Study On Improving The Numerical Optimization Efficiency Of Real-coded Genetic Algorithms

People are interested in Genetic Algorithm (GA) because the algorithm is simple to use and has the potential to solve complex problems. There are more and more applications of GA in the fields of science, engineering, medicine, literature and art. Compared with classical binary-coded GA, real-coded GA has the advantages of simpler expression, higher speed and more applicable to solve problems having wider define areas. So in recent years, many people prefer using real-coded GA in solving practical problems. Based on the discussion of basic theory of GA, some methods to improve the efficiency of real-coded GA are put forward and the methods are tested by some emulation experiments.In chapter 1 (Introduction), not only the basic structure, property, history and new study of GA but also the other aspects of evolutionary computation are introduced. Based on the summary of the approaches to improve the optimization efficiency of GA, the main work of this dissertation is explained.In chapter 2 (Rationale of GA), schema theory and convergence theory of GA are discussed in detail. Some common operators of GA are introduced and the differences of standard GA and real-coded GA are analyzed. A concept of roughness is designed to judge the solution space implied in a real-coded individual. Three approaches to improve the efficiency of real-coded GA are put forward.In chapter 3 (Improvement of real-coded genetic operators), the method to choose mutation probability, population size and mutation operator are suggested based on the concept of roughness. Since the offspring caused by uniform and non-uniform crossover has a trend to congregate in the center of define area, two new crossover operators are designed. Some indexes to judge the efficiency of GA are discussed and the results of function optimization are listed.In chapter 4 (Adaptive real-coded GA), population property in searching process is detected and random floating seems to be the main phenomenon when real-coded GA using the selection based on fitness proportion traps in a local value. A kind of adaptive scaling method based on the detection of population property is used to improve the population convergence rate. When searching process has a trend to trap in a local value, a chaos sequence is added to the population. This inactive factor improves the precision of the algorithm. A kind of adaptive algorithm based on field partition and transfer improves the precision and stability of two-dimension function optimization results. But the method is not proper to solve high dimension problems.In chapter 5 (Application of real-coded genetic algorithm), many kinds of real-coded GAs are used in equation solving and parameter estimate. Simple real-coded GA can solve equations in high precision and improved real-coded GAs are effective in parameter estimate. The real-coded GA using chaos sequence as a stimulate factor is most effective in nonlinear regression. Since real-coded GA get bad results in solving equations having 3 unknown variables, the design of fitness function seems to be a key step in using real-coded GA to solve practical problems. The more sufficient the fitness function expresses the optimization problem, the better optimization result will get.