GAMS_软件介绍

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1、GAMS简介 主要內容 agamsA统及特点 AGAMS模型整体结构 A GAMS语言分析 A工程应用实例 O GAMS系统及特点 • GAMS一 “ General Algebraic Modeling System^^ (一般桂代薮仿煮紊统)的缩写， 最早是1992年由美国的世界银行(World Bank)的 Meeraus 和 Brooke 所发展。 • GAMS是一种面向应用的构造模型的高级计 算机语言，融合了关系数据库技术与数学规 划理论，使数学模型与数据彼此独立，为用 户在模型、算法和数据之间提供了一个便捷 的接口。包含了编译器和高效能的求解引擎 • G

2、AMS提供的描述大型复杂模型的语舌 体系十分简洁，并将算法封装于系统内 部 •输入文件形式与模型描述的自然语言一 致，便于理解和掌握。 | •易于操作，封装的算法均可直接调用， 无须改变用户的模型描述。 •可求解各种类型的实际问题，女口LP （线 性规划）、NLP、ILP、MLP等 O Chemical Ensineerine： No. Name Model Type Alkylation Process Optimization 20 process nip Chemical Equilibrium Problem 21 diem nip Chemic

3、al Equilibrium Pioblem 76 wall nip Stmctiiral Optiimzation of Process Plowslieets 116 procsei miiilp Simultaneous Optimization for Hen S^itliesis 117 svnheat >1 mmlp Heat hitegiated Distillation Sequences 118 minlphi nip, imp Optimal Design for Chemical Batch Processing 119 batchd

4、es mmlp Synthesis of General Distillation Sequences 120 lions harp nip, mip Logical Infeience for Reaction path synthesis 121 reaction 1P Optimum Feed Plate Location 122 feedtrav mmlp Synthesis: Hvdrodealkvlation of Toluene 123 hda* liiinlp Chemical Equilibrium Problem as MCP 127

5、 wallmcp mcp Simplified Alkylation Process 16? alkvl ■ nip 举一个线性规划的例子 Shipping Distances Supplies Markets Plants New York Chicago Topeka Seattle 15 1.7 1.8 350 San Dieao Z5 L8 1.4 600 Demands 325 300 275 ・矩阵为供销地区的距离（单位：千公里） ・每公里运费为$90/千公里 ・Supplies一供应商的

6、生产量 • Demands一采购商的需求量 •优化曰标：运斎最低 运输问题数学语言描述 Indices: i = plants j = markets Given Data: %= supply of commodity of plant i (in cases) bj = demand for commodity at market / (cases) Qj = cost per unil shipment between plant i and market j ($/case) Decision Variables: X/j amount of comnux

7、lily Io ship from plant i to market j (casesX where t > 0, for all ij Constraints: Observe supply limit al plant i:〉.仏 < a. for all i (cases) Satisfy demand at market j\》产打 > /br all J (cases) Objective l unction: Minimi空工工儿 ($K) i canning pl ants- / E-eatt le., an-Diegi^ / j market.! / New

8、- York r Ch.icagar Topelta / ； GAMS 语言描述 FoK-3n=t>=177 a (i ] capac i Dy of pl ant ./ Seattle 2ari・ Diego in cacec 3&0 6DQ / b < j] demand at narket / York Zhiaago Top-ska in cases 325 300 2T5 / ； lV=w- York iZhicago -eattle 2・5 L •丁 S-an-Die-go 2・5 L.P Table d (i. j ] di

9、stance i n thcusands of n i Len in dz-llarc per cace per Topeka l.E 1.4 ； Scalar f freight thousand miles 790/ Parameter c ( i r j l trannpz-rt ods t in 1000s of -dollars p-=r case cCi. j) ■ f*dd, jJ/LODO ; Xr3fiablefl x(ij] shipment quantities in cases z total tranorportat

10、ion costs in lODOs of c3ollars ； Equations ods t supply l： i) di-mand (j ) Positive variable x ； z -e- sun( (i r j ). define objec:t:ive function obsein/e supply Lin it at plant i satisfy demsnd at market j - ODSt・・ supply I： i)・・ aum f j r x：i, j ] ： -1- a •： i ; demand (j ) .. nun •： i ,

11、x (i r j J]・g・ b (j )； hfodel transport /all/ ； solve transport timing Ip minimizing 工 - display sc.l.工.n ； GAMS模型整体结构 Inputs • Sets (指定) • Data (Parameters, Tables, Scalar) • Variables • Equations • Model and Solve statements • Displav statement (opfionQl) GAMS模型整体结构 Outputs Echo Prin

12、t Eiror Messages Reference Maps Echo Print Reference Maps Equation Listings Model Statistics Status Reports Solution R 已 ports Remarks •先定义，再引用 •每条语句由分号结束 • GAMS编译器不区分大小写 •标注由星号引出，或将标注直接插入到 语句中 Equations包含等式和不等式约束 GAMS语言分析 • Sets 用于指定数学模型中的下标 i canning plants / Seattle, Edn-Di亡go

13、 / j markets J Hew-York. Chi cage P Topck-a /) 即定义：i代表生产地，j代表销售地 • Data (1) Lists Faraneters •a (i) of plan七 Sea t七］.亡 San-Dieao in ca.5es 350 600 Q in cases 300 b (j ) demand at market j / New-York Chicago Topeka Remarks:所有参数默认初值为0 多字情况，例如，New York需要加连字符

14、 标量的定义如下: Scalar>f freight- in dollars per cass per thousand rr.iles / 9 0 / ; (2) Tables Topeka Table d( i. j 1 distance in thousands c-f riilec tfew- York iZhicago Seattle 2.5 1.7 -3n-Dii&gD 2.5 1 . E (3) Direct assignment (直接定义) Parameter c(i r j) tranopz-rt cost in IDDQs of dolliara p

15、eir cafse □

16、 dollars ; (3) 对自变量定义类型 Positive variable x ; • Equations (1)常用符号 Suit, (index of su^imationf 5t:m]T.and) 〜jXij. ―► Suir.( j , x (ir j )) □j巧.―► prod (j r x (i< j )) (2)定义步骤 定义等式的名称一运算的控制维一控制维的约束(可选) 一 标记“… 一^-左边表达 一符 一-右边表达式 ⑶符号类型 =1= =*3= =e= less than o

17、r equal to greater than or equal to equal to (4)举例 Zquations cost supply (i) deir.a.nd (j ) define objective function observe supply limit at plant i sa.-isfy demand at market j ; cost. - z 二己二 suir.( (ir j ) r c (1/ j ) (iz j )); supply (i) . . sum( j x (l,j) ) =1= a (i); demand(j) . - sum (

18、1f x(i z j)) =g- ; Remark：在约束式的两边均可以出现变量，而且同一变量可以出现多次 (1) 模型定义 (2) 模型求解 (3) 求解方法 • Model And Solve n-.odel transport /all/ ; all：包括所有的变量和等式 rr.cdel transport / ccstf supply, derriand / ; solve transport us ing Ip z ; lp for

19、 lineal* programming nip for nonlinear programming mip for mixed integer programming rnip for relaxed mixed integer piogrammiiig ir.inlp for mixed integer nonlinear progranuning rrninlp for relaxed mixed mteger nonlmear progranuning ir.cp for mixed c□mpleiiieiitarify problems cns for constrained no

20、nlinear systems • Display (1)结果输出 display x.lr x.m ; (2)输出类型 •丄 o = lower bound ・丄 = level or primal value ・ up = upper bound ・ m = marginal or dual value .lo表示输出变量的下限 .1表示输出变量的最终结果 ・up表示输出变量的上限 j . m表示输的边际效应 Outputs Echo Print Eiror Messages Reference Maps

21、 27 Echo Print Reference Maps Equation Listings Model Statistics Status Reports Solution Reports Echo Prints 3 28 4 厶 sets 29 5 i canning plart5 / sestcle, san-diegc / 30 6 j markets / new-york, chicagor topeks / ; 31 7 32 8 parameters 33

22、 a J 34 10 a(i) c&pscLty of plant i in cases 35 11 / 3cS3tlc 35D 36 12 san-diegc GOO / 37 13 38 14 b(j) cenand a二 market ] in case3 39 15 / new・york 325 40 16 Chicago 300 41 17 topeka 275 / ; 42 18 43 19 table d(i,j) distance i.r thousancs of ic

23、iles 44 20 new-ycrk Chicago topeka 45 21 seattlE 2.5 1.7 1.8 46 22 san・diEgo 2.5 1.8 1.4 / 47 2 48 r A 鎳 scalar z freight in collars per qasz per 100C ir.iles “0/ ; 49 25 50 26 paxametEi c(i,j) trarspcrz cost in lOQGs cf dollars per case; 51 c(ij)二 fM(irj)/1000

24、 ； variables x(if j) shipment quanin esses z total transportution costs in 1000s of dollars; positiv己 variable x ; equations cost define objictiv■己 function supply (i) observe supply limit at plant i demand (j) satisfy demand at market j ; cost ・・ z =e= sum((i,j), c(1,j)(1,j)); supply(i) .

25、. sum{jr x(i,j)) =1= a(i); demand (j)・■ 5um(ir x(ir j)) =g= b (j); model transport /all/ ; solve transport- using Ip zninimizing z ; display x・l< x.m ; 27 Error Massages set q quarterly time periods / spring, sum, allz wtr / ； results in tlie echo 1 set. q quarterly time periods / spring,

26、 sum, fall 4 wtr / ； **** $160 (2 \ parameter c (i,j) transport cost in 1000s of dollars per case )C (i,j) = * a(i,j)/ 1000 ； 16 parameter c (ir j) transport cost in 1000s of dollars per case 17 c(i7j) = f*d(irj)/1000 **** $97 $195$96$L94$1 ERROR MESSAGES 1 REAL NUMBER EXPECTED 96 BLANK NE

27、EDED BETWEEN IDENTIFIER AND TEXT (-OR-ILLEGAL CHARACTER IN IDENTIFIER) (・0R-CHECK FOR HISSING ；r ON PREVIOUS LINE) 97 EXPLANATORY TEXT CAN NOT START WITH or ■…， (・0R-CHECK FOR MISSING ；r ON PREVIOUS LINE) 194 SYhEOL REDEFINED 195 SYMBOL REDEFINED WITH A DIFFERENT TYPE Error Massages ⑶ 4 se

28、ts 5 i canning plants /seattie, san/ 6 j markets /new-york, Chicago, topeka / ； 7 7 table distance in thousand of miles 8 new-york Chicago topeka 9 seatie 2.5 1.7 1.8 **** $170 11 gan-diego 2.5 1.8 1.4 Status Reports SOLVE MCD5：L T RAM S PORT TYFZ LF SOLVER ECKL? OBJ

29、ECTIVE Z EIRECTZCN MINIMIZE FROM LIKZ 49 SOLVZR STATUS MODEL STATUS OBJECTIVE VALUZ 1 NORMAL COMPLETION 1 OFTI2-IAL 153 • 750 RESOURCE USAGEz LIKIT ITZRATION COUNT, LIMIT 0.1€8 1000・000 1000 」目标值 运算时间 迭代次数 下限 冃标值 上限 边际值 Solution EQU SUPPLY obser

30、ve supply liniT at Massages LOWER LEVEL UPPER >1ARG INAL SEATTLE -INF SAN-DIEGO -INF 353.000 350.000 550.000 600.000 EQU DEMAND satisfy demand at market j NEW-YO^K 325 .000 325.000 + INF 0.225 CHICAGO 300. 000 300.000 +IKF 0.153 TOPZKA 275. 000

31、275.000 + IKF 0.126 LOW5R LEVEL UPPZR M^RGIXAL VAR X shipment quantities in cases LCGiER LEVZL •HEW-YORK ・ .CHICAGO ・ •TOPZKA • SEATTLZ SEAT7LZ SEATTLE 3直卫-DIZGO ■ NEP；-YORK .SAN-DI EGO ・ CHICAGO SA2J-DIZGO. TCFEKA UFFER MARGINAL 50・000 +INF ・ 3GO ・000 +LNF ・ ・ +INF 0.036 275.000 4-inf . ・ +INF 0.002 275.000 +INF ■ Thanks Question ?