Research On Multi-objective Genetic Algorithms Based On Fixed Point Theory

Genetic algorithm is according to the principle of biological genetic stochasticsearch algorithms for solving the global optimal problems. It’s a simple, universal,strong robust, suitable for parallel distribution processing, but the genetic algorithm haspoor stability, convergence judgment has the disadvantages such as subjectivity.The fixed point theory of the "split-label-split" idea is introduced into the geneticalgorithms to slove genetic efficiency, locking the optimal solution looking forcompletely labeled simplexes, finding their internal completely labeled simplexes in theresubdivision of simplexes in the previous step make the optimal solution regionsfurther reduced. Genetic Algorithms randomly selecte points in the completely labeledsimplexes as the initial group in the relative size of the fitness,which greatly improvedthe efficiency of genetic algorithm. Genetic variation occurred in completely labeledsimplexes or near them,which makes the precision of the optimal solution greatlyimproved.Many problems in theory of mathematics can be converted to the simplexcontinuous mapping fixed point problem. This paper proposed a improvedmulti-objective genetic algorithm based onK1subdivision, the fixed point theory ofthought is the function within the solution space into a standard simplex, and doK1subdivision for space of transformation and the subdivision vertex labelaccording to certain rules of label for integer, classified according to the labelinformation on individuals, on different kinds of individuals of different geneticoperation, increase the diversity of the population, avoid the algorithm falls into localoptimum. By changing the profile control step by step is long, will get differentprecision requirement of optimization solution of optimization problem. And whetherpopulation convergence to the standard genetic algorithm simplex as more objectivecriterion of convergence. Through the test function for simulation, the results show thatthe stability of improved genetic algorithm is better than the traditional numericaloptimization method and the standard genetic algorithm.