A Weaker Sufficient Condition for the Chaoticity of Extended Perturbation-Based Updating System for Global Optimization

作者：Tatsumi Keiji^*

来源：International Journal of Bifurcation and Chaos, 2017, 27(6): 1750085.

DOI：10.1142/S0218127417500857

• Metaheuristics
• chaos dynamics
• global optimization
• perturbations
• snap-back repeller

Recently, the gradient method with perturbation (GP) was proposed for metaheuristic methods of solving continuous global optimization problems. Its updating system based on the steepest descent method is chaotic because of its perturbations along the standard basis vectors, which can strengthen the diversification of search. The sufficient condition for its chaoticity was theoretically shown, which implies that two kinds of influence degrees of the perturbations in the updating system should be greater than some constants. In this paper, we extend the updating system of the GP into a more general one for metaheuristic methods, which does not necessarily require the descent direction of the objective function, and which can have perturbations along appropriate orthogonal basis vectors for each problem. Furthermore, since the condition for the chaoticity shown in the previous work is too restricted for practical use, we theoretically show a weaker sufficient condition for the extended system, which is derived by varying the constant lower bounds for the two kinds of influence degrees.

• 出版日期2017-6-15