NEW REAL CODED GENETIC ALGORITHMS AND THEIR APPLICATIONS TO BIO-RELATED PROBLEMS

Abstract

In many real world nonlinear optimization problems it is often required to determine a global optimal solution rather than a local optimal solution. Determining the global optimal solution is generally more difficult as compared to determining a local optimal solution. However because of the practical necessity the search for global optimum solution often becomes mandatory. Conventional computing techniques usually face difficulty in dealing with such real world problems. There comes the role of nature inspired computing paradigms which can be used where conventional computing techniques perform unsatisfactorily. Genetic Algorithm (GA) is one of the most effective and popular natural computing technique which takes its inspiration from Darwin's theory of "Survival of Fittest". GA has undergone many changes since its introduction. As researchers have learned about the technique, they have derived new versions, developed new applications, and published theoretical studies of the effects of the various operators, parameters and aspects of the algorithm. One such important part of GA family is Real Coded Genetic Algorithms (RCGAs) where the encoding of population is done as vectors of real numbers. This Thesis is computationally dominant and interdisciplinary in nature which aims to improve the efficiency and reliability of RCGAs and their application to bio-related disciplines. The main contribution of this Thesis in the development of new RCGAs is the proposal of three new operators — two crossover operators and one mutation operator for real coded genetic algorithms for determining the global optimal solution of unconstrained nonlinear continuous optimization problems. Firstly, two new operators - a new real coded crossover operator called Weibull Crossover (WX) and a new real coded mutation operator called Log Logistic Mutation (LLM) are proposed. Both WX and LLM are used in conjunction with two well known crossover and mutation operators viz. Laplace Crossover (LX) (Deep and Thakur, 2007a) and Power Mutation (PM) (Deep and Thakur, 2007b). Using the various combinations of two crossover (Weibull crossover, Laplace crossover) and two mutation (Log Logistic Mutation, Power Mutation) operators, three new generational RCGAs are defined WX-PM, LX-LLM and WX-LLM. A set of 35 benchmark problems (15 nonscalable and 20 scalable), of different degrees of complexity and multimodality, available in literature is used to test the performance of these three newly developed RCGAs along with the existing RCGA viz. LX-PM (Deep and Thakur, 2007b). Then, a new crossover operator based on a novel idea of merging of existing crossover operators is proposed, with a view that it retains the strength of the both the considered crossover operators. This operator is called as Double Distribution Crossover (DDX) as in the Thesis DDX is obtained from WX (Weibull Crossover) which makes use of Weibull distribution and LX (Laplace Crossover) which makes use of Laplace distribution. DDX is used with two mutation operators LLM (Log Logistic Mutation) and PM (Power Mutation) to define two new generational RCGAs DDX-PM and DDX-LLM. For scalable and nonscalable problems these two RCGAs are compared with WX-PM and LX-LLM respectively as these are found to be the best performing RCGAs, amongst WX-PM, LX-PM, LX-LLM and WX-LLM. All the six RCGAs have been applied to problems of different degree of complexity and multimodality. Broadly two types of problems are solved using newly developed RCGAs. In the first type of problems, all RCGAs have been applied to obtain the global minimum of some specific energy function which is responsible for the interaction among the atoms of a molecule. Three problems of this type are solved using all six RCGAs. In all the three problems the number of local minima grows exponentially with problem size. The second type of problems is from the field of herbal extraction. Two problems of this type are solved in the Thesis. In the first problem the yields of three main bioactive compounds: Crocin, Geniposide and Total Phenolic Compounds from Gardenia fruits are first modeled in terms of the input variables viz. Ethanol Concentration, extraction temperature, extraction time and then the yields are optimized simultaneously. The problem of simultaneous optimization of all the three objectives turns out to be a multiobjective optimization problem. The popular methodology of weighted sum approach is used to solve this problem by converting it to a single objective optimization problem. In the second problem of herbal extraction, a novel attempt is made to extract, two main bioactive compounds viz. Withaferin-A and Withanolide-A of a valued herbal medicine: Ashwagandha (Withania somnifera) optimally from its roots. Firstly, the experiments are designed for obtaining different yields (content %) of both the bioactive compounds which are affected by concentration of the solvent used for extraction (Methanol) and the temperature at which the process is carried out. The yields are calculated ii by experimentation by the method of High Pressure Liquid Chromatography (HPLC). Then the obtained data is modeled for each of the two bioactive compounds and simultaneous optimization of both the objectives is done using weighted sum approach of multi-objective optimization. The final obtained results are validated by experimenting again at the obtained inputs. To best of our knowledge this is for the first time that this approach is being used for Ashwagandha. iii