A Precise Evolutionary Approach to Solve Multivariable Functional Optimization

Abstract

Mankind has been facing optimization problems throughout history and making the great efforts to solve them. Optimization problems, in simple terms, are to find the best or close to the best solutions to the problems. The task of optimization in solving engineering problems is also crucial and the biologically motivated computing techniques have waxed and waned over the period of time. Evolutionary approach is a common technique that uses natural phenomena like biological genes, population, mating etc., to solve optimization problems. In an evolutionary approach a population of solution is maintained and tries to improve the solutions for better performance as better fitted species survive. Among several different methods of evolutionary approach Genetic Algorithm (GA) is the most popular due to its simplicity. Genetic Algorithm is a stochastic search and optimization method imitating the metaphor of natural biological evolution. It works on the population of individuals instead of single solution. Although GA draws attention for functional optimization, it may search same point again due to its probabilistic operations that hinder its performance. Generally, GAs are time-consuming in computing due to the large number of fitness function evaluations required and the implementation of many operators and parameters, but sometimes they cannot produce the desired results. it is always challenging for GA for functional optimization to achieve optimal solution in acceptable time. In this thesis, we make a novel approach of standard Genetic Algorithm (sGA) that minimizes the shortcomings of sGA. The proposed method is called Precise Genetic Algorithm (PGA). The primary motivation for the proposed PGA is to ensure the successive convergence in optimization problems to reach optimal solution with a minimal time. PGA searches the target space efficiently and it shows several potential advantages over the conventional GA for solving both single and multivariable functional problems. We have shown that the proposed method reveals the good performance in the context of the quality and the time needed to reach the optimal solutions compared to sGA.