Hybrid Type of Global Optimization Methods with Discretized Chaos Mappings and Increase Accepting Methods
Kazuaki Masuda, Eitaro Aiyoshi · IEEJ Transactions on Electronics Information and Systems · 2002
In global optimization, there is a method using discretized chaos map of continuous gradient model by Euler method. On the other hand, another method is suggested that enables to escape from local minima by permitting some degrees of increase. In this paper, we suggest a new hybrid method of combining these methods, which make it possible to find the global minimum with a higher rate and more efficiently. The essence of discretized chaos mapping lies in containing nonlinear elements which bounds the trajectory in the constraint domain. Applying the chaotic annealing method which decreases bifurcation parameter stabilizes the trajectory and leads it to local minima, while there is a difficulty in choosing appropriate annealing parameters. On the other hand, increase accepting method are essentially used in combinatorial optimization. Because it generates a new candidate from finite sets, it is inefficient to use for continuous optimization. In our hybrid approach, however, a new candidate is generated by the chaos mapping with chaotic annealing, then accepting method judges if it is chosen as a new solution. In this paper, we introduce two types of discretized chaos mapping models first. Next, we show the concept of the chaotic annealing and the hybrid type of algorithm. The efficiency is tested by numerical simulation, and it is concluded that the hybrid type is applicable to both chaotic models and any problem independently.