二進(jìn)制PSO有關(guān)理論參考

1、二進(jìn)制PSO有關(guān)理論參考:U 13.4遺傳莫法流程圖隨機(jī)算子種群1 a種群213.2.2遺傳算法的關(guān)鍵實(shí)現(xiàn)技術(shù)遺傳算法的基本實(shí)現(xiàn)技術(shù)主要有編碼方法、適應(yīng)度函數(shù)、選擇算于、交叉算 子和變異算于五個(gè)方面：編碼g將可行解從其解空間轉(zhuǎn)換到遺傳算法所能處理的搜索空間的 轉(zhuǎn)換操作或方法稱為綠碼。概括而言，編碼方法可以分為以下三類(lèi):瓦- 進(jìn)制繾碼，h實(shí)數(shù)編碼,c.符號(hào)綠碼口適應(yīng)度函數(shù):度量個(gè)純適應(yīng)度的函數(shù)稱為適應(yīng)度函數(shù)(Fitness Function )t 遺傳算法使用適應(yīng)度這個(gè)概念來(lái)度量群體中各個(gè)個(gè)體在優(yōu)化計(jì)算中有 可能達(dá)到或接近于或有助于找到最優(yōu)解的優(yōu)良程度，適應(yīng)度較高的個(gè)體 遺傳到下一代的概率就較大

2、；而適應(yīng)度較低的個(gè)體遺傳到下一代的概率 就相對(duì)小一些，遺傳算法的一個(gè)特點(diǎn)是它僅使用所求問(wèn)題的目標(biāo)函數(shù)值 就可得到下一步的有關(guān)搜索信息，而對(duì)耳標(biāo)函數(shù)值的使用是通過(guò)評(píng)價(jià)個(gè) 體的適應(yīng)度來(lái)體現(xiàn)的選擇算子：遺傳算法根據(jù)個(gè)體的適應(yīng)度，使用選擇算于(或稱復(fù)制算于 (Reproduction Operator)來(lái)對(duì)群體中的個(gè)體進(jìn)行優(yōu)勝劣汰操作，即確 定如何從父代群體中按某種方法選取哪些個(gè)體遺傳到下一代群體中的 一種遺傳運(yùn)算對(duì)于各種不同的問(wèn)題，人們提出了各種各樣的迷擇算子* 其中最常用的選擇算子是:土比例選擇法，b.最優(yōu)保存策略，。.排序選擇 法.交叉算子：交叉運(yùn)算是指對(duì)兩個(gè)相互配對(duì)的染色體按某種方式相互交換

3、其部分基因，M而形成兩個(gè)新的個(gè)體。在交叉運(yùn)算之前，常用流機(jī)配對(duì) 策略先對(duì)群體中的個(gè)體進(jìn)行配對(duì)。交叉算子的設(shè)計(jì)要求不能太多地破壞 優(yōu)臭個(gè)體的模式，且能有效地產(chǎn)生出一些較好的新個(gè)體模式.最常用的 交叉算子有&多點(diǎn)、交叉，h均勻交叉,七.算交交叉n變異算子：變異運(yùn)算是指將個(gè)體編碼串中的某些基因座上的基因值，以 一較小概率用其他等位基因來(lái)替換，從而形成一個(gè)新的個(gè)體，使用變異 算子可以改善遺傳算法的局部搜索能力，維持群體的多樣性，防止出現(xiàn) 早熟現(xiàn)象莒用的變異算子有：基本位變異，b.均勻變異，c.非均勻變 異，d.自適應(yīng)變異。1323遺佐算法求解函數(shù)優(yōu)化問(wèn)題MATLAB R2OIOa中提供了遺傳算法工具箱

4、*下而對(duì)該工具箱進(jìn)行詳細(xì)介紹匚在Global Optimization Toolbox ZL具箱下的遺傳算法工具箱提供了 4個(gè)函數(shù)于 它們分別是goptimset函數(shù)、gaoptimget函數(shù)、學(xué)函數(shù)gmultiobj函數(shù)匚卜-面 對(duì)上述4個(gè)函數(shù)的功能及調(diào)用格式進(jìn)行詳細(xì)介紹蚌IUseParall el以弁行的方式計(jì)算種群淘w叫& ever5適應(yīng)度Real number space & Discrete spaceKennedy,1997在連續(xù)空間，粒子群算法 TOC o 1-5 h z V(t +1) = V(t) + c - rP- X(t) + c - r- G- X(t)(1)i, ji

5、, j11, ji, ji, j22, jji, jX . (t +1) = X . (t) + V . (t +1)(2)其中，i = 1,2,N; j = 1,2,D; D為維數(shù)，N為種群規(guī)模，匕、c2為學(xué)習(xí)因子，建議取 值2.0； r為(0，1)之間的均勻分布的隨機(jī)數(shù)。然而，實(shí)際工程優(yōu)化問(wèn)題中，常遇到離散數(shù)空間。2011 Binary Particle Swarm Optimization with Crossover Operation for Discrete Optimization.優(yōu)化精度：優(yōu)化所得最優(yōu)解和理論最優(yōu)解的相對(duì)誤差。成功率：連續(xù)運(yùn)行runtime次，其中優(yōu)化精度在容

6、許的閾值范圍內(nèi)的次數(shù)與運(yùn)行總次數(shù)的比 值，用百分?jǐn)?shù)表示。該參數(shù)一定程度上反映了當(dāng)前所用的優(yōu)化算法的計(jì)算精度和魯棒性。當(dāng) 然該參數(shù)也可作為參數(shù)選取的依據(jù)，即通過(guò)參數(shù)敏感性分析，參數(shù)分別選取不同的值，優(yōu)先 選取優(yōu)化成功率高的那次優(yōu)化所取的參數(shù)值。To tackle this problem, Kennedy and Eberhart proposed KBPSO algorithm, where the particles take the values of binary vectors of length n and the velocity defined the probability o

7、f bit 易 to take the value 1. KBPSO reserved the updating formula of the velocity (see (1) while velocity was constrained to the interval 0.0, 1.0 by a limiting transformation function, that is, the particle changes its bit value by (3N) in KBPSOS(v0 = l/(1-)ifrand()WS(%)0 etherise where the value of

8、 rand() drawn from U(0,l) and the function S(v) is a sigmoid limiting transformation.As the optimization ability of KBPSO is not ideal, Qi developed a modified discrete binary PSO algorithm (MBPSO). In MBPSO, the updating formulas are defined by th巳 following equations 13(5)(6)If (0Vjj (i) then (new

9、)=孔(old),f (ot捋j J_ (1-a) then 孔(new) = p(J ,ff(L(l+(gj I) then 氣(*)=疏，where a named static probability is a random value in the range of (0,1). The initial value of a is 0.5.& The Probability Binary Particle Swarm Optimization AlgorithmAs KBPSO and MBPSO are very easy to trap in the local optimum a

10、nd KBPSO updating formulas is complexity, we propose a novel algorithm named probability binary particle swarm optimization algorithm (PBPSO) to tackle these problems in this paper. Here (1) and (2) are all reserved for iterative evolution in PBPSO, and then we adopt a novel formula to determine a b

11、inary bit pxy which can be denoted as follows:Lg)二國(guó)-RQ (* -尺頃)，(8)嚴(yán) 5),where Z(x) is a linear function, its output value belongs to (0,1); rand。is a stochastic number selected from a uniform distribution in 0,0, 1,0; and /?iyiax, 7fmin is a predefined range for gaining the probability value with L版)

12、 function.SteelTable=1,2,3,.,n；A=A1,A2,A3,.,An；Elon S. Correa Alex A. Freitas Colin G . Johnson. ().A New Discrete Particle Swarm Algorithm Applied to Attribute Selection in a Bioinformatics Data Set, 35-42.function f itness= evaluat e (positiorij 虬 J var5 K_maXj f itnessj Num_func) for i= 1:N %對(duì)每個(gè)粒

13、子計(jì)算其話應(yīng)值，1旦是fitness (ij :) ?列號(hào)k表示當(dāng)前迭代次數(shù)端號(hào);for j=1:vartemp=position(ij (j-1) *L+1: j#L):Z (j)=decode (tempj Lj s_max) : 3S#ol end% now X is m real-number space.swit ch Num fxmc為L(zhǎng)；%第二個(gè)粒子的第位串，每個(gè)位串長(zhǎng)度均：AGROW另相當(dāng)于多維實(shí)數(shù)空間中的Nj都可以、用一個(gè)長(zhǎng)度.為L(zhǎng)的位串表示，是嗎？case 1result 二 sum (Z.2);case 2result = swn(abs (X) + prod(abs (

14、X) case 3result 二 0 :for ii=1:varresult 二 result + sum(X(1:ii). 2;endcase 4result 二 max (abs(X);case 5result = 0:for ii=1:var-1result = result + 100* (X (ii+l)-X (ii)2)2+(X(ii)-l)2); endendfitness (ij k.)二 result :end1- returnfunction Z=decode rtempj Lj K_max) z=0;for i=l:LK=K+t emp f i)*2ri-l);endz

15、=k/(2T-1):X= (2*x_max)/ (1-0)* z-0)-K_maxreturn3. THE STANDARD BIARY PSO ALGORITHMIhe standard binaiy version cf the PSO algorithm 9 works as fbllcws. iJutenTial so hit io ns (particles) to the target pmblFin are encoded as fixed length binan;, strings; i .e. 熟i) = (w%i)點(diǎn)網(wǎng)珅:，工(饑where 欠危 E 也 1, i = 1

16、.如.、A; and j = 1. 2.，幾 Given a list cf attributes A = (A2.A2. An). the first element of X(i). from the left tc the right hand side, ccrrcspmds to the first aitribute . the second to the second attribute . and sc fbrth. A value cf 0 on rhe site associated to aii attribute signifies that the respectiv

17、e attribute is net ielected A value cf 1 means that it is selected. For exampls given the list cf attributes A = A. Al A3. Ai. As) and Ar = 4. a swarm could look like this:vt/1 oO.L5 J1 oL S*J _T o 1/X /f-XI/12 3 4 vrf fv MX Mix1 1 rJ 1 o-sT 1 1T 1 /f-In this example., particle X (T： = (D, J. J, 0.

18、1 ： represents a candidate solution where attributes A2： A3 euicI Az are the only attributes aelected3 J The initial population for the standard binary PSO algorithmFor the initial population. A binaiy strings of length n ar丑 randomly generated. Each pailiclp X i is mdependently Igenerated as follow

19、s. For every position rr；：.d；, of X4) a uniform Iandcm number p is drawn on the inteival 0 1 ：. If 戶 町 = L otherwise 工厘心 =0.3*2 Lpdatinj; the recordsAt the beginning, the previous best position of X (ij. denoted by B(!). is emptj Therefore, once the initia particle Xi) is generated, B(i) is set to 8

20、( = X(4). After that,!i .I .U_eveiy time that X (Q is updated. B2) is also updated if is better than f I： 8 ( ；, Qtheiise. H (2) remains as it is. A similar process is used to update the global best posi- _l_l3ticn C. At the beginning. C is also empty. Therefore., once ji ji all the 8(時(shí) hmve been de

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