Global Optimization Algorithm Based on One-Dimensional Chaotic Maps and Gradient Descent Technique

摘要

A hybrid algorithm for searching the global minimum of a multimodal function is proposed in the paper. It is a two stages search technique, the first stage is the twice carrier wave based chaotic optimization algorithm (COA) for global searching, and the second stage is the gradient descent algorithm (GDA) for accurate local searching. The chaotic dynamics is realized through one-dimensional map in three variants: logistic, cubic and sine map. Three testing functions are used. A hundred simulations (each starting from different initial point generated randomly) were carried out for each of the test functions using two optimization algorithms: the proposed hybrid algorithm and the GDA working alone. The success and accuracy of locating the extremum, as well as the convergence of the algorithms using the three different chaotic maps were discussed.