Discontinuous Parameter Function's Identification Method Based On Evolutionary Computation

Discontinuous parameter function's identification problem is defined as given a series of data, to find a discontinuous function that fits the data weil. This is a hard problem. A discontinuous function's domain has been divided into several sub-domains by its discontinuities. There is an independent sub-function in each sub-domain. To find the function as a whole, you must find the sub-domains and sub-functions at one time. This complexity makes the identification problem a challenge hard problem.Evolutionary computation (EC) is an intelligence algorithm that learns from the evolutionary process in the nature. EC employs a coding technology and some genetic operations. Under the pressure of selection, which means "fits survive", the algorithm can produce an optimal solution. Because EC is simple and it seldom needs any additional information about the problem, EC becomes a general solver of challenge problems.According to the essential property of the discontinuous function, we designa new hybrid coding structure--point-tree structure, which uses a point topresent a discontinuity and a tree to present a sub-function. We evolve them together to obtain a proper solution. We call this method point-tree structure genetic programming algorithm (PTGP). This algorithm has been applied into symbolic regression and parameter identification. The results show that PTGP is a good method.