【正文】 其被選擇的概率就越高，反之亦然。此優(yōu)化設(shè)計中我們隨機產(chǎn)生一隨機數(shù) temp_a，當(dāng)累計概率大于 temp_a 時，則選擇對應(yīng)的個體，并用 temp_b 來記錄。選擇的輪盤賭函數(shù)程序如下：Function select_lunpandu()RandomizeDim temp_a As DoubleDim temp_b As Integertemp_a = Rnd()For i = 1 To popsizeIf leijigailv(i) temp_a Thentemp_b = iselect_lunpandu = temp_bExit ForEnd IfNext i 交叉操作遺傳算法的交叉是產(chǎn)生新個體的主要操作過程。某兩個個體之間的部分染色體是以某一概率，進行部分基因交換，產(chǎn)生兩個新的染色體。這一過程是模擬生物進化過程中繁殖的雜交現(xiàn)象。對于整數(shù)和實數(shù)編碼的染色體可采用算術(shù)交叉的方法 [6]。它是由兩個個體的線形組合而產(chǎn)生出兩個新個體，若兩個個體 、 之間進行算術(shù)交叉，則交叉運算后所產(chǎn)tAXtB生出的兩個新個體為： （411）??????????ttt BA1B?式中： 為一隨機產(chǎn)生的[0，1]間的隨機數(shù)。?本設(shè)計程序中用 temp_gema 表示 。程序中利用隨機產(chǎn)生的 temp_pc，若temp_pc=jiaochagailv_pc（交叉概率）則兩個個體進行交叉，從而得到新的兩個個體；若不交叉則個體保持不變。在交叉操作的過程中，交叉概率的選擇是要認(rèn)真考慮的。交叉概率的取值范圍按經(jīng)驗得一般是[，]，本例中交叉概率為 。程序如下：Public Sub cross(n1 As Integer, n2 As Integer, i As Integer) RandomizeDim temp_gema As DoubleDim temp_pc As Doubletemp_pc =Rnd()If temp_pc = jiaochagailv_pc Thentemp_gema = Rnd()newpop_m(i)=Int(temp_gema*pop_m(n1)+(1temp_gema)*pop_m(n2))newpop_m(i+1)=Int(temp_gema*pop_m(n2)+(1temp_gema)*pop_m(n1))newpop_z(i)=CInt(temp_gema*pop_z(n1)+(1temp_gema)*pop_z(n2))newpop_z(i+1)=CInt(temp_gema*pop_z(n2)+(1temp_gema)*pop_z(n1))newpop_faidi(i)=temp_gema*pop_faidi(n1)+(1temp_gema)*pop_faidi(n2)newpop_faidi(i+1)=temp_gema*pop_faidi(n2)+(1temp_gema)*pop_faidi(n1)Elsenewpop_m(i)=pop_m(i)newpop_m(i+1)=pop_m(i+1)newpop_z(i)=pop_z(i)newpop_z(i+1)=pop_z(i+1)newpop_faidi(i)=pop_faidi(i)newpop_faidi(i+1)=pop_faidi(i+1)End IfEnd Sub 變異運算變異的目的是為了防止丟失一些有用的遺傳基因，即增強遺傳算法搜索最優(yōu)解的能力，尤其是當(dāng)群體中的個體經(jīng)遺傳算法可能使某些串位失去多樣性，從而可能失去檢驗有用遺傳基因的機會。目前有多種主要的變異算子，我選擇了非均勻變異算子。所謂非均勻變異即對原有的基因值作一隨機擾動，以擾動后的結(jié)果作為變異后的新基因值。對每一個基因都以相同的概率進行變異之后，相當(dāng)于整個解矢量在解空間中作一個輕微的變動。非均勻變異的操作過程不同之處在于重點搜索原個體附近的微小區(qū)域 [6]。由第 2 章得，對于實數(shù)編碼的個體，隨機選擇某位基因，其一般形式為： （412）????x式中： 為一較小的波動量，其選擇比較困難，最優(yōu)值視具體情況而定，甚至在優(yōu)化?過程中可以改變。本論文中有三個設(shè)計變量，即相當(dāng)于三個基因。為了保持選擇交叉后得到的優(yōu)秀個體，每個個體只有一個基因進行變異。函數(shù) Int(Rnd * 3 + 1)只能產(chǎn)生 2 或 3，即隨機產(chǎn)生為 1 時，第一個設(shè)計變量摸數(shù)進行變異，而其它兩個變量保持不變（函數(shù)隨機產(chǎn)生 2 或 3 時類似，即 2 時是齒數(shù)變量進行變異，3 時為設(shè)計變量齒寬系數(shù)進行變異），這樣就保證了每次只有一個基因進行變異。至于基因變異時是“ ”還是“ ”問題，???可通過一隨機數(shù) 0 或 1，當(dāng)為 0 時進行 操作，為 1 時進行 操作。三個設(shè)計變量???的 視具體情況可選取如下：模數(shù)的 = temp2 * temp4（temp2 為一隨機數(shù)，temp4 = ??3） ；齒數(shù)的 = temp3 * temp7（temp3 為一隨機數(shù)，temp7 = 8） ；齒寬系數(shù)的 = temp5 ?* temp8（temp5 為隨機數(shù)，temp8 = ）在進行變異處理后，產(chǎn)生的新染色體即生成了一組新的設(shè)計變量。若產(chǎn)生的新的基因值超過約束條件，則強迫產(chǎn)生的新的基因返回到原先的最大或最小基因，例如若某一基因變異后得到的新基因值大于了約束條件要求的最大值，則強迫新的基因值為原先的最大值。變異運算中的變異概率的選擇也是十分關(guān)鍵的。如果變異概率選擇過大，特別是對規(guī)模較大的算例時，會造成解的振蕩，使收斂速度緩慢。變異概率一般取值范圍為[， ]，本例變異概率取為：bianyigailv_pm=。變異程序如下：Sub mut(i As Integer)RandomizeDim mutionjiyin_num As IntegerDim temp1 As DoubleDim temp2 As DoubleDim temp3 As DoubleDim temp4 As DoubleDim temp5 As DoubleDim temp6 As DoubleDim temp7 As DoubleDim temp8 As Doubletemp4 = 3temp7 = 8temp8 = temp6 = Int(Rnd() + )temp1 = Rnd()If temp1 = bianyigailv_pm Thentemp2 = Rnd()temp3 = Rnd()temp5 = Rnd()mutionjiyin_num = Int(Rnd * 3 + 1)Select Case mutionjiyin_numCase 1If temp6 = 0 Thennewpop_m(i) = Int(newpop_m(i) + temp2 * temp4)If newpop_m(i) 18 Then newpop_m(i) = 18Elsenewpop_m(i) = Int(newpop_m(i) temp2 * temp4)If newpop_m(i) 1 Then newpop_m(i) = 1End IfCase 2If temp6 = 0 Thennewpop_z(i) = CInt(newpop_z(i) + temp3 * temp7)If newpop_z(i) 40 Then newpop_z(i) = 40Elsenewpop_z(i) = CInt(newpop_z(i) temp3 * temp7)If newpop_z(i) 20 Then newpop_z(i) = 20End IfCase 3If temp6 = 0 Thennewpop_faidi(i) = newpop_faidi(i) + temp5 * temp8If newpop_faidi(i) Then newpop_faidi(i) = Elsenewpop_faidi(i) = newpop_faidi(i) temp5 * temp8If newpop_faidi(i) Then newpop_faidi(i) = End IfEnd SelectEnd IfEnd Sub 終止規(guī)則通過監(jiān)測最優(yōu)染色體的變化情況來判斷算法是否終止。實施時，當(dāng)種群中最優(yōu)染色體至少連續(xù) q_numMax 代沒有發(fā)生變化時可認(rèn)為算法收斂，停止計算，輸出最優(yōu)解。 優(yōu)化算例針對本論文的題目，分別采用常規(guī)優(yōu)化設(shè)計方法、遺傳算法優(yōu)化方法進行優(yōu)化設(shè)計，優(yōu)化結(jié)果見表 1。從優(yōu)化結(jié)果中可以看到，采用本文遺傳算法優(yōu)化比采用常規(guī)優(yōu)化方法時體積降低了 %，其優(yōu)化效果十分顯著。表 1 優(yōu)化結(jié)果對比表Table 1 Comparison between optimization results設(shè)計方法 模數(shù) 小齒輪齒數(shù) 齒寬系數(shù) 目標(biāo)函數(shù)/mm 3常規(guī)優(yōu)化設(shè)計方法 3 27 ?遺傳算法優(yōu)化方法 3 28 794 優(yōu)化設(shè)計程序代碼Dim popsize As IntegerDim pop_m(200) As IntegerDim pop_z(200) As IntegerDim pop_faidi(200) As DoubleDim const_m(18) As DoubleDim objf(200) As DoubleDim fitness(200) As DoubleConst pai = Const chishubi_u = Dim max_objf As DoubleDim min_objf As DoubleDim max_fitness_num As IntegerDim max_fitness As DoubleDim a(200) As DoubleDim cycle_num As IntegerDim quanju_min_objf As SingleDim q_num As IntegerDim newpop_z(200) As DoubleDim newpop_faidi(200) As DoubleDim newpop_m(200) As IntegerDim leijigailv(200) As DoubleConst jiaochagailv_pc = Const bianyigailv_pm = 初始解：Private Sub generateori()RandomizeFor i = 1 To popsizepop_m(i) = Int(Rnd() * 18) + 1pop_z(i) = CInt(Rnd() * 20 + 20)pop_faidi(i) = (Rnd() * 600 + 800) / 1000Next iEnd SubPrivate Sub Command2_Click()RandomizeDim q_numMax As Integer q_numMax = 20Dim sel_num1 As Integer Dim sel_num2 As IntegerDim i As Integerconst_m(1) = 2const_m(2) = const_m(3) = const_m(4) = const_m(5) = 3const_m(6) = const_m(7) = 4const_m(8) = const_m(9) = 5const_m(10) = const_m(11) = 6const_m(12) = 7const_m(13) = 8const_m(14) = 9const_m(15) = 10const_m(16) = 12const_m(17) = 14const_m(18) = 16popsize = 200Call generateoriCall pute_fand_fitpop_m(0) = pop_m(max_fitness_num)pop_z(0) = pop_z(max_fitness_num)pop_faidi(0) = pop_faidi(max_fitness_num) = min_objf = Str$(const_m(pop_m(0)))+Str$(pop_z(0))+Str$(pop_faidi(0))q_num = 0cycle_num = 0quanju_min_objf = min_objfstart:Randomizecycle_num = cycle_num + 1q_num = q_num + 1For i = 1 To popsize Step 2sel_num1 = select_lunpandusel_num2 = select_lunpanduCall cross(sel_num1, sel_num2, i)Call mut(i)Call mut(i + 1)Next iFor i = 1 To popsizepop_m(i) = newpop_m(i)pop_z(i) = newpop_z(i)pop_faidi(i) = newpop_faidi(i)Next i產(chǎn)生新一代中的最優(yōu)解：Call pute_fand_fitCls If quanju_min_objf min_