Two Methods Based On Filter For Solving Nonlinear Programming Problems

This paper mainly discusses two different ways of solving nonlinear optimization problems. Both of them are based on the filter and work with other effective ways of solving nonlinear optimization problems.The first method discussed in this paper is filled function method based on filter. There are two phases in the algorithm, the first phase is minimizing objective function and the second is filling phase. A new filled function is constructed here and proved to be a filled function, and the new method is given. Filter keeps those pairs that are close to the feasible region or have a better optimum with constraints satisfied. Here a three-dimension filter adapts to filled function and it works in the second phase well.In the second part, we discuss a new method calculating with the filter method and the genetic algorithm which is one of the modern evolution algorithms. Here filter is also used as criterion of choosing better points in solving constraint optimizing. Genetic algorithm plays an important role in escaping from local optima and filter ensures minima. Numerical results of the examples given in the paper show the success of the algorithm. After that, we try to use this method in general optimization programming, the equality and inequality constraints are discussed separately. Two constraints violation functions are constructed, together with objective function, we get a three-dimension filter, and we can get convergent results as well.