The Application of Improved Hill-climbing in the Multiple Nonlinear Regression

The hill-climbing has been improved by using the percentage random step and by changing variable values instantly, which is under the condition of an improvement in the objective function having been made by a step forward of a variable in a certain direction, and the improved hill-climbing has been used to solve nonlinear regression problems, and the specific algorithm steps is given, and it has been validated with satisfactory results by using practical examples. As a taboo search, hill-climbing is simple and effective,[1-3] and many improvements could be made for different applications. The multiple nonlinear regression is a widely used basic tool in chemistry and chemical engineering. We used improved hill-climbing in the calculation of the multiple nonlinear regression and have achieved good results. The method is described as follows: The improvement of hill climbing Algorithm There are two main improvements: (1) The controlled percentage of random step: step= present*ratio- present*ratio*random_ ratio+ present*ratio*random() ratio-percentage of step; present-the current value of the variable randomr_ratio-the ratio of random,maximum value is 1, minimum value is 0 (fixed step) random()-the random figure of 0-1 When regression analysis is used in chemical engineering, constantly there is a very large difference among the regression parameters; yet if the percentage of step is used, the searching would be very effective and evenly distributed in different directions. (2)The change is moving In the case of multiple variables, for every specific variable, the change in value which may have an influence on the results could only be an increased value, or a reduced value, or it would remain in situ. Therefore, when a specific variable is increased, reduced, or remains in situ, its influence on the results is determined, if the moving (increased or reduced value of the variables) can cause the objective function optimization, the new value of the variable can be adopted. Unlike ordinary hill-climbing, a step is moved only after all variables have been tested. Test has shown that it is very effective for multiple non-linear regression.