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 CSA6 A6 m7 f" l: _$ L9 m- Z
2 N3 _5 g% a% l* V2 a Public Function obFun(ByVal x As Double) As Double' X. W: u* J9 P# H* L
Return 2 * Math.Pow(x, 2) - x - 1! R7 p1 N0 @9 b0 Z
End Function
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! ^, U2 S$ F+ ]. K ''' <summary>. e0 z' L. F: \ M: z5 y# O- P/ K
''' 传统的模拟退火算法
) |7 f- h5 d. O Z6 z3 w% u5 Y& ^ ''' </summary>
; X" N! S6 l1 a1 W ''' <param name="Ux ">参数的取值范围上限</param>, L0 r. f) z" u1 O- E7 A
''' <param name="Lx ">参数的取值范围下限</param>5 j3 L2 c' z6 G6 s/ y4 K M; L7 e6 M
''' <returns></returns>
! k+ Y! u$ \2 t+ F; ~" ]( x. V ''' <remarks></remarks>, w- @# r2 m) x. u
Public Function CSA(ByVal Ux As Double, ByVal Lx As Double) As Double
3 Z8 ]- Z7 |6 W; A 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& c, M7 k9 B. R- ~" t
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, [% s5 s5 E5 I7 }4 M& ~) a
- b6 J5 {9 W- Z+ H; m3 M '初始化SA参数4 _" S0 w! j, x( K7 K
init_temperature = 0.01$ }8 e+ \1 B- e' ]: q. H" c1 k% e
total_numk = 1000
& |8 G' m3 c+ C1 h7 ?0 X' O, {$ [' D step_size = 0.001, C6 {& T1 E+ f' N& F
receivnum = 50
V) b) `3 w' ?" {2 S' T# A x = (Lx - Ux) * Rnd() + Ux '随机产生变量x
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Dim k As Integer = 0 '温度下降次数控制变量
: a, K( H; O% }9 k2 k+ U3 N Dim temperature_k As Double = init_temperature '定义第k次温度
% l9 f; O5 g6 U5 G; W- A& \ Dim best_x As Double
8 B* i; x8 e$ A3 \8 l Dim de As Double = 0.0
% c# s- T c0 C& `/ s Dim fcur As Double = 0.08 F1 F& E; o% J/ n; j
Dim xi As Double
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Dim fprevs As Double = obFun(x)
$ e' u; r& A* F+ L; e( M Dim xprevs As Double = x6 k% x8 m5 Y, @
'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0 t0 ]& a: M& q8 X: s" t* H4 I
Dim rec_num As Integer = 0 '接受次数计数器/ G$ o5 k& b. z5 a$ b9 S5 y9 j
Dim temp_i As Double = 0 '记录下面for循环的循环次数
2 Q# v9 e6 L4 d$ I Dim temp_num = 0 '记录fxi<fx的次数
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f1 D# n7 m5 p# f For i As Integer = 1 To total_numk. Y3 j. M' z/ j m Y0 h1 q
'产生满足要求的下一个数! ?: i& y% J9 r. @9 E7 b. ]
Do# g5 N5 h3 g5 b0 Q
xi = x + (2 * Rnd() - 1) * step_size
$ O& \& C2 R1 o Loop While (xi > Ux Or xi < Lx)0 X, t4 e7 z- _# D1 D
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fcur = obFun(xi)9 {" u7 V$ z6 ]6 n6 t1 W! O
de = fcur - fprevs
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If de < 0 Then '函数值小的直接进入下次迭代: }+ r4 ` H* _2 F8 z/ j) u9 S
best_x = xi
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rec_num += 1- L1 S0 Y$ S4 o& m
temp_num += 1
0 P' {# `4 y$ H6 a& { g fprevs = fcur7 G- c( X: J$ B( q4 B I1 C8 V% d
Else
4 N& h- T! W; a6 j+ `/ |% d7 b Dim p As Double, r As Double
/ y) z! \8 f4 e- V( { p = Math.Exp(-de / temperature_k)% x% W6 o/ R, ], G5 t7 z
r = Rnd()2 T) g: Y) E! _5 h }( F. S/ I" r
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If p > r Then9 _. B0 W% y W/ }$ G! V
'以概率的形式接受使函数值变大的数
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" d Z% k3 P" k3 o( ] rec_num += 1% H, l3 Y* N' S2 d% P. M
fprevs = fcur4 J$ V) U6 p4 T: y5 ]# y3 |
End If
0 V- \- a& R# A/ }; {0 }# [+ |" ?8 n End If
# U, z3 _8 V2 w* h If rec_num > receivnum Then: }) | r! B' g% n& d; @
temp_i = i - 1
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End If. \# q( L& H) \( ^) ~
Next
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# ` `% k7 X6 s1 L5 [0 @ k += 1
7 h. _/ W, j$ ^6 M temperature_k = init_temperature / (k + 1) '温度下降原则+ ] x! X( T0 g7 z8 G
; n7 l/ }9 e7 ?* d If Math.Abs(best_x - 0.25) < 0.00001 Then Exit Do% `8 S/ M- B0 w7 x$ U7 k8 @
/ y9 T7 o) x- ^' ?. W" K Loop While (k < 5000 )7 @" L4 c5 N8 N# R% C) g/ b6 W
xprevs = x
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3 b$ \/ z4 J+ w& m- A Return best_x
6 V8 H& w; T' W# `- k End Function# B, Y! }$ C' W h% V
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End Class & t, Y* s/ o i
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算法测试: 8 x( u" e8 j. X& Q
在窗口中添加一个按钮
* H3 W w* |+ NPrivate Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
4 B( j! X* x& \" E; \8 j) y: j L Dim csa As CSA_Cnhup = New CSA_Cnhup! H4 m9 n/ i8 G2 d/ F, k
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Dim x1 As Double, x2 As Double
: p# q4 T6 g9 Y* I0 N x1 = 2 'CDbl(InputBox("参数上限", "参数范围", 2) & " ")4 [! T9 C3 b- g7 S2 e, o
x2 = -2 'CDbl(InputBox("参数下限", "参数范围", -2) & " ")8 w, [0 S" ?+ q7 y
Dim y As Double
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For i As Integer = 0 To 192 j) {9 l1 y Z! S* p9 v8 U* f
y = csa.CSA(x1, x2)
* c. m2 m4 J6 V6 Z Debug.Print("(" & y.ToString & "," & csa.obFun(y).ToString & ")")
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Debug.Print((New System.Text.StringBuilder).Append("-", 60).ToString)
/ g5 f: }6 | `8 g- f( OEnd Sub
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