0.6 18 method, also known as the golden section method, is one of the optimization methods. Is to put the pilot on the golden section and find the best choice for optimization.
The 0.6 18 method was put forward by American mathematician Jack Keefer in 1953. China's famous mathematician Hua simplified and supplemented it in 1960s and 1970s, and popularized it in China. Currently, it is widely used in various fields.
The golden ratio φ of two numbers A and B satisfies:?
One way to find the value of φ is to start with the left fraction. By simplifying the fraction and replacing it with b/a= 1/φ in the above formula, we get:
Therefore, there are:
Multiply both sides by φ at the same time to get:
Namely:
Using the quadratic formula, two solutions of the above equation are obtained as follows:
Since φ is the ratio of two numbers and must be a positive number, the value is 1.6 180339887.
Extended data:
0.6 18 method is an interval elimination method. It is a method of searching unimodal function according to symmetry rule with the length of search interval (approximate value of golden section number) being 0.6 18 times. Each test point is 0.6 18 times the interval (0.382= 1-0.6 18 from the other end). It replaces the different shortening rates in Fibonacci method with the constant interval shortening rate of 0.6 18.
When n→∞, the shortening rate of 0.6 18 method is about 1. 17 times that of Fibonacci method, so 0.6 18 method can also be regarded as an approximation of Fibonacci method. 0.6 18 method is easy to implement and has good effect, and it is also a common method for single factor test in optimization method.
At the same time, it is also the most commonly used method of single factor experimental design. It is known that a test factor has an interval [a, b], and the method of 0.6 18 is to take the value at 0.6 18 of this interval for the first time; Then take the value of the symmetry point of 0.6 18 at 0.382 for the second test; Compare the results of two experiments.
Remove the range of test factors outside the intersection, then take the values at the symmetrical points of other better test points, conduct the third test, compare the results of the two tests again, remove the range of test factors outside the intersection, gradually narrow the test range, find the best test point and determine the best value of the factor.
References:
Baidu encyclopedia -0.6 18 method