Differential Evolution in Chemical Engineering

The following sections are included:

• Preface
• About the Editors
• List of Contributors
• Contents
• Supplementary Materials

The following sections are included:

• Process Optimization
• Classification of Optimization Methods
• Metaheuristics
• Multi-objective Optimization Problems and Their Solutions
• Differential Evolution
• Applications of Differential Evolution in Chemical Engineering
• A Simple Application of DE
• Scope and Outline of Chapters
• Conclusions
• Exercises
• References

This chapter describes differential evolution (DE), its parameters and their values. Then, proposed modifications to various components of DE algorithm until the year 2009 are summarized; these modifications have improved DE capabilities for tackling a variety of optimization problems. Finally, chemical engineering applications of DE reported until the year 2009 are reviewed. In particular, DE has found many applications for parameter estimation and modeling in addition to process design and operation. Further developments and applications of DE since the year 2009 are outlined in Chapter 1. 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.

Differential evolution (DE) has been widely used on chemical engineering problems. It is a simple, efficient and robust technique, which can be used for optimization of nonlinear and complicated mathematical models resulting from mass and energy balances combined with intricate thermodynamic and other auxiliary equations. Besides, considerable effort has been made to optimize reactor operating conditions by means of DE. This chapter aims to provide an overview on the application of DE in chemical reaction engineering. At first, DE algorithm is explained and different aspects of reactor and kinetic modeling are introduced. Afterwards, key decision variables and objective functions are discussed in detail. Based on the previous publications, the decision variable section is divided into temperature, pressure, flow rate, membrane thickness, reactor size, feed concentration and kinetic parameters. This review summarizes the main aspects of using DE in chemical reaction engineering, providing an overview for future researchers.

Differential evolution (DE), an evolutionary optimization technique is receiving greater attention due to its simplicity and ability to handle nonlinear and non-differentiable functions. Recently, we proposed differential evolution with tabu list (DETL) by incorporating the concept of tabu search (TS) (i.e., avoiding re-visits during the search) using tabu list in the generation step of DE (Srinivas and Rangaiah, 2007b). In this chapter, implementing tabu list in the evaluation step of DEis studied. These two versions: DETL-G and DETL-E are then evaluated for several benchmark problems and challenging phase stability problems. Benchmark problems consist of 2 to 20 variables and a few to hundreds of local minima whereas phase stability problems involve multiple components and comparable minima. A new benchmark problem with similar characteristics as in phase stability problems is also proposed and used. The results show that the performance of the two versions of DETL is comparable; both of them are better than DE in terms of function evaluations and better than TS in terms of reliability.

This chapter presents the Integrated Multi-Objective Differential Evolution (IMODE) program, useful for solving Multi-Objective Optimization (MOO) problems. The algorithm in this program has four main parts: multi-objective differential evolution, tabu list for avoiding revisit of search space, self-adaptation of algorithm parameters, and two search termination criteria besides maximum number of generations. All these features of the IMODE make it reliable and efficient for solving engineering optimization problems. As MS Excel is familiar and readily available to practitioners and researchers, the IMODE program is implemented in MS Excel. In natural gas industry, Amine Absorption Process (AAP) is commonly used to remove acid gases from natural gas. To illustrate the application of the IMODE program, this process 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 improves the energy efficiency of current processes by reducing utilities required. It is complicated involving many integer and continuous variables, and numerous combinations; thus an optimization technique is used for solving HEN retrofitting problems. In this work, multi-objective differential evolution (MODE) program is developed in R and applied to four case studies on HEN retrofitting. Results obtained by this program are assessed and compared with those using a MATLAB program (known as NGPM), which is based on the elitist non-dominated sorting genetic algorithm. Results show that MODE program in R is effective and better than NGPM for HEN retrofit problems tested.

In the context of Chemical Engineering, thermodynamics of phase equilibrium in reactive systems is an important topic due to the growing interest in the design, synthesis and optimization of a wide variety of chemical processing operations and technologies. For reactive systems, several thermodynamic calculations can be formulated as constrained or unconstrained optimization problems. Some examples of them are phase stability and equilibriumproblems, parameter estimation in thermodynamic models, calculation of critical points, among others. Generally, these problems are non-linear, multivariable and the objective function used as the optimization criterion is non-convex even for simple reactive systems. Hence, their solution using local optimization methods is not reliable, and these thermodynamic problems are good for assessing stochastic optimization methods. This chapter describes the application and testing of differential evolution (DE) and tabu search (TS) methods for phase stability analysis and Gibbs energy minimization in multi-component reactive mixtures using different thermodynamicmodels.We combine the stochastic methods with a variable transformation approach to offer a reliable thermodynamic framework to model the phase equilibrium behavior of reactive mixtures. Results show that DE is better than TS for the applications tested, but requires more computational effort.

When distillation is chosen as the separation method for multicomponent mixtures, the design and optimization of all possible alternatives could be too time consuming or simply not possible. The systematic synthesis methodology, proposed in this chapter, allows the definition of a search space of alternatives where the simple column sequences are directly related to all the alternatives. When this correspondence is extended to the distillation column design, it is possible to define the so called “Sequential Design Method”, able to speed up the optimization step. The combination of the sequential design method, together with the multiobjective differential evolution algorithm, results in a successful methodology to obtain the optimal design in a reasonable time avoiding the evaluation of all the alternatives included in the search space.

Currently, process intensification is a great tool for process synthesis since the design problems can be improved at early synthesis stages. It exhibits several advantages over conventional processes like reduction in equipment size, reduction in byproducts that could be further toxic or hazardous, significant improvements in performance, among others. Moreover, the major benefit is related to the economic aspect; in almost all cases, important savings in process costs can be obtained. Despite these advantages, the modeling and optimization of intensified process are still a great challenge since the used models are highly non-linear with continuous and discrete variables causing potentially non-convex objective functions for the targets of interest. Differential evolution with tabu list is a stochastic optimization algorithm that has been proven successful for solving this kind of complex problems with one or several objective functions. With this in mind, this chapter discusses and illustrates the capabilities of this hybrid stochastic algorithm for the intensification of separation processes. Two case studies have been analyzed. The first one involves an example of reactive distillation for manufacturing diphenyl carbonate as a green product alternative in the large chain production of polycarbonate, minimizing both the total annual cost and the condition number obtained from control properties. The second case study is the separation and purification of an effluent coming from a fermentation broth of biobutanol where the separation of a mixture of acetone/ butanol/ethanol/water is analyzed. This mixture is purified by means of a dividing wall column minimizing the total annual cost as economic index, the eco-indicator 99 as environmental indicator and the condition number as controllability index.

Reduction of greenhouse gas emissions (GHG) in the automobile sector is one of the main reasons supporting bioethanol production. Bioethanol obtained from biomass fermentation is dilute and unsuitable for use as an automobile fuel. For recovery (pre-concentration) and dehydration (purification) of bioethanol from the fermentation broth, distillation is widely used although ethanol and water separation by distillation is complex due to the presence of a minimum-boiling azeotrope. Membrane separation is increasingly promising for use in bioethanol production. Hence, this chapter presents development of a hybrid process of distillation followed by vapor permeation (DVP) to produce fuel-grade (99.8 wt.%) ethanol. Process optimization with one objective can reduce energy consumption. For deeper insights and meaningful conclusions, this study investigates multi-objective optimization of DVP process for bioethanol recovery and dehydration, using multi-objective differential evolution. Pareto-optimal solutions for minimizing GHG and cost of manufacture are presented and discussed. DVP process at 134 kPa has a lower cost of manufacture of $0.1829/kg of bioethanol with 99.8% recovery of bioethanol from the fermentation broth.

This chapter reports the application of Differential Evolution (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 laboratoryscale unit. Different operating scenarios for this fermentation process have been considered, and where the impact of the decision variables has been analyzed. Numerical performance of DE algorithm has been compared with the results obtained using Particle Swarm Optimization (PSO) and Artificial Bee Colony (ABC). This comparison shows that DE algorithm is a reliable method for the dynamic optimization of xylitol production in a fed-batch fermentation process, and it can outperform both PSO and ABC algorithms.

Numerous 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. However, this approach can exponentially increase computation time because the number of decision variables is increased, and that a growth-coupled production strain would be obtained cannot be guaranteed. This chapter introduces an equality constraint to minimize and maximize flux variability in the strain design problem, which guarantees a growthcoupled strain. However, transforming a bi-level optimization problem into a single-level optimization problem by using the Kuhn–Tucker theory and an equality constraint is still generally difficult. A nested hybrid differential evolution algorithm is proposed that can easily solve 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.

This chapter focuses on applications of differential evolution (DE) in the field of polymerization reaction engineering. DE can be applied for modeling and for process optimization; it is being used in different variants, according to the specific characteristics of the system and the required accuracy. First, difficulties in modeling the polymerization processes are presented to justify the use of artificial intelligence tools, particularly artificial neural networks (ANN) and DE. These difficulties are related to the complexity of the reaction medium, lack of complete knowledge of the reaction mechanism, problems in developing and solving phenomenological models, their accuracy and/or potential for inclusion in on-line control procedures. Neuro-evolutive techniques are recommended methodologies for modeling and optimizing such complex polymerization processes. A special section is dedicated to general aspects of how DE can be used 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.

The following section is included:

• Index