Hebei University of Engineering, Handan 056038, Hebei, China

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Abstract—An improved genetic algorithm is proposed to solve optimal problems, which is based on fixed point algorithms of continuous self-mapping in Euclidean space. The algorithm operates on a simplicial subdivision of searching space and generates the integer labels at the vertices, then, applied crossover operators and increasing dimension operators according to these labels. In this case, it is used as an objective convergence criterion and termination criterion that the labels of every individual are completely labeled simplexes. The algorithm combines genetic algorithms with fixed point algorithms and triangulation theory to maintain the proper diversity, stability and convergence of the population. Several numerical examples are provided to be examined and the numerical results illustrate that the proposed algorithm has higher global optimization capability, computing efficiency and stronger stability than traditional numerical optimization methods and the standard genetic algorithm.

Index Terms—Genetic algorithm, fixed point, simplicial subdivision, integer label, completely labeled simplex.

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Cite: Ruizhen Gao, Jingjun Zhang, Yanmin Shang, Yuzhen Dong, "An Improve Genetic Algorithm Based on Fixed Point Algorithms," Journal of Computers vol. 7, no. 5, pp. 1109-1115, 2012.