Probabilistic Model Based Evolutionary Algorithm And Preference Based Selection In Evolutionary Multi-objective Algorithm

As a new type of evolutionary algorithm, probabilistic model based evolutionary algorithm derives from both evolutionary computation and statistical learning theory. Compared with the traditional evolutionary algorithms, probabilistic model based evolutionary algorithms do not use traditional genetic operation such as crossover and mutation. Instead, it uses the learning and sampling from probabilistic model to produce new individuals. In probabilistic model based evolutionary algorithm, statistical learning methods are used to build a probabilistic model from the macroscopic view of entire population to describe the distribution of the individuals. The new generation of population are generated by random sampling from the new probabilistic model. Since the probabilistic model is estimated by good individuals of the population, the new generated individuals will have better fitness than the previous generation. Therefore the population become evolutionary.Evolutionary multi-objective optimization algorithm is the most active topic of evolutionary computing. Since there is no single solution optimal all objectives simultaneously, preferences information from decision maker is necessary for multi-objective optimization evolutionary algorithm. The Preference information in evolutionary algorithm aims to make the search for preferred solutions more effective.This dissertation mainly focuses on probabilistic model based evolutionary algorithm: and preference based evolutionary multi-objective algorithm. Probabilistic model based evolutionary algorithm can be classified as quantum evolutionary algorithm and estimation of distribution algorithm by the theory origin. The main work and innovations are as follows:1. Based on the analysis of the basic concepts and principles in quantum computing, a quantum chromosome mutation operation is proposed based on quantum controlled not gate. This operation eliminates local convergence problem in the quantum evolutionary algorithm caused by just using the update method by quantum rotation gate, and enhances the global convergence performance of the algorithm. The experimental results show that the convergence performance of new algorithm has a great improvement.2. A non parameter distribution estimation algorithm by kernel density estimation is proposed. In this algorithm, the distribution of the current population is directly used to build up probabilistic model by kernel density estimation. This algorithm does not require any prior assumption of the distribution model of solutions. The distribution characteristics can be obtained from individual species itself which are used to estimate the probabilistic density function of arbitrary shapes without distribution assumption. In order to improve the convergence performance, the differential evolution algorithm is introduced to learn from the excellent individuals. And overall information in current excellent area can be used by mutation of individuals to generate more excellent individuals at greater probabilistic Numerical experiments show that the new algorithm has better convergence performance.3. The utility functions are introduced into evolutionary multi-objective algorithm to quantify decision makers’ satisfaction on an objective value. The domination between solutions maintains is proved when the objective functions are mapped to utility functions. The utility functions are aggregated by total utility and then integrated into SMS-EMOA, an hypervolume based evolutionary algorithm. Furthermore, the solutions generated by this algorithm will located in the interesting area through the relationship between the marginal utility function. Numerical experiments show that the algorithm can produce better solutions in decision maker’s interested regions.