第26卷第11期計(jì)算機(jī)與應(yīng)用化學(xué)Vol. 26, No, 112009年11月28日Computers and Applied ChemistryNovember, 2009連續(xù)過程的多目標(biāo)優(yōu)化岳金彩"2,程華農(nóng)”，楊霞’,鄭世清”,韓方煜^(1.華南理工大學(xué)化工與能源學(xué)院，廣東,廣州, 510640; 2.青島科技大學(xué)計(jì)算機(jī)與化工研究所,山東,青島，266042)摘要:在模塊環(huán)境( Aspen PIlus)下,建立了基于多目標(biāo)遺傳算法NSCA- I求解多目標(biāo)優(yōu)化問題的系統(tǒng)結(jié)構(gòu),并對(duì)含循環(huán)物流的連續(xù)過程廢料最小化問題進(jìn)行求解。在求解過程中遭傳算法需要反復(fù)調(diào)用流程模擬,而流程中循環(huán)物流的迭代收斂使優(yōu)化計(jì)算效率較低。為減少流程迭代次數(shù)本文提出2個(gè)加速策略:一是變收斂精度策略,在優(yōu)化計(jì)算初始階段,使流程在較低精度下收斂,快速淘汰劣點(diǎn),隨著優(yōu)化的進(jìn)行,將流程收斂精度逐步提高,得到高質(zhì)量的非劣解;二是循環(huán)流初值策略,利用已有的計(jì)算值,回歸決策變量與循環(huán)流變量的對(duì)應(yīng)關(guān)系,改善循環(huán)流初值。實(shí)例結(jié)果表明,加速策略減少了一半左右的流程迭代次數(shù),效率提高50% ,本文提出的求解多目標(biāo)問題的方法能方便地得到問題的Pareto最優(yōu)解集，可應(yīng)用于- -般連續(xù)化I過程的多目標(biāo)優(yōu)化。關(guān)鍵詞: NSGA-I;模塊環(huán)境;多目標(biāo)優(yōu)化;連續(xù)過程中圖分類號(hào): TQ028; TQ015.9; 0 6-39文獻(xiàn)標(biāo)識(shí)碼: A文章編號(hào): 1001-4160(2009)11-1433-14371引言的處理方法[5-14] ,但遺傳算法需要反復(fù)大量計(jì)算目標(biāo)函數(shù),過程工業(yè)在改善人類衣食住行的同時(shí),也大最消耗著資特別是當(dāng)流程存在循環(huán)流時(shí),絕大部分機(jī)時(shí)消耗在流程收斂源、能源并產(chǎn)生污染。21世紀(jì)的過程工業(yè)正面臨由可持續(xù)上,效率較低。本文在模塊環(huán)境下( Aspen Plus) 應(yīng)用NSCA-發(fā)展要求,特別是環(huán)境保護(hù)帶來的一系列嚴(yán)重挑戰(zhàn)。過程工l對(duì)連續(xù)流程的多目標(biāo)優(yōu)化進(jìn)行研究,針對(duì)循環(huán)流的收斂提出兩種加速策略,取得了很好的效果。業(yè)的經(jīng)營(yíng)目標(biāo)不再僅僅局限于經(jīng)濟(jì)利益的最大化,而是資源節(jié)約、環(huán)境友好和經(jīng)濟(jì)效益等多個(gè)目標(biāo)的最優(yōu)化。多目標(biāo)2系統(tǒng)結(jié)構(gòu)及加速策略優(yōu)化要同時(shí)優(yōu)化多個(gè)可能相互沖突的目標(biāo)函數(shù),因而有一個(gè)Aspen Plus用戶界面是-一個(gè)ActiveX服務(wù)器應(yīng)用程序,非劣解集,又稱Pareto解集。多目標(biāo)優(yōu)化問題有2種處理策略,一種是先轉(zhuǎn)化為單目利用接口程序能把Aspen Plus所模擬過程的輸人輸出與其標(biāo)問題,再用各種單目標(biāo)優(yōu)化方法求出非劣解集['2 ,這需要它一些應(yīng)用程序如優(yōu)化算法連接起來，實(shí)現(xiàn)軟件集成[15-16]。接口程序一般用Visual Basic( VB)語言設(shè)計(jì),通過VB編程多次構(gòu)造目標(biāo)函數(shù)并求解,比較繁瑣,而且隨著目標(biāo)函數(shù)的環(huán)境可直接操作Aspen Plus提供的對(duì)象,并使用它們的屬增加,計(jì)算量呈指數(shù)增長(zhǎng)。另一種策略是直接求解,最常用性、方法和事件,實(shí)現(xiàn)Aspen Plus的功能。的算法是多目標(biāo)遺傳算法( MOGA) ,已開發(fā)多種算法[)) ,如:本文將NSGA-II與Aspen Plus集成,用于過程的多目標(biāo)NSCA[4] ,NPCA[5] , SPEA(6] , NSCA-I7]等。MOGA計(jì)算量?jī)?yōu)化。Aspen Plus作為模擬器用于計(jì)算NSCA-II 中每一個(gè)較大,但算法簡(jiǎn)單。體所代表的工況。個(gè)體中包含的優(yōu)化變量及Aspen Plus的近十幾年人們對(duì)遺傳算法求解化工過程多目標(biāo)問題進(jìn)計(jì)算結(jié)果和信息(包括是否收斂,迭代次數(shù),收斂精度等)都行了一些研究。Gupal8-1] 等人應(yīng)用NSGA先后對(duì)T.業(yè)反應(yīng)通過接口進(jìn)行傳遞。系統(tǒng)結(jié)構(gòu)如圖1所示。器分離器和過程流程等進(jìn)行了設(shè)計(jì)優(yōu)化和操作優(yōu)化研究,遺傳算法計(jì)算個(gè)體的適應(yīng)值時(shí),需要反復(fù)調(diào)用Aspen與常規(guī)優(yōu)化方法的對(duì)照研究表明利用NSGA求解多目標(biāo)優(yōu)Plus。提高Aspen Plus的計(jì)算效率非常重要。對(duì)于有循環(huán)流化問題具有- -定優(yōu)勢(shì)。Amyl2] 等人應(yīng)用NSGA對(duì)苯乙烯反的連續(xù)過程,本文提出2種策略以減少流程迭代次數(shù)。應(yīng)器進(jìn)行了3個(gè)目標(biāo)的優(yōu)化。以上研究的問題模型比較簡(jiǎn)計(jì)算開始時(shí)遺傳算法的個(gè)體是隨機(jī)產(chǎn)生的,經(jīng)過各代優(yōu)單,過程模型多是基于方程的。對(duì)復(fù)雜大系統(tǒng)的研究還很不化,逐步向Pareto前沿道近。在計(jì)算初期,非劣解的數(shù)不充分,難以指導(dǎo)實(shí)際化工過程的優(yōu)化和設(shè)計(jì)。若使用嚴(yán)格熱多,各個(gè)體離Pareto前沿還較遠(yuǎn),流程迭代沒有必要以高精力學(xué)、動(dòng)力學(xué)模型又會(huì)導(dǎo)致問題過于復(fù)雜，難以收斂。將過度收中國(guó)煤化工t模擬計(jì)算量,可迅速程看作黑箱,使用成熟的模擬器簡(jiǎn)化優(yōu)化模型,是很有前景淘汰i Pareto前沿,提高流TYHCNMHG收稿日期:009-0608;修回日期: 200906-08作者簡(jiǎn)介:岳金彩(1969- -) ,男,博士,副研究員,E-mail:yjc@ qust. edu. cn.1434什算機(jī)與雇用化學(xué)2009 ,26(11)flowshescodification andw=物流S4中內(nèi)酮+物流SI0中丙酮。constructionparametersser目標(biāo)函數(shù)表達(dá)如下:optimalvariablesmax p= 34.524F14.40-4.5x10-u. -0.1x(ua55 000+ug)simulationmin 0=uw +4no(1)inputASPENinterfaceMOGA約束方程:plusdata processingfitness丙酮回收率η =99% ;分流器B2分流分率s=0.95。output優(yōu)化變量:S1流率u, kmol/h,10≤u.≤100;精餾塔B6Fi 1 The architecture of the eyatem.回流比R, 1≤R≤10。81 系統(tǒng)結(jié)構(gòu)其中:p為利潤(rùn), $/h; w為廢料量,kg/h; F為回收內(nèi)酮程收斂精度,保證得到的非劣解為叮行解。這種變化循環(huán)流量,kg/h; Q為精餾塔熱負(fù)荷, kcal/h; ug,4s 分別為物流收斂精度的策略類似于過程優(yōu)化中的不可行路徑法。S2. ,S6中水的流率,kmol/h;us, ,4so0 分別為物流S4 ,S10中丙模擬計(jì)算時(shí)循環(huán)流的初值-般由Aspen Plus自動(dòng)給出,酮的流率,kg/h。也可人工給出。利用遺傳算法所計(jì)算的大量個(gè)體,回歸出循此問題為帶循環(huán)流的連續(xù)過程廢料最少問題,優(yōu)化變量環(huán)流中各組分流率與自變最的關(guān)系表達(dá)式,據(jù)此給出比較準(zhǔn)都是連續(xù)變量。采用本文提出的集成策略進(jìn)行優(yōu)化,并對(duì)加確的循環(huán)流初值,可有效減少流程迭代次數(shù)。速策略的應(yīng)用與否進(jìn)行比較。對(duì)于不同策略NSGA-都統(tǒng)3計(jì)算實(shí)例一采用實(shí)型編碼,種群規(guī)模40,遺傳代數(shù)50,交叉概率0.8,變異概率0.01,以便于結(jié)果比較。3.1丙酮回收流 程及優(yōu)化模型3.2計(jì)算結(jié)果及討論丙酮和空氣的混合物(物流S3)進(jìn)入吸收塔B4,用水吸本文根據(jù)遺傳算法代數(shù),給出不同的循環(huán)流收斂判據(jù),1收其中的丙酮。吸收塔底出來的物流s5加熱后,到蒸餾塔到10代收斂判據(jù)為0.1,11到20代為0.01,21到30代為B6中回收丙酮，回收率要求為99%。蒸餾塔底出來的物流0.001,31到50代為0.0001。S8冷卻后一部分作為廢料排出,一部分循環(huán)到吸收塔作溶遺傳算法計(jì)算過程中產(chǎn)生大最數(shù)據(jù),可以用來改善流程劑用"”。流程圖如圖2所示。模擬計(jì)算效率。根據(jù)初始種群計(jì)算結(jié)果,將循環(huán)流的組分流率與優(yōu)化變量的關(guān)系進(jìn)行回歸?；貧w計(jì)算式如下:F = 0.035339 + 0.028 4092u。+ 0.095273R -_S0. 000 105 44 -0. 004 941R2(2)B6Fa=100F.rectificationSFr=0.152713 +0.0125464u。-0.000079 63u2 +column0. 013 089R -0.000 439R*(3)N B2 spliers6s3,對(duì)不同策略的非劣解及流程計(jì)算次數(shù)進(jìn)行比較,結(jié)果見B5 hearter表1。表1第1列數(shù)據(jù)為循環(huán)流收斂判據(jù)固定為0.0001、循39Ss環(huán)流初值缺省給出、遺傳代數(shù)為50時(shí)的非劣解,總流程計(jì)算BI cooler次數(shù)為17 893。第2列數(shù)據(jù)為采用了變收斂判據(jù)策略的非劣O←解，總流程計(jì)算次數(shù)為7399次,下降了近60%。2列數(shù)據(jù)進(jìn)Fig2 The flow chart of acelone recovery.行比較,第I列有3個(gè)劣解,第2列6個(gè)劣解(粗體標(biāo)出),數(shù)圖2丙酮回收流程圖據(jù)質(zhì)量有所下降。這可以通過增加代數(shù),犧牲部分計(jì)算效率B1.冷卻器; B2.分流器; B3.混合器;得到改善。表中第3列數(shù)據(jù)為采用變收斂判據(jù)策略、遺傳代B4.吸收塔; Bs.加熱器; B6.蒸餾塔數(shù)為60時(shí)的非劣解,總流程計(jì)算次數(shù)為9841 .2列數(shù)據(jù)進(jìn)行流程優(yōu)化目標(biāo)有2個(gè):一個(gè)是利潤(rùn)最大,另一個(gè)是排出比較,第1列有3個(gè)劣解,第3列只有1個(gè)劣解(下劃線標(biāo)的丙酮廢料:量最少。出) ,數(shù)據(jù)質(zhì)量提高的代價(jià)是效率下降。若利用回歸式計(jì)算流程利潤(rùn):循環(huán)流中國(guó)煤化工1下降至8992?？梢詐=丙酮價(jià)格x丙酮回收量-操作費(fèi)用-水價(jià)格x原料看出變lYHCNMH(G值策略效果要好。水量-設(shè)備投資。圖3為切始解分布情況，圖4~圖口分別為表1中3種丙酮廢料:情況下的非劣解分布。209 ,26(11)岳金彩，等:連續(xù)過程的多目標(biāo)優(yōu)化1435表1非劣解集 .Table 1 Noninferior solution set.第50代解集第60代解集(收斂精度固定為0. 000 1)(變收斂精度(變收斂精度)號(hào)solution set of 50th ( convergencesolution set of 50thsolution set of 60thNo.tolerance is fixed on 0.000 1)(convergence tolerance is changed)利潤(rùn)廢料waste, kg/hproft, $/hprofit, $/h10.710 12664.206 52. 348 433173. 258 72. 14333173. 31822168 318173.1580.711 28964.13940.711 05364.546 .0. 800 505.91. 262 42.136 457173.232 10.886 34112. 17531.231 047154. 549 30.924 154120. 638 60.848 894105. 842 70. 825 47499.12830.859 76108. 459 10.927 033118. 692 81. 820 489171. 164 60. 748 8778.41520.972 468124. 293 91.615 623167. 877 51.031 795133. 182 31. 370 067160. 708 90.866 475109. 866 70. 998 654129.648 60.820 70899. 17110.751 71579.1111. 169 985149. 779 71. 431 539102.031 856172.728 21.111 802144. 288.1.655 686168. 879111.06 267139. 6950.729 51970. 494 12. 000 482172. 572 7120.722 47867. 8671.935 47172.139 91. 209 234152.8631130.899 722113. 946 71.754 118170. 272 51.583 376166. 44851.45812.163. 257 71.720 35168. 475 10.813 10197. 36041:1.305 299158. 1391. 4429163. 1871.258 422155. 888 4160.767 5683. 64232. 052 05172. 782 I0.793 92790. 498 9170.777 46487.344 31.062 333139. 1792.0. 7238 7368.681 1181. 915 655172.02782.017 763172. 610 61. 744 02169.782 1191.106 76142. 92481. 107 127143.737 91.631 596167. 988 1201.376 199161. 141 41. 302 563158. 0641. 327 8291S8. 931 7210.833 394102. 12441.056 145138.667 90.731 07171. 260 3221.041 199136. 89721.831 278170.705 81. 466 772164. 169 81.033 733133. 861 40.773 59485. 85720. 983 972129. 807 621.551 128166. 477 20.833 597102. 0621. 539 978166. 21082. 123 87172. 965 70. 838 986 .103. 495 31. 500 308165. 1548261.530 625 ;165. 982 80.827 712%6. 689 91.083 02140.938 2270. 735 49873. 3861. 632 154168. 058 21. 116 784143. 113 1281.150 899148. 268 70.717 27266. 289 91. 050 297137. 455 6291.974 735172. 441 61.518814165.40992. 088 51172. 749 2，301.767 635170.411 80.764 38681. 5651.920 21172. 056 8310.736 83674. 234 50.858 492107. 479 11. 037 048134. 825 131. 682 678169. 141 11.641 904168. 446 91.302 79157. 999331.199 961152. 2030. 789 37189.942 61. 961 398172. 375340. 933 304119. 748 91. 877 063172.100 80. 776 41186. 6408350.906 752117. 589 30.978 655126. 421 10.942 891 .121. 287 4.361. 747 702169.515 21. 258 172155.845 51. 009 562132.951 4.321. 475 867164. 53281. 332 701159. 268 20.744 5575. 726 3381. 000 376130. 207 91. 567 201中國(guó)煤化工79.9773390.975 831127.033 91.387 108HHCNMHG148. 794 9401. 183 493149.831 60. 806 851. 150”146. 8581436計(jì)算機(jī)與應(yīng)用化學(xué)2009 ,26(11)80 r160 F60 -40 t40 F20 -遇10080 -00s0 F0t20 Fo40.5.525waste 1 (kgh")waste/ (kgh")Fig3 Disrbution of preliminary solution.Fig 4 Distribution of the 50th generation solution圖3初始解集分布(convergence tolerance is fixed).圖4第50代解集分布( 固定收斂精度)中鐘16(120H.色120100 H80 Fs0 t1.52.s0.52.5waste 1(kghrI)waste/(kgh')Fig5 Distribution of the 50th generation solutionFig 6 Distribution of the 60th generation Bolution.(convergence tolerance is changed).(convergence tolerance is changed)圖5第50 代解集分布(變收斂精度)圖6第60 代解集分布(變收斂精度)4結(jié)論gres on Computational Ielligence. Piscalaway NJ: IEEE Pres,1994, 1:82 -87.將多目標(biāo)遺傳算法NSGA-I與Aspen Plus集成起來建6 Zitzler E, Thiele L An evolutionary algorithm for mulibiective p立了一個(gè)用于化工過程多目標(biāo)優(yōu)化的求解平臺(tái)。由于過程timization:The strength pareto approach. Computer Engineering and模型為嚴(yán)格模型,所得結(jié)果能夠反映過程的本質(zhì),對(duì)實(shí)際生Communication Networks Lab (TK). Zurich: Swiss Federal Inati-產(chǎn)及過程設(shè)計(jì)具有指導(dǎo)意義。在求解過程中流程模擬占用tute of Technology (ETH) Zurich, 1998.7 Deb K, AgrawalS, Pratap A, et al. A fast elitist non-doninated了大部分機(jī)時(shí),提高流程模擬效率成為關(guān)鍵。針對(duì)具有循環(huán)sorting genetic algritim for multi. objective optimization: NSCA-I.流的連續(xù)過程,本文提出了2個(gè)加速循環(huán)流收斂策略,結(jié)果Parallel Problem Solving from Nature, Berlin, 2000:849 -858.表明總流程模擬次數(shù)大大減少,效果顯著。本文設(shè)計(jì)的接口8 Mitma K, Deb K and Gupta s K. Mutiobijictive dynanic optimzr.程序經(jīng)改造后叮應(yīng)用于其他連續(xù)過程的多目標(biāo)優(yōu)化。tion of an industrial mylon 6 semi-batch reactor using genetic algo-References:nithm. 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Multiojective Optimization and Nonlocal Sensitiv-設(shè)計(jì)[J].計(jì)算機(jī)與應(yīng)用化學(xué), 2005, 22(11) :980 -984.iy in Proces Soure Reduction Problems ;otinuous Optimization16孔祥兵， 岳金彩,譚心舜,焦巍. Aspen Plus服務(wù)器在軟件集成Problems. I&EC Special Sympoium on Emereing Technologies in中的應(yīng)用[J].計(jì)算機(jī)與應(yīng)用化學(xué), 2007, 24(2) :255 -258.Hazardous Waste Management, Alanta, GA, ept 21 -22, 1992.Multiobjective optimization of continuous processYue Jincail.2 , Cheng Huanong' , Yang Xia', Zheng Shiqing2 and Han Fangyu'(1. College of Chemical Engineering and Energy, South China University of Technology, Guangzhou, 510640, Guang-dong, China; 2. Research Center for Computer and Chemical Engineering, Qingdao University of Science and Technolo-gy, Qingdao, 266042, Shandong, China)Abstract: A framework baed on NSGA- I in modular environment (Aspen Plus) is posed and a waste minimizaion problem of acontinuous process which contains reyele is solved on this platform. MOGA needs to spend lots of computer time to simulate flowheet,especially when the flowsheet contains recycle. For reducing iteration number of simulation, we propose two strategies: one is changingtolerance strategy, that at initial stage of optimization the convergence tolerance of recycle is lower in order to get rid of inferior solutionquickly, then the tolerance is higher gadually in order to get better non-nfeior solution set, the other strategy is improved initial reey-cle stratey, that the initial value of reeycle is calculated by a crrelation which is acquiredfrom the initial flowsheet simulation. Resulsshowed that the number of iteration is reduced about a half. The method in this paper can ttain the Pareto front of the problem and theframework can be easily used to optimize other continuous processes.Key words: NSGA- I , modular enironment, muliobjective, continuous process( Received :2009-06 08 ; Revised :2009-08-01)中國(guó)煤化工MYHCNMHG