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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; F8 ?1 Q* b. j2 Z6 D% ^. LPublic Class CSA
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1 B* G0 O; |4 m+ F3 T j Public Function obFun(ByVal x As Double) As Double5 W9 B! J( K8 V, ^; Y
Return 2 * Math.Pow(x, 2) - x - 1/ E: H' G, T9 k4 _( X6 ^
End Function
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''' <summary>
6 f D% A7 E6 U" N- _' E, n5 f ''' 传统的模拟退火算法
2 ^: C2 D% Z9 P ''' </summary>; o2 R" R; Z( S( Q0 f
''' <param name="Ux ">参数的取值范围上限</param>. z% L u( @9 C, z" [$ K* [9 M
''' <param name="Lx ">参数的取值范围下限</param>
9 H5 I3 B* X7 O+ ^+ C ''' <returns></returns>1 r" z8 S2 ?$ y" z+ H
''' <remarks></remarks>
9 m! V. @0 D! O/ u; d' j Public Function CSA(ByVal Ux As Double, ByVal Lx As Double) As Double' t: z: u* F1 c. |
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
& C! ] L I. ^5 [4 j1 r* a( K 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' W' v5 C# O" {3 A4 t
- I& D3 [. o& _. }0 I- N$ I '初始化SA参数. k! }8 B8 c0 W8 q2 M5 {
init_temperature = 0.01
( x* g* R) ~. x2 V" x# Q total_numk = 1000* a5 t% V/ W3 D* p4 z
step_size = 0.0016 K% v6 I K' Z. O3 _: O
receivnum = 50% e: s! I3 [* O E. G& i
x = (Lx - Ux) * Rnd() + Ux '随机产生变量x+ A/ [+ K+ ~2 H$ G
8 n1 H: k8 u- n# e Dim k As Integer = 0 '温度下降次数控制变量: _# B& {+ b1 I$ [9 J
Dim temperature_k As Double = init_temperature '定义第k次温度$ N% V$ x5 M# l
Dim best_x As Double* i& X0 g. ^. B
Dim de As Double = 0.0$ p$ ? }; x, `' ^8 ]1 E( @- [% A
Dim fcur As Double = 0.0( h H. F2 ~. A H$ K4 q
Dim xi As Double g7 N7 H* ]/ e- ^* @5 F4 A
) q: G8 {$ }) I0 I8 Y& I2 P Dim fprevs As Double = obFun(x)
8 K9 g# d6 {& [! u x0 V Dim xprevs As Double = x2 p; h2 F% q N7 G4 ~
'SA算法核心+ ^5 w0 F! N" T) S( _
Do
8 V. W- W a9 f3 {8 m 'xprevs = x '保留前一个变量值2 C, m' x' x8 o, H p
% A/ L/ I) h n. E2 d/ R+ U '以下三个参数用于估算接受概率
# `/ N1 [+ h! Z' u6 D0 H: a: Z! ^ Dim rec_num As Integer = 0 '接受次数计数器, p- Z6 d1 o1 n0 [, o+ w4 W1 i* x1 o# \
Dim temp_i As Double = 0 '记录下面for循环的循环次数4 O. q2 v/ j1 q# [. p
Dim temp_num = 0 '记录fxi<fx的次数3 Y8 E2 L @/ O2 |
2 P1 c2 y6 I. A" g3 b For i As Integer = 1 To total_numk" L7 w7 E2 u7 f( O! x) w( n3 c
'产生满足要求的下一个数
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xi = x + (2 * Rnd() - 1) * step_size5 I0 w2 O" D! d( `$ w% l
Loop While (xi > Ux Or xi < Lx)
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6 \+ ~6 V3 E# I7 O D+ c) ? fcur = obFun(xi)* i% ?5 f( r' F$ X4 Z% J& |, w+ ^
de = fcur - fprevs
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If de < 0 Then '函数值小的直接进入下次迭代
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x = xi: C h$ E+ B9 f( b5 N. A$ ?
rec_num += 1' ?/ W8 ~& Q. H# Z% O- [
temp_num += 1
' U# b; Q% Z: L* H fprevs = fcur
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Dim p As Double, r As Double |, ^5 W4 a8 i# a
p = Math.Exp(-de / temperature_k), i& A4 I5 a/ c- K% g
r = Rnd()
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If p > r Then5 W' d( R1 d) l1 _0 k3 m- N5 b
'以概率的形式接受使函数值变大的数4 k0 S# A) p! t! t' L4 |0 B
x = xi
6 g$ t. g' s- ?' a. ~ rec_num += 14 y" ?: \# r1 E
fprevs = fcur2 C8 _4 G+ Y0 C N4 d% b
End If* z, t# j1 U w& o5 d
End If o+ ]% E5 x: P7 }
If rec_num > receivnum Then
- P L, [; }3 t* \ temp_i = i - 1
4 A! ~9 L5 F& z' _7 ~ Exit For
1 Y1 ^' |5 [, ]' W: S End If
( g" ?8 ?8 Y8 b5 N/ `0 U9 Y, U Next: A* d! d+ J( q
. y8 g7 V* J+ |0 M k += 1& @& X4 M# `8 ]; Q# o6 ]4 [# H3 c
temperature_k = init_temperature / (k + 1) '温度下降原则
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5 Z# d( q* k" r If Math.Abs(best_x - 0.25) < 0.00001 Then Exit Do
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Loop While (k < 5000 )
9 o6 T/ o% L# G3 V xprevs = x, Z5 n& [& S- N8 i3 j* ?
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Return best_x
1 j& @ y$ I0 U* M7 R) A { End Function
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End Class
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算法测试:
& P) |6 _) l S7 O. U在窗口中添加一个按钮
* s- C' V9 ^9 e2 T: J5 DPrivate Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click/ [0 m. @( E9 M$ Z) @, N7 w
Dim csa As CSA_Cnhup = New CSA_Cnhup
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, r9 j6 {% \, p' e& m8 x/ I Dim x1 As Double, x2 As Double
; U/ \$ B7 N7 n6 T/ W x1 = 2 'CDbl(InputBox("参数上限", "参数范围", 2) & " ")
! Q# L6 L0 g) D5 A6 v# A2 t x2 = -2 'CDbl(InputBox("参数下限", "参数范围", -2) & " ")6 M1 U& v0 S9 {" U$ L
Dim y As Double j3 V6 X7 k( }$ f5 w# E
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For i As Integer = 0 To 19
" \3 s- I# @1 x( ~. F y = csa.CSA(x1, x2)
4 L( H# L [3 W: D7 W Debug.Print("(" & y.ToString & "," & csa.obFun(y).ToString & ")")
6 Q4 ]* a, {% l; i9 [7 n) p) l Next
" A1 l% W3 f" O8 H- c Debug.Print((New System.Text.StringBuilder).Append("-", 60).ToString). E2 T& l' G3 h8 X5 Y
End Sub ! U+ ]( x4 W1 V
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