Abstract
Intuitionistic fuzzy logic has been implemented in this investigation aiming to derive intuitionistic fuzzy estimations of model parameters of yeast fed-batch cultivation. Considered here are standard simple and multi-population genetic algorithms as well as their modifications differ from each other in execution order of main genetic operators (selection, crossover, and mutation). All are applied for the purpose of parameter identification of S. cerevisiae fed-batch cultivation. Performances of the examined algorithms have been assessed before and after the application of a procedure for narrowing the range of model parameters variation. Behavior of standard simple genetic algorithm has been also examined for different values of proof as the most sensitive genetic algorithms parameter toward convergence time, namely, generation gap (GGAP). Results obtained after the intuitionistic fuzzy logic implementation for assessment of genetic algorithms performance have been compared. As a result, the most reliable algorithm/value of GGAP ensuring the fastest and the most valuable solution is distinguished.
TopIntroduction
Fermentation Processes (FP) as representatives of biotechnological processes have enjoyed an enormous progress in recent years. Biotechnological processes, and in particular FP, differ from processes occur in the nonliving nature in many aspects. FP combine the dynamic of two fundamental components–biological and non-biological That is why their specific peculiarities are largely determined from characteristics of live microorganisms. Investigations of FP, because of its multidisciplinary essence, attract a great number of specialists such as microbiologists, biochemists, bioengineers, chemical engineers, food and pharmaceutical chemists. Due to the fact that FP are complex, dynamic systems with interdependent and time-varying process variables, their modeling, optimization and high quality control is a real challenge. An important step for adequate modeling of non-linear FP is the choice of a certain optimization procedure for model parameter identification. Failure of conventional optimization methods to lead to a satisfied solution provokes an idea some stochastic algorithms to be applied. As a quite promising stochastic global optimization method, genetic algorithms (GA), originally presented by Holland (Holland, 1975), are widely applied for solving a variety of complex problems (Goldberg, 1989; Cordon, 2001; Kuo, 2001; Carrillo-Ureta, 2001; Na, 2002; Jones, 2006; Vasant, 2009, 2013; Wang, 2009; Zhang, 2010; Chauhan, 2011; Milani, 2011). Among a number of searching tools, GA are one of the methods based on biological evolution and inspired by Darwin’s theory of “survival of the fittest”. GA are directed random search techniques, based on the mechanics of natural selection and genetics, and seek for the global optimal solution in complex multidimensional search space by simultaneously evaluating many points in the parameter space. GA require only information concerning the quality of the solution and do not require linearity in the parameters. Properties like hard problems solving, noise tolerance, easy to interface and hybridize make GA suitable and more workable for a parameter identification of fermentation models (Vassileva, 1999; Ranganath, 1999; Pencheva, 2006; Roeva, 2004, 2005, 2006, 2008, 2010, 2012, 2013; Roeva & Fidanova. 2013; Slavov, 2011; Adeyemo, 2011; Angelova, 2011, 2012a, 2012b, 2012c, 2012d).
Key Terms in this Chapter
Yeast Cultivation: By fermentation, the yeast species Saccharomyces cerevisiae converts carbohydrates to carbon dioxide and alcohols – for thousands of years the carbon dioxide has been used in baking and the alcohol in alcoholic beverages.
Genetic Algorithm: Stochastic global optimization method, based on biological evolution and inspired by Darwin’s theory of “survival of the fittest”.
Fermentation Process: Process by which the living cell is able to obtain energy through the breakdown of glucose and other simple sugar molecules.
Intuitionistic Fuzzy Logic: The theory of intuitionistic fuzzy sets further extends both concepts of classical set theory and fuzzy set theory by allowing the assessment of the elements by two functions: for membership and for non-membership, which belong to the real unit interval [0, 1] and whose sum belongs to the same interval, as well.
Modeling: The model is always a simplification of the reality. Models need to be constructed in a simple manner in order to reproduce the true process behavior.
Intuitionistic Fuzzy Estimation: Different new values that might be constructed based on IFL allowing this type of logic to be used for a concrete application.
Parameter Identification: Estimation of process model parameters using objective function.