測(cè)試函數(shù)2D圖

1、1、一維函數(shù) 一維單峰函數(shù) 一維多峰單全局最優(yōu)解函數(shù) 一維多峰多局部最優(yōu)解函數(shù) 2、二維函數(shù) 2.1二維單峰函數(shù) 2-2二維多峰單全局最優(yōu)解函數(shù) 2.2.1 SHUBERT FUNCTION Shubert Fund on x2 W1O /(X)= ( f i cos(” + 1)叼 + i) i=l Shutes Function zcos(i + 1)X2 + i) Description: Dimensions: 2 The Shubert function has several local minima and many global minima. The second plot

2、shows the the function on a smaller input domain, to allow for easier viewing. Input Domain: The function is usually evaluated on the square Xj G -10. 10, for all i = 1, 2, although this may be restricted to the square Xi G -5.12,5.12, for all i= 1,2. Global Minimum: /(x-) = 186.7309 Schwefel Functi

3、on n /(t)二 418.98288727243：加一龍叭 siii(VW) i=l Dimensions: n Domain: -500.0 航 500.0 Global Optirnuni: f(x) v 0.0 at x = (420.9687,420.9687,，420.9687) Operator: ScliwefelE valuator Char ts; 1600 1400 1200 1000 800 600 400 200 0 Figure 9: Schwefel function -500.0, 50(10. 2.2.2 EGGHOLDER FUNCTION Egghold

4、er Function 1500 1000 - 500 _ 0 一 600 -500 400 200 -200 400 200 400 -200 -400 -600 xl -600 x2 -1000 600 f(x)=(龍2 +47) sin - Hi sin (衍 + 47)|) Description: Dimensions: 2 The Eggholder function is a difficult function to optimize, because of the large number of local minima. Input Domain: Tlic functio

5、n is usually evaluated on the square x, G -512, 512, for all i = 1, 2 Global Minimum: f(xj = -959.6407, at = (512,404.2319) 2.2.3 Levy 5 test objective function. This class defines the Levy 5 global optimization problem. This is a multimodal minimization problem defined as follows: 55 /Lcvj05(x) =|(

6、i - 1)rri + 2 x 刀 J cos |(J + 1)2 + j + (ti + 1.42513)2 + (切 + 0.80032) i=ij=l Here, n represents the number of dimensions and xi -10,10 for 1 , a 4 j . Two-dimensional Levy 5 function Global optimum f) = 176禹75 for x = -1.3068,-1.42481 224 LANGERMANN FUNCTION fLangermann(X)=- 5 Ci cos(7T (T - aj2 +

7、 (x2 一 bi)2 2=1 （円一1,）24（工2 一坷尸 4 10 0 Description: Dimensions: d The Langermann function is multimodal, with many unevenly distributed local minima. The recommended values of m, c and A, as given by Molga a larger ni leads to a more difficult search The recommended value of m is m = 10. The functio

8、ns two-dimensional form is shown in the plot above Input Domain: The function is usually evaluated on the hypercube x】G 0, tt, for all i = 1,.d. Global Minima:at d = 2； f(x)=-1.8013, at x* = (2.20,1.57) at d = 5: /(x*) = 4.687658 at d= 10: /(x-) = -9.66015 多維多峰多局部最優(yōu)解函數(shù) STYBLINSKI-TANG FUNCTION Styblin$ki-Tang Function /(x)=扌 f (時(shí) - 1