連續過(guò)程的多目標優(yōu)化

第26卷第11期計算機與應用化學(xué)Vol. 26, No, 112009年11月28日Computers and Applied ChemistryNovember, 2009連續過(guò)程的多目標優(yōu)化岳金彩"2,程華農”，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)計算機與化工研究所,山東,青島，266042)摘要:在模塊環(huán)境( Aspen PIlus)下,建立了基于多目標遺傳算法NSCA- I求解多目標優(yōu)化問(wèn)題的系統結構,并對含循環(huán)物流的連續過(guò)程廢料最小化問(wèn)題進(jìn)行求解。在求解過(guò)程中遭傳算法需要反復調用流程模擬,而流程中循環(huán)物流的迭代收斂使優(yōu)化計算效率較低。為減少流程迭代次數本文提出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(zhù)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,利用已有的計算值,回歸決策變量與循環(huán)流變量的對應關(guān)系,改善循環(huán)流初值。實(shí)例結果表明,加速策略減少了一半左右的流程迭代次數,效率提高50% ,本文提出的求解多目標問(wèn)題的方法能方便地得到問(wèn)題的Pareto最優(yōu)解集，可應用于- -般連續化I過(guò)程的多目標優(yōu)化。關(guān)鍵詞: NSGA-I;模塊環(huán)境;多目標優(yōu)化;連續過(guò)程中圖分類(lèi)號: TQ028; TQ015.9; 0 6-39文獻標識碼: A文章編號: 1001-4160(2009)11-1433-14371引言的處理方法[5-14] ,但遺傳算法需要反復大量計算目標函數,過(guò)程工業(yè)在改善人類(lèi)衣食住行的同時(shí),也大最消耗著(zhù)資特別是當流程存在循環(huán)流時(shí),絕大部分機時(shí)消耗在流程收斂源、能源并產(chǎn)生污染。21世紀的過(guò)程工業(yè)正面臨由可持續上,效率較低。本文在模塊環(huán)境下( Aspen Plus) 應用NSCA-發(fā)展要求,特別是環(huán)境保護帶來(lái)的一系列嚴重挑戰。過(guò)程工l對連續流程的多目標優(yōu)化進(jìn)行研究,針對循環(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)目標不再僅僅局限于經(jīng)濟利益的最大化,而是資源節約、環(huán)境友好和經(jīng)濟效益等多個(gè)目標的最優(yōu)化。多目標2系統結構及加速策略?xún)?yōu)化要同時(shí)優(yōu)化多個(gè)可能相互沖突的目標函數,因而有一個(gè)Aspen Plus用戶(hù)界面是-一個(gè)ActiveX服務(wù)器應用程序,非劣解集,又稱(chēng)Pareto解集。多目標優(yōu)化問(wèn)題有2種處理策略,一種是先轉化為單目利用接口程序能把Aspen Plus所模擬過(guò)程的輸人輸出與其標問(wèn)題,再用各種單目標優(yōu)化方法求出非劣解集['2 ,這需要它一些應用程序如優(yōu)化算法連接起來(lái)，實(shí)現軟件集成[15-16]。接口程序一般用Visual Basic( VB)語(yǔ)言設計,通過(guò)VB編程多次構造目標函數并求解,比較繁瑣,而且隨著(zhù)目標函數的環(huán)境可直接操作Aspen Plus提供的對象,并使用它們的屬增加,計算量呈指數增長(cháng)。另一種策略是直接求解,最常用性、方法和事件,實(shí)現Aspen Plus的功能。的算法是多目標遺傳算法( MOGA) ,已開(kāi)發(fā)多種算法[)) ,如:本文將NSGA-II與Aspen Plus集成,用于過(guò)程的多目標NSCA[4] ,NPCA[5] , SPEA(6] , NSCA-I7]等。MOGA計算量?jì)?yōu)化。Aspen Plus作為模擬器用于計算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的近十幾年人們對遺傳算法求解化工過(guò)程多目標問(wèn)題進(jìn)計算結果和信息(包括是否收斂,迭代次數,收斂精度等)都行了一些研究。Gupal8-1] 等人應用NSGA先后對T.業(yè)反應通過(guò)接口進(jìn)行傳遞。系統結構如圖1所示。器分離器和過(guò)程流程等進(jìn)行了設計優(yōu)化和操作優(yōu)化研究,遺傳算法計算個(gè)體的適應值時(shí),需要反復調用Aspen與常規優(yōu)化方法的對照研究表明利用NSGA求解多目標優(yōu)Plus。提高Aspen Plus的計算效率非常重要。對于有循環(huán)流化問(wèn)題具有- -定優(yōu)勢。Amyl2] 等人應用NSGA對苯乙烯反的連續過(guò)程,本文提出2種策略以減少流程迭代次數。應器進(jìn)行了3個(gè)目標的優(yōu)化。以上研究的問(wèn)題模型比較簡(jiǎn)計算開(kāi)始時(shí)遺傳算法的個(gè)體是隨機產(chǎn)生的,經(jīng)過(guò)各代優(yōu)單,過(guò)程模型多是基于方程的。對復雜大系統的研究還很不化,逐步向Pareto前沿道近。在計算初期,非劣解的數不充分,難以指導實(shí)際化工過(guò)程的優(yōu)化和設計。若使用嚴格熱多,各個(gè)體離Pareto前沿還較遠,流程迭代沒(méi)有必要以高精力學(xué)、動(dòng)力學(xué)模型又會(huì )導致問(wèn)題過(guò)于復雜，難以收斂。將過(guò)度收中國煤化工t模擬計算量,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.1434什算機與雇用化學(xué)2009 ,26(11)flowshescodification andw=物流S4中內酮+物流SI0中丙酮。constructionparametersser目標函數表達如下: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 系統結構其中:p為利潤, $/h; w為廢料量,kg/h; F為回收內酮程收斂精度,保證得到的非劣解為叮行解。這種變化循環(huán)流量,kg/h; Q為精餾塔熱負荷, kcal/h; ug,4s 分別為物流收斂精度的策略類(lèi)似于過(guò)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。利用遺傳算法所計算的大量個(gè)體,回歸出循此問(wèn)題為帶循環(huán)流的連續過(guò)程廢料最少問(wèn)題,優(yōu)化變量環(huán)流中各組分流率與自變最的關(guān)系表達式,據此給出比較準都是連續變量。采用本文提出的集成策略進(jìn)行優(yōu)化,并對加確的循環(huán)流初值,可有效減少流程迭代次數。速策略的應用與否進(jìn)行比較。對于不同策略NSGA-都統3計算實(shí)例一采用實(shí)型編碼,種群規模40,遺傳代數50,交叉概率0.8,變異概率0.01,以便于結果比較。3.1丙酮回收流 程及優(yōu)化模型3.2計算結果及討論丙酮和空氣的混合物(物流S3)進(jìn)入吸收塔B4,用水吸本文根據遺傳算法代數,給出不同的循環(huán)流收斂判據,1收其中的丙酮。吸收塔底出來(lái)的物流s5加熱后,到蒸餾塔到10代收斂判據為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(lái)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算過(guò)程中產(chǎn)生大最數據,可以用來(lái)改善流程劑用"”。流程圖如圖2所示。模擬計算效率。根據初始種群計算結果,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,對不同策略的非劣解及流程計算次數進(jìn)行比較,結果見(jiàn)B5 hearter表1。表1第1列數據為循環(huán)流收斂判據固定為0.0001、循39Ss環(huán)流初值缺省給出、遺傳代數為50時(shí)的非劣解,總流程計算BI cooler次數為17 893。第2列數據為采用了變收斂判據策略的非劣O←解，總流程計算次數為7399次,下降了近60%。2列數據進(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(粗體標出),數圖2丙酮回收流程圖據質(zhì)量有所下降。這可以通過(guò)增加代數,犧牲部分計算效率B1.冷卻器; B2.分流器; B3.混合器;得到改善。表中第3列數據為采用變收斂判據策略、遺傳代B4.吸收塔; Bs.加熱器; B6.蒸餾塔數為60時(shí)的非劣解,總流程計算次數為9841 .2列數據進(jìn)行流程優(yōu)化目標有2個(gè):一個(gè)是利潤最大,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(xiàn)標的丙酮廢料:量最少。出) ,數據質(zhì)量提高的代價(jià)是效率下降。若利用回歸式計算流程利潤:循環(huán)流中國煤化工1下降至8992?？梢詐=丙酮價(jià)格x丙酮回收量-操作費用-水價(jià)格x原料看出變lYHCNMH(G值策略效果要好。水量-設備投資。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:連續過(guò)程的多目標優(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solution set of 50th ( convergencesolution set of 50thsolution set of 60thNo.tolerance is fixed on 0.000 1)(convergence tolerance is changed)利潤廢料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中國煤化工79.9773390.975 831127.033 91.387 108HHCNMHG148. 794 9401. 183 493149.831 60. 806 851. 150”146. 8581436計算機與應用化學(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結論gres on Computational Ielligence. Piscalaway NJ: IEEE Pres,1994, 1:82 -87.將多目標遺傳算法NSGA-I與Aspen Plus集成起來(lái)建6 Zitzler E, Thiele L An evolutionary algorithm for mulibiective p立了一個(gè)用于化工過(guò)程多目標優(yōu)化的求解平臺。由于過(guò)程timization:The strength pareto approach. Computer Engineering and模型為嚴格模型,所得結果能夠反映過(guò)程的本質(zhì),對實(shí)際生Communication Networks Lab (TK). Zurich: Swiss Federal Inati-產(chǎn)及過(guò)程設計具有指導意義。在求解過(guò)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了大部分機時(shí),提高流程模擬效率成為關(guān)鍵。針對具有循環(huán)sorting genetic algritim for multi. objective optimization: NSCA-I.流的連續過(guò)程,本文提出了2個(gè)加速循環(huán)流收斂策略,結果Parallel Problem Solving from Nature, Berlin, 2000:849 -858.表明總流程模擬次數大大減少,效果顯著(zhù)。本文設計的接口8 Mitma K, Deb K and Gupta s K. Mutiobijictive dynanic optimzr.程序經(jīng)改造后叮應用于其他連續過(guò)程的多目標優(yōu)化。tion of an industrial mylon 6 semi-batch reactor using genetic algo-References:nithm. J Appl Polym Sci, 1998, 69(1) :69 -87.9 Bhaskar V, GuptaS K and Ray A K. Multi-objective optimization of1 Yang Youqi and Cheng Siwei. Moderm Process System Engineering.Bejing: Idutrial Chemisty Prese, 2003, 180 - 184.an industrial wiped film poly ( ethylene terephthalate) reactor.2 Zheng Shiqing Study on muliobjetive process syntheis in modularAIChE J, 2000, 46 (5) :1046 - 1058.simulator environment. Doctor Degree Paper of South China Univer-10 Ravi G, Gupta s K and Ray M B. Muliobjetive opimization ofsity of Technology, 2001 , 43 -47.eyelone separatrs. Ind Eng Chem Res, 2000, 39(11):4272 -3 Yue jincai, Zheng Shiqing and Hang Fangyu. Muliobjetive genet-4286. .ic algorithms and its pplication in process synthesis. Computers and11 Ksat R B, Cupta s K. Muliobjective optimiation of an indutrialApplied Chemistry, 2006, 23(8) :748 -752.fuidized-bed catalytic cracking umi( FCCU) using geneie algorihm4 Srinivas N, Deb K. Muliobjective optimization using non dominated中國煤化工Computers and Chemicalsoting in genetic algorithme. Evolutionary Computation, 1994, 212FYHCN MH G,Muliobjecive optiniaiHorm J], Nafpliotis N and Goldberg D E. A niched pareto genetic ation of an indutial styrene recor. Computerns and Chemiceal Engi-gorithm for multiobjective optimization//Proceedines of the Firstneering, 2003 , 27(1):111 -130.IEEE Confrence on Evolutionary Computation. IEEE World Con-13 Yue Jinceai, Qu Bo, Cheng Huanong, et al. Muliobjective opimiza-2009 ,26(11)岳金彩,等:連續過(guò)程的多目標優(yōu)化1437tion of phosgene abeorber wing NSGA-I. Computers and Applied中文參考文獻Chenisty, 2008, 25(2):181 -184.1楊友麒, 成思?，F代過(guò)程系統工程[M].北京:化學(xué)工業(yè)出版14 Yue Jincai, Zheng Shiqing and Han Fangyu. Strategy of muliob社, 2003.jective process synthesis based on modular simulator. CIESC Jour2鄭世清.基于模塊環(huán)境的多目標過(guò)程系統綜合的研究[D].華nal, 2009, 60(1):177 -182.南理工大學(xué)博士學(xué)位論文. 2001:43 -47.15 Hu Yangdong, Wu Lamying and Liu Qinghi. Mebod of ralize da3岳金彩, 鄭世清,韓方煜.多目標遺傳算法及在過(guò)程優(yōu)化綜合tabase- oriented integrated environment of chemical engineering sof-中的應用[J].計算機與應用化學(xué), 2006, 23(8) :748 -752.ware. Computers and Applied Chenity, 2005, 22(11):980 -13岳金彩， 曲波，鄭世清，等NSCA- I用于光氣吸收塔的多目標優(yōu)化[J].計算機與應用化學(xué), 2008, 25(2):181 -184.16 Kong Xiangbing, Yue Jincai and Tan Xinehun, et al. The aplica-14岳金彩， 鄭世清，韓方燈.基于模塊模擬器的多目標過(guò)程綜合tion of Aspen Plus server in sofware integration. Computern and Ap-解算策略[J].化工學(xué)報，2009, 60(1):177-182.plied Chemisty, 2007 ,24(2) :255 -258.15 胡仰棟，伍聯(lián)營(yíng),劉清芝面向數據庫的化工軟件集成環(huán)境的17 Cirie A R, Jia T. Multiojective Optimization and Nonlocal Sensitiv-設計[J].計算機與應用化學(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中的應用[J].計算機與應用化學(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)中國煤化工MYHCNMHG