Variants of Hybrid Genetic Algorithms for Optimizing Likelihood ARMA Model Function and Many of Problems

Optimization is essentially the art, science and mathematics of choosing the best among a given set of finite or infinite alternatives. Though currently optimization is an interdisciplinary subject cutting through the boundaries of mathematics, economics, engineering, natural sciences, and many other fields of human Endeavour it had its root in antiquity. In modern day language the problem mathematically is as follows Among all closed curves of a given length find the one that closes maximum area. This is called the Isoperimetric problem. This problem is now mentioned in a regular fashion in any course in the Calculus of Variations. However, most problems of antiquity came from geometry and since there were no general methods to solve such problems, each one of them was solved by very different approaches. Generally, optimization algorithms can be divided in two basic classes: deterministic probability algorithm. Deterministic algorithm are most often used if a clear relation between the characteristic of possible solutions and their utility for a given problem exists. If the relation between a solution candidate and its fitness are not so obvious or too complicated, or the dimensionality of the search space is very high, it becomes harder to solve a problem deterministically. Trying it would possible result in exhaustive enumeration of the search space, which is not feasible even for relatively small problem. Then, the probabilistic algorithm come in to play. The increased availability of computing power in past two decades has been used to develop new techniques of optimization Today's computational capacity and the widespread Availability of computers have enabled development of new generation of intelligent computing techniques, such as genetic algorithm. Evolutionary Algorithm are population met heuristic optimization algorithms that use biologicinspired mechanisms like mutation, crossover, natural selection, and survival of the fittest in order to refine a set of solution candidates iteratively [ Weise, 2009]. All evolutionary algorithms proceed in principle according to the scheme illustrated in fig.(1). A simple Genetic Algorithm 嫌罫畦 is search algorithms based on the mechanics of natural selection and neutral genetics. They combine survival of fittest among string structures with a structure yet randomized information exchange to form a search algorithm with some of