Application Research Of Genetic Algorithm In Function Optimization

Genetic Algorithm (GA) is a highly parallel, random and adaptive searching probabilistic method based on the mechanics of natural selection and genetic. The scholars of domestic and foreign pay much emphasis on the research of genetic algorithm's theory and application, and have made an amazing progress. The achievement of genetic algorithm has permeated to many fields. But the theory and method of genetic algorithm are not mature. Some insufficiencies of algorithm also wait for further improvement and consummation. Function optimization is a common example of genetic algorithm. So, this paper chooses the function optimization question based on genetic algorithm as an object of study. It analyzes the mechanism of genetic algorithm, studies the fitness function and genetic operators. Aiming at the deficiency of general genetic algorithm and general real-coded genetic algorithm in solving complex function global optimization problem, the paper proposes improvements of fitness function and genetic operators. It realizes the function optimization with genetic algorithm in MATLAB. Finally, the paper selects some typical multi-dimensional or high dimensional complex functions to have a test, and compares these improvements with other algorithms. The simulation results demonstrate that the proposed algorithms can not only prevent premature convergence effectively, and improve the convergence speed and the probability of convergence, but also obtain the solution with high precision even if it is not the best.This paper improves genetic algorithm in the following aspects.1. The primary basis of genetic algorithm guiding search is the individual fitness value. So this paper chooses it as one of the key objects for study, analyzes the characteristics of index transformation fitness function and the change rule of the objective values in the genetic operating process, and proposes a new fitness function which based on index transformation. The index coefficient in it can adapt to evolutionary process of algorithm. Calculating with the proposed fitness function, linear scaling transformation fitness function of Golderg and general index transformation fitness function respectively, numerical experiment has shown that the proposed fitness function can greatly improve the accuracy of optimization algorithms, the convergence speed and the probability of convergence.2. Improving the genetic operators is also a common method to improve the performance of GA. An improved real-coded genetic algorithm which includes several improved genetic operators is proposed. This paper analyzes the advantages and disadvantages of each method, proposes using a hybrid selection strategy which combines selection of stochastic universal sampling with the elitist method and the selection of offspring replacing the worst individuals of parents. It analyzes the basic search characteristics of discrete recombination operator and arithmetic crossover operator in real-coded genetic algorithms, proposes a crossover strategy with a linear approximation concept according to function fitness. The use of such a crossover strategy can fully use the advantageous information of the contemporary population, provide the capacity of quickly moving offspring toward regions with improved fitness. In selection and crossover operators, the fitness values of the individuals are gotten directly from the objective values'orders. That is to say, if the objective values of the individuals are close at the late stage of evolution, the fitness values of the individuals still become the appropriate grading, so the ranking fitness function can not only refrain from falling into local optimum at the late stage of evolution, but also be advantageous to the selection operator, and enable the algorithm to have the good robustness. This paper also analyzes influences of the mutation probability to genetic algorithm, and proposes a real-valued mutation strategy, in which the mutation probability reduces gradually while the evolution generation increases. Finally, calculating 16 typical complex functions with the improved real-coded genetic algorithm and other three GAs respectively, the experiments demonstrate that the improved algorithm is quite better than other three GAs, it can solve not only the multi-dimensional functions well, but also efficiently solves several non-restraint test functions with 30, 100, 400, and even higher dimension.3. By the MATLAB genetic algorithm toolbox, function optimization is solved efficiently. In order to identify the effectiveness and commonality of the improved algorithm, 16 test functions are calculated with several kinds of algorithms. Through analyzing and contrasting a large number of experimental results, the conclusion is given.Finally, through concluding the research work, the advantages and the weaknesses have been clear, which provide certain reference value for further research of GA.