Genetic algorithm and its application in node numbering optimization in FEM

By comparing the commonness between Traveling Salesman Problem (TSP) and node numbering problem, full permutation coding scheme of chromosome in nodes numbering optimization is proposed. Fitness function of each chromosome is established considering corresponding relations between nodes number and row-column value of coefficient matrix. Crossover operator of genetic population adopts improved order-crossover method. Mutation operator works adaptively by using evolutional reversed operator in which chromosome mutates upwardly. Selection operator, which combines the Roulette wheel approach and elitist model, creates a new generation including the optimal chromosome within parent generation and random backup chromosomes within filial generation so as to ensure the overall astringency of genetic search as well as the diversity of generation. At last, an example using the suggested method has proved that the genetic algorithm in node numbering optimization works effectively and efficiently.