A closed loop algorithms based on chaos theory for global optimization

Abstract

Numerical optimization problems enjoy a significant popularity in chaos theory fields. All major chaotic techniques use such problems for various tests and experiments. However, many of these techniques encounter difficulties in solving some real-world problems which include non-trivial constrains. This paper discusses a closed loop algorithms (CLA) which based on chaos theory. Thus, for many constrained numerical optimization problems it might be beneficial to add a constraint, and make up of closed loop, using feedback theory. Given an initial best function value (BFV), after the first runs computation we subtract variable increment from obtained BFV, and name it as the new value. That the new value subtracts the new BFV in the next runs computation is defined the accessional constraints. Substituting the new BFV in the next runs for the old BFV and go on, until the global solution is searched. Eventually, some difficult test cases illustrate this approach is very available. © Springer-Verlag Berlin Heidelberg 2005.