Research On Combination Of Crossover Operators Of Real Coded Genetic Algorithms

Premature convergence and low accuracy in search have been often encountered when applying conventional genetic algorithms to solve function optimization problems, especially those with high dimensions. For this reason, researchers have proposed various measures to improve the performance of GAs, among which is the method using multiple genetic operators in GAs. But this approach has been lack of systematic study. In view of such situation, the combination of crossover operators in real coded genetic algorithms was studied in this dissertation, emphasizing on the combination effect of crossover operators and the cooperation of mutation operator with the combined crossover operators, etc. A new evolutionary algorithm framework has been constructed based on this study.The basic search characteristics of various crossover operators in real coded genetic algorithms were firstly analyzed. For discreet recombination operators, the combination capabilities of three types of discrete recombination operators, one point crossover, multiple point crossover and uniform crossover operators are analyzed with combinatorics. The combination capability of the operator is measured by the number of different chromosomes produced by the operator. It is shown that uniform crossover operator is the most capable. Numerical experiment has shown that the performance of algorithm is relevant to the combination capability of discreet recombination operators, but there exists no simple relation such as the more capable the operator, the better the performance of the algorithm using the operator. Which operator is suitable for an algorithm also depends on the problem to be optimized, that is, discreet recombination operators are problem-dependent. The local property of search with selection and crossover operators was analyzed. It has been pointed out that searching with selection and crossover operators, the search scope is limited within the maximum rectangular solid determined by the initial population. For arithmetic crossover operators, the contractibility of arithmetic crossover operators was analyzed. The local property of search with selection and arithmetic crossover operators was also analyzed. It has been pointed out that searching with selection and arithmetic crossover operators, the search scope is also limited within the maximum rectangular solid determined by the initial population. The random extensibility and contractibility of extended arithmetic crossover operators were analyzed. It has been pointed out that the search scope of these operators is larger than discreet recombination and arithmetic crossover operators.The combination effects of 12 parallel combinations and 12 confined parallel combinations of 10 extended arithmetic crossover operators were studied through numerical experiment. Numerical experimental results have shown that under the same experimental conditions (population size, computing cost and number of experiment are all the same), there exist 3 types of combination effects, that is, restraint, synergy and equivalence. The search performance of combined operators is not always better than single operator. The combination with more operators is not always better than the combination with fewer operators. Combined operators are problem-dependent as single operator. Comparatively speaking, most combined operators are weaker in problem-dependence than single operator.Theoretical analyses and numerical experiment have shown that some extended arithmetic crossover operators or their combination have some capabilities to explore the solution space. Considering this point, a new evolutionary algorithm framework based on hydride crossover and intermittent mutation is constructed. Intermittent mutation is introduced into the algorithm, which means that mutation is not taken place in each generation, but intermittently. During the mutation interval, each local subspace of the solution space and the whole solution space are searched by the extended arithmetic crossover operators or their combination. When the population has gathered to some degree, and hence the exploring capabilities of the extended arithmetic crossover operators or their combination decrease, the population undergoes mutation, to recover the diversity of the population in order to increase the exploring capabilities of the extended arithmetic crossover operators or their combination. Based on this new evolutionary algorithm framework, an evolutionary algorithm for unconstrained optimization problems is proposed, in which some extended arithmetic crossover operators are combined together through confined parallel combination and series-parallel combination to enhance the search capability and to widen the application scope of the algorithm. The proposed algorithm is used to solve some benchmark problems with dimensions from 100 to 500, obtaining more accurate and more stable optimization results than some other evolutionary algorithms. The constraint handling method of direct comparison and the nondifferentiable exact penalty function method were discussed, and respectively, they were introduced into the new evolutionary algorithm framework based on hydride crossover and intermittent mutation. Several evolutionary algorithms were proposed for constrained optimization problems, some of which use a network of discreet recombination operators and extended arithmetic crossover operators. The proposed algorithms were used to solve constrained benchmark problems with equality and inequality constraints with dimensions from 5 to 200, obtaining also more accurate and more stable optimization results with better constraint satisfaction than some other evolutionary algorithms including those newly proposed ones.To seek new mechanism of evolutionary algorithms is also encouraged. In this dissertation, a new search algorithm for global optimization -population migration algorithm is proposed by simulation of population migration. The algorithm mainly simulated population transition with economics and dispersion with population pressure increment. Numerical experiment has shown the global optimization capability of the proposed algorithm. It is proved by means of probability that the algorithm converges to the global optimum in probability. The estimation of convergent speed and computational time complexity in the worst case were given. A relatively sound foundation is laid for the proposed algorithm.