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Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization
作者姓名:Dai Xiaoming  Sun Rang  Zou Runmin  Xu Chao & Shao Huihe
作者单位:. Dept. of Auto.,School of Electric and Information,Shanghai Jiaotong University,Shanghai 200030,P. R. China; College of Information Science and Enginereing,Central South University,Changsha
摘    要:Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.


Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization
Dai Xiaoming,Sun Rang,Zou Runmin,Xu Chao & Shao Huihe.Global Convergence Analysis of Non-Crossover Genetic Algorithm and Its Application to Optimization[J].Journal of Systems Engineering and Electronics,2002,13(2).
Authors:Dai Xiaoming  SUN Rong  Zou Runmin  Xu Chao  Shao Huihe
Abstract:Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.
Keywords:Canonical  Genetic algorithm  Ergodic homogeneous Markov chain  Global convergence  
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