applications for solving chemical engineering problems. Given these developments and applications, DE is attractive and useful both as a simple general optimizer and as a sophisticated tool to solve complex chemical engineering applications.
Chapter 3 by Rahimpour and Hamedi provides an overview on DE applications in chemical reaction engineering. DE is a simple and robust technique suitable for optimization of nonlinear and complicated models resulting from mass and energy balances combined with intricate thermodynamic and other auxiliary equations. Considerable effort has been made to optimize reactor operating conditions using DE. In Chapter 3, DE algorithm is first explained, and then different aspects of reactor and kinetic modeling are introduced. Afterwards, key decision variables and objective functions are discussed. Based on previous publications, the decision variable section is divided into temperature, pressure, flow rate, membrane thickness, reactor size, feed concentration and kinetic parameters. Chapter 3 summarizes the main aspects of using DE in chemical reaction engineering, thus providing an overview for future researchers.
Srinivas and Rangaiah describe two versions of DE with a Tabu List (DETL) in Chapter 4. One version incorporates the concept of avoiding revisits during the search, using tabu check in the generation step of DE.
Another version implements the same in the evaluation step of DE.
These versions are evaluated on benchmark and phase stability problems.
Benchmark problems consist of 2 to 20 decision variables and a few to hundreds of local minima whereas phase stability problems involve multiple components and comparable minima. Further, a new benchmark problem with characteristics similar to phase stability problems is proposed and used. The results show that the performance of the two versions of DETL is comparable, and it is better than DE in number of function evaluations and better than TS in reliability.
Chapter 5 by Sharma et al. presents the Integrated Multi-Objective Differential Evolution (IMODE) program in MS Excel, useful for solving MOO problems. The algorithm in this program has four main
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parts: multi-objective DE, tabu list for avoiding revisit of search space, self-adaptation of DE parameters, and two search termination criteria besides maximum number of generations. All these features of the IMODE program make it reliable and efficient for solving engineering optimization problems. To illustrate the application of this program, amine absorption process, commonly used to remove acid gases from the natural gas, is simulated in Aspen HYSYS and then optimized using the IMODE program for two objectives: capital and operating costs. Finally, performance of the two improvement-based termination criteria in the IMODE program is compared using the multi-objective performance metrics.
Heat Exchanger Network (HEN) retrofitting, the application in Chapter 6 by Sreepathi et al., improves the energy efficiency of current processes by reducing utilities required through suitable changes. It is complicated involving many integer and continuous variables, and numerous combinations. In this chapter, a Multi-Objective DE (MODE) program is developed in R, and then applied to four case studies on HEN retrofitting. Results obtained by this program are compared with those using the NGPM program, based on the elitist non-dominated sorting genetic algorithm, in MATLAB. Results show that the MODE program gives better solutions than NGPM for HEN retrofit problems tested.
In Chapter 7, Bonilla-Petriciolet et al. apply DE and TS, each along with a local optimizer, to phase stability and equilibrium calculations in reactive systems, which are formulated using transformed composition variables. This study shows, for the first time, that both DE and TS are successful for solving phase stability and equilibrium calculations in multi-component and multi-reactive systems using transformed composition variables. Also, Bonilla-Petriciolet et al. demonstrate the use of performance profiles for tuning algorithm parameters. Results show that DE is better than TS for the applications tested, but requires more computational effort. For both phase stability and equilibrium calculations, maximum number of generations significantly affects the performance of these stochastic methods, and hence a suitable termination criterion should be selected to improve the performance.
Design and optimization of all possible alternatives for the separation of multicomponent mixtures by distillation could be too time consuming or simply not possible. The systematic synthesis methodology, proposed in Chapter 8 by Errico et al., allows the definition of a search space of alternatives, where the simple column sequences are directly related to
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all the alternatives. When this correspondence is extended to the distillation column design, it is possible to define ‘Sequential Design Method’. This method together with the multi-objective DE algorithm, results in a successful methodology to obtain the optimal design in reasonable computation time avoiding the evaluation of all alternatives included in the search space.
In Chapter 9, Sánchez-Ramírez et al. optimize intensified separation processes using DE with tabu list. Despite many advantages, optimization of intensified processes is challenging since the used models are highly non-linear with continuous and discrete variables. DE with tabu list has been successful for solving this kind of complex problems for one or several objective functions. Hence, this chapter illustrates its capabilities for intensified separation processes considering two examples. One example is reactive distillation for manufacturing diphenyl carbonate as a green product alternative, minimizing both the total annual cost and the condition number obtained from control properties. Another example is separation of acetone/butanol/ethanol/
water mixture in the fermentation broth. This separation using a dividing wall column is optimized for minimizing the total annual cost, eco-indicator 99 and the condition number.
Chapter 10 by Singh and Rangaiah is on DE application to bioethanol recovery and dehydration by Distillation and Vapor Permeation (DVP).
Bioethanol obtained from biomass fermentation is dilute and unsuitable for use in automobiles. For recovery (pre-concentration) and dehydration (purification) of bioethanol from the fermentation broth, distillation is widely used. Membrane separation is increasingly promising for bioethanol separation. Hence, this chapter presents the development of a hybrid DVP process to produce fuel-grade (99.8 wt.%) ethanol, and then MOO of DVP process using DE. Pareto-optimal solutions for mini-mizing GHG and cost of manufacturing are presented and discussed.
Manufacturing cost of separation by DVP process is 0.1829 $/(kg of bioethanol) with 99.8% recovery of bioethanol.
Chapter 11 by Koop et al. reports the application of DE to optimize the performance of a fermentation process for xylitol production by Candida mogii yeast using a fed-batch reactor. A dynamic model that assumes the growth of cells without mortality rate was used; it has been validated earlier via experimental studies on a laboratory-scale unit.
Different operating scenarios for this fermentation process have been considered, and the impact of the decision variables has been analyzed.
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Numerical performance of DE has been compared with the results obtained using Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC). This comparison shows that DE is a reliable method for dynamic optimization of xylitol production in a fed-batch fermentation process, and it can outperform both PSO and ABC.
In Chapter 12, Wang investigates nested DE for mixed-integer bi-level optimization in genome-scale metabolic networks. Many bi-bi-level optimization methods have been used to determine optimal strain designs for the genome-scale metabolic networks of bacteria. Such bi-level optimization problems are generally reduced to single-level problems using strong duality theory. This approach can exponentially increase computation time, and does not guarantee that a growth-coupled production strain would be obtained. Chapter 12 introduces an equality constraint to minimize and maximize flux variability in the strain design problem, which guarantees a growth-coupled strain. A nested hybrid DE algorithm is proposed for solving the constrained optimization problem to obtain a set of growth-coupled production strains. It is tested through the simulation of the iAF1260 metabolic network of E. coli.
The last chapter in this book, Chapter 13 by Dragoi and Curteanu focuses on DE applications for modeling and optimization in polymerization reaction engineering. First, difficulties in the modeling polymerization processes are presented to justify the use of Artificial Neural Networks (ANN) and DE. These difficulties are due to com-plexity of the reaction medium, lack of complete knowledge of reaction mechanism, problems in developing and solving phenomenological models, their accuracy and/or potential for inclusion of on-line control procedures. Neuro-evolutive techniques are recommended for modeling and optimizing such complex polymerization processes. A section is dedicated to general aspects of using DE in combination with ANN for developing optimal neural models and for determining optimal operating conditions. Two applications: synthesis of polyacrylamide based hydrogels and of siloxane-siloxane copolymers, are discussed in detail.
1.9 Conclusions
Systematic and thorough optimization is essential in chemical engineering and many other fields for efficient and sustainable industries producing goods needed by the modern society.
Stochastic optimization methods, also known as metaheuristics, are
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attractive because of their applicability to any type of problems irrespective of discontinuities, nonlinearities and derivative availability. Of these, DE proposed by Storn and Price in 1995 is a simple and effective technique for both global optimization and MOO.
Since its proposal, DE has undergone many changes and developments, and its performance and applicability have been improved. Its code and concepts are readily available on the internet (http://www.icsi.berkeley.edu/~storn/code.html). DE developments and applications to chemical engineering are reviewed in Chapter 2 of this book and in Dragoi and Curteanu (2016). Recent advances in DE are summarized by Das et al.
(2016). A number of computer programs for DE are available at the website mentioned earlier in this paragraph. MS-Excel based program for MOO is described in Chapter 5; it is based on DE, and incorporates parameter adaptation and performance-based termination criteria besides the common maximum number of generations. It can be used for both SOO (by putting a constant value to the second objective) and MOO by engineers and scientists from any field.
Many chapters in this book describe important applications of DE to chemical engineering application, in detail. These include phase stability and equilibrium calculations, retrofitting heat exchanger networks, amine absorption process for CO2, distillation sequences, intensified separation processes, distillation-vapor permeation process for bioethanol, fermentation process for xylitol, metabolic networks and polymerization reactions.
DE developments and applications in chemical engineering covered in this book will be useful to both researchers and practitioners. Many chapters in this book have exercises at the end for practice by interested readers. Several useful programs are available at the book website or by contacting the relevant contributor of the chapters. After going through this Introduction chapter, each chapter can be read and used on its own. The editors hope that each of the chapters in this book will benefit many
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readers and will lead to further developments and applications of DE.
Exercises
1.1. Describe a scenario requiring optimization. The scenario can be in chemical engineering, any other field or daily life (e.g., career plan of a graduate student). In this scenario, identify and state the objectives, decision variables and constraints, qualitatively or quantitatively.
1.2. Solve the HEN problem in Section 1.7, and reproduce the presented results using the IMODE program (described in Chapter 5 in this book) or any other MOO program. Analyze the sensitivity of the non-dominated solutions in Section 1.7 with respect to ±10% changes in the mass flow rates and temperatures of feed and effluent. Which of these variables has the significant effect on the non-dominated solutions?
1.3. An important process in petroleum refining is the alkylation process, whose product is used for blending with refinery products such as gasoline and aviation fuel in order to increase their Octane Number. See Rangaiah (2009) for more details on alkylation process. Bi-objective optimization problem of alkylation process is as follows.
Maximize Revenue, R ($/day) = 0.063x4x7 (1.9a) Minimize Cost, C ($/day) = 5.04x1+0.035x2+10.0x3+3.36x5 (1.9b)
With respect to x1, x7 and x8
Subject to
0 x1 2,000 (1.9c)
90 x7 95 (1.9d)
3 x8 12 (1.9e)
0 [x2 x1 x8 – x5] 16,000 (1.9f) 0 [x3 0.001 (x4 x6 x9)/(98-x6)] 120 (1.9g) 0 [x4 x1(1.12 + 0.13167x8 – 0.006667x82)] 5,000 (1.9h) 0 [x5 1.22x4 – x1] 2,000 (1.9i)
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85 [x6 89 + (x7 - (86.35 + 1.098x8 – 0.038x82))/0.325] 93 (1.9j)
1.2 [x9 35.82 – 0.222x10] 4 (1.9k) 145 [x10 – 133 + 3x7] 162 (1.9l) In this problem, the 7 inequality constraints in equations 1.9f to 1.9l are the bounds on the 7 variables (x2, x3, x4, x5, x6, x9 and x10) in the original problem, and they arise from the elimination of these variables from the 7 equality constraints in the model, thus making them dependent variables. Solve the above problem using IMODE program (described in Chapter 5) or any other MOO program. Discuss the trend of values of objectives, decision variables and dependent variables of the non-dominated solutions obtained.
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