贴上本人自己写的模拟退火算法的源代码,开发环境 Visual Basic.net 2005
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Public Class CSA( H# k' D* S, M* }+ n, u
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Public Function obFun(ByVal x As Double) As Double" }/ _) D! `) i8 r
Return 2 * Math.Pow(x, 2) - x - 14 z) H7 z5 K8 o$ @: A# D" g
End Function
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''' <summary>7 }( z' g0 Y1 s5 w( q# M
''' 传统的模拟退火算法
5 s M0 B$ j: ]# T C" L5 _& [ ''' </summary>
$ L6 ]' n! w8 g! ]. I ''' <param name="Ux ">参数的取值范围上限</param>
8 Z0 [( l, H. v# j. A5 @ ''' <param name="Lx ">参数的取值范围下限</param>
`# K& X4 { ]/ O& T ''' <returns></returns>* E+ r. f, \' i& N
''' <remarks></remarks>
) D9 q" `# W, d; n Public Function CSA(ByVal Ux As Double, ByVal Lx As Double) As Double. S1 u. z4 d* }0 _" T$ Z2 r' ]
Dim init_temperature As Double, total_numk As Double, step_size As Double '定义初始温度,温度k时循环总次数,步长
3 I1 O$ J% c1 [- F" V: O$ l | Dim x As Double, receivnum As Double '定义变量当前值,前一个值,内循环的接受数据3 t. l5 D$ ~5 p) T8 ` Y1 d
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'初始化SA参数
- ~3 U4 Y, q$ T$ p4 Q init_temperature = 0.01( o9 a9 U- I9 c5 K, O B
total_numk = 10004 e P) t( l h5 M3 D
step_size = 0.001" ?9 ?. K" _" V; i$ T5 b4 Q
receivnum = 50/ E* f5 e6 V) D! k* t
x = (Lx - Ux) * Rnd() + Ux '随机产生变量x ~, ?0 O$ ^2 X+ N& t& e
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Dim k As Integer = 0 '温度下降次数控制变量. x( J9 F2 ?) w- e& h
Dim temperature_k As Double = init_temperature '定义第k次温度
, s6 w! [: y7 w* z3 @ Dim best_x As Double n- `+ j. M% H
Dim de As Double = 0.0$ \. h" j9 \* ?* t# |# ^2 K
Dim fcur As Double = 0.03 x. ~! M; `! m. H) H) Y2 j n0 c! C2 K
Dim xi As Double' O- o- ~) R1 Y
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Dim fprevs As Double = obFun(x)* l+ p( Y' }/ v% s! `
Dim xprevs As Double = x4 c$ m4 P0 K" O: K9 r6 i
'SA算法核心
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'xprevs = x '保留前一个变量值
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'以下三个参数用于估算接受概率
, k8 P4 r( |; h B, ]$ P Dim rec_num As Integer = 0 '接受次数计数器
) \5 d, Z4 `' t7 m1 p: V4 d Dim temp_i As Double = 0 '记录下面for循环的循环次数0 B3 |. q# T8 B* o5 o0 d
Dim temp_num = 0 '记录fxi<fx的次数2 N+ n4 i2 `9 a2 u
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For i As Integer = 1 To total_numk
8 q3 [0 `* s2 E& t: m '产生满足要求的下一个数5 z! v0 a7 V+ ~9 [
Do
( m' x1 d/ N- A' `. c6 A7 m xi = x + (2 * Rnd() - 1) * step_size8 Z3 E- H6 n3 g! W, \3 P- g
Loop While (xi > Ux Or xi < Lx). b/ U% ^4 W1 Z
6 x; g7 { T y. v1 F, Y fcur = obFun(xi)
" V- A; L- r7 H de = fcur - fprevs5 `4 k' {3 B5 B+ I O" A$ C
! q M4 x% g" o6 K# v7 R$ A9 M If de < 0 Then '函数值小的直接进入下次迭代
2 h- J$ W9 F9 A5 c7 C$ `4 ^: U best_x = xi
! Q! u; F- q- C# z7 d9 I/ [5 ~ x = xi
1 ?% o& u* O/ ]* l/ A' } rec_num += 1: R5 [ z* s* O% l
temp_num += 1 V5 O. q$ S% T) @6 z4 {( O3 h/ u/ f
fprevs = fcur
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Dim p As Double, r As Double
/ C0 R0 ]& P" i3 Q' B p = Math.Exp(-de / temperature_k)! J- [1 l) W# f$ ]/ Y
r = Rnd()
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6 J; }# {& ` O) g0 r. ]0 D, { If p > r Then
% K) g# ?! m& C% M; h9 ~, I '以概率的形式接受使函数值变大的数
7 P5 ^) r6 {. Z x = xi( w! R: `) B( ^ d
rec_num += 19 o6 _3 j& D5 K1 N* q& q
fprevs = fcur
3 v1 Q; M" |- K$ a- x2 f End If
, F/ g$ h( l5 S: g7 G6 k End If
6 {6 Z2 d2 o" H3 b+ k If rec_num > receivnum Then/ l9 s2 b1 e* y2 C3 \
temp_i = i - 1) ]2 h$ g! h+ p' M+ ^5 } l1 F4 r1 ?
Exit For4 l! \) A% O7 _8 E$ Q' L
End If# ]6 P- q+ A: L0 P% M6 P/ o
Next
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k += 1
+ B) D3 L1 c: _3 m1 h temperature_k = init_temperature / (k + 1) '温度下降原则5 K, Q' J$ D5 v+ ?) f! G
R3 A+ L! V1 H& A5 o% Q If Math.Abs(best_x - 0.25) < 0.00001 Then Exit Do
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' M7 ~. ~. ~0 d8 H2 W8 W- _ Loop While (k < 5000 ): g8 d" Q# }. }6 h- p
xprevs = x7 s& Q! E0 D% _' ^1 @' e3 \
, G* m+ I* ^0 ^$ a4 a9 O6 t |5 d Return best_x8 J: y* W" F R$ z P
End Function( |2 ~% U; e2 \1 z2 U
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End Class e. p+ a& @) M$ u6 O, V
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& f I R+ p- R! l/ m5 U5 t算法测试:
6 w! \" N1 s- q4 M5 a在窗口中添加一个按钮
" Z3 Y7 t" z5 E1 s% L8 mPrivate Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
* E0 Y1 v1 A' I Dim csa As CSA_Cnhup = New CSA_Cnhup. Y+ z, K/ j, `/ v. o
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Dim x1 As Double, x2 As Double
" {1 Z+ }) D% u x1 = 2 'CDbl(InputBox("参数上限", "参数范围", 2) & " ")
0 J. ?0 L. M) n' w" ^ x2 = -2 'CDbl(InputBox("参数下限", "参数范围", -2) & " ")7 C! f( B; p/ v+ o0 P4 f
Dim y As Double
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For i As Integer = 0 To 19. {6 p @# U; i( J
y = csa.CSA(x1, x2)" s$ K, H1 n% `8 l9 C; K$ x! H- O
Debug.Print("(" & y.ToString & "," & csa.obFun(y).ToString & ")")
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# y9 E. @% g. } Debug.Print((New System.Text.StringBuilder).Append("-", 60).ToString). |/ U; m3 @' z2 X! w
End Sub
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