Numerical Optimizer SIMPLE チュートリアル V20 株式会社 NTT データ数理システム 2018 年 1 月

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1 Numerical Optimizer SIMPLE チュートリアル V20 株式会社 NTT データ数理システム 2018 年 1 月

2 Windows Nuorium Visual Analytics Platform UNIX Linux

3 1 Numerical Optimizer GUI Nuorium Numerical Optimizer/ Numerical Optimizer/ Numerical Optimizer 1.1 x 0 3x + 2 x 0 3x + 2 x 3x + 2 x 0 2 x = 0

4 Windows Numerical Optimizer GUI Nuorium Windows MSI Solutions Nuorium 1 Numerical Optimizer 1 Windows7 MSI Solutions NUOPT Nuorium

5 1.2 3 Numerical Optimizer 3x + 2 x 0

7 X, Y / X 6t 4t Y 1t 6t / 12t 24t X, Y X 180 Y 160 / X, Y 5 x y X / Y / 180x + 160y /

8 6 2 6x + y 12 / 4x + 6y 24 / 0 x 5 X 0 y 5 Y // X Y / Variable x(name=" X "); Variable y(name=" Y "); // ( ) Objective cost(name=" ", type=minimize); cost = 180*x + 160*y; // 6*x + y >= 12; // / 4*x + 6*y >= 24; // / // 0 <= x <= 5; // X 0 <= y <= 5; // Y // solve(); // x.val.print(); y.val.print(); cost.val.print(); // X Y / Variable x(name=" X "); Variable y(name=" Y ");

9 2.1 7 name="..." name="..." "//" // ( ) Objective cost(name=" ", type=minimize); name="..." name="..." type=minimize type=maximize cost = 180*x + 160*y; = * + exp(), sin()... // 6*x + y >= 12; // / 4*x + 6*y >= 24; // / >= SIMPLE >= <= == = // 0 <= x <= 5; // X 0 <= y <= 5; // Y x, y

10 8 2 // solve(); solve() solve() // x.val.print(); y.val.print(); cost.val.print(); solve() 3 [Expand Constraints and Objectives] sample.smp:7:info: (1/5) name=" " sample.smp:10:info: (2/5) name="" sample.smp:11:info: (3/5) name="" sample.smp:14:info: (4/5) name="" sample.smp:15:info: (5/5) name="" [About Numerical Optimizer] MSI Numerical Optimizer xx.x.x (NLP/LP/IP/SDP module) <with META-HEURISTICS engine "wcsp"/"rcpsp"> <with GLOBAL-OPTIMIZATION add-on "global"> <with DERIVATIVE-FREE-OPTIMIZATION add-on "DFO"> <with Netlib BLAS>, Copyright (C) 1991 NTT DATA Mathematical Systems Inc. [Problem and Algorithm] PROBLEM_NAME sample NUMBER_OF_VARIABLES 2 NUMBER_OF_FUNCTIONS 3 PROBLEM_TYPE MINIMIZATION METHOD HIGHER_ORDER

11 2.2 9 [Progress] <preprocess begin>...<preprocess end> <iteration begin> res=4.0e e-005 <iteration end> 1.4e-007 [Result] STATUS OPTIMAL VALUE_OF_OBJECTIVE ITERATION_COUNT 6 FUNC_EVAL_COUNT 9 FACTORIZATION_COUNT 7 RESIDUAL e-007 ELAPSED_TIME(sec.) 0.20 X =1.5 Y =3 =750 = name="..." 2.2 costx x + costy y / costx costy X / Y / costx, costy X, Y / cost = 180*x + 160*y;

12 10 2 Parameter costx(name=" X "); Parameter costy(name=" Y "); cost = costx*x + costy*y; Parameter name="...".dat " X " = 180; " Y " = 160; = name="..." ; "..." 3 X =1.5 Y =3 =750 Parameter " X " = 100; " Y " = 170; X =5 Y = =

13 x 5 X 0 y 5 Y x, y x 0, x 1 OilField = {0, 1} x i, i OilField i / costx costy 0 / 1 / costx x 0 + costy x 1 / 6x 0 + x 1 12 / 4x 0 + 6x 1 24 / 0 x i 5, i OilField i // Set OilField(name=" "); OilField = "0 1"; Element i(set=oilfield); // i / Variable x(name=" ", index=i);

14 12 2 // / Parameter costx(name=" X "); Parameter costy(name=" Y "); // / ( ) Objective cost(name=" ", type=minimize); cost = costx*x[0] + costy*x[1]; // 6*x[0] + x[1] >= 12; 4*x[0] + 6*x[1] >= 24; // // // i 0 <= x[i] <= 5; // solve(); // x[i].val.print(); cost.val.print(); Set OilField(name=" "); name="..." name="..." OilField = "0 1"; {0, 1} 0, 1 Element i(set=oilfield); OilField i set=...

15 Variable x(name=" ", index=i); index=i cost = costx*x[0] + costy*x[1]; x[ ] // 6*x[0] + x[1] >= 12; 4*x[0] + 6*x[1] >= 24; x, y x[0], x[1] // 0 <= x[i] <= 5; i i OilField // x[i].val.print(); i i OilField x[i] x[i].val.print() [0]=1.5 [1]=3 OilField x[i] costx, costy i costx i, i OilField i / costx 0, costx 1 costx, costy

16 14 2 Parameter costx(name=" X "); Parameter costy(name=" Y "); cost = costx*x[0] + costy*x[1]; Parameter costx(name=" ", index=i); cost = costx[0]*x[0] + costx[1]*x[1]; index=i " " = [0] 180 [1] 160; [ ] [ ]... 3 [0]=1.5 [1]=3 =750 0, 1 0, 1 OilField = "0 1"; Product = {, }

17 norma j, j Product j / 6*x[0] + x[1] >= 12; 4*x[0] + 6*x[1] >= 24; Set Product(name=" "); Element j(set=product); Parameter norma(name=" ", index=j); 6*x[0] + x[1] >= norma[" "]; 4*x[0] + 6*x[1] >= norma[" "]; j "..." " " = [0] 180 [1] 160; " " = [" "] 12 [" "] 24; " " " " SIMPLE OilField = {0, 1} Product = {, } costx i, i OilField norma j, j Product i / j / x i, i OilField i /

18 16 2 costx 0 x 0 + costx 1 x 1 / 6x 0 + x 1 norma / 4x 0 + 6x 1 norma / 0 x i 5, i OilField i // Set OilField(name=" "); Element i(set=oilfield); // Set Product(name=" "); Element j(set=product); // i / Parameter costx(name=" ", index=i); // j / Parameter norma(name=" ", index=j); // i / Variable x(name=" ", index=i); // / Objective cost(name=" ", type=minimize); cost = costx[0]*x[0]+costx[1]*x[1]; // 6*x[0] + x[1] >= norma[" "]; // / 4*x[0] + 6*x[1] >= norma[" "]; // / // i 0 <= x[i] <= 5; //

19 solve(); // x[i].val.print(); cost.val.print(); 2.4 cost = costx[0]*x[0] + costx[1]*x[1]; cost = costx i x i i cost = sum(costx[i]*x[i], i); sum() sum(, ) sum() 6*x[0] + x[1] >= norma[" "]; 4*x[0] + 6*x[1] >= norma[" "]; prodx i, j prodx i, j x i norma j, j Product i OilField j / prodx i, j, i OilField, j Product norma j, j Product i j / j /

20 18 2 Parameter prodx(name=" ", index=(i,j)); sum(prodx[i,j]*x[i], i) >= norma[j]; index=(i,j,..) sum() i i, j sum(,(i,j)) " " = [0] 180 [1] 160; " " = [" "] 12 [" "] 24; " " = [0, " "] 6 [1, " "] 1 [0, " "] 4 [1, " "] 6 ; OilField = {0, 1} Product = {, } costx i, i OilField norma j, j Product prodx i, j, i OilField, j Product i / j / i j / x i, i OilField i / costx i x i i OilField / prodx i, j x i norma j, j Product i OilField j /

21 x i 5, i OilField i // Set OilField(name=" "); Element i(set=oilfield); // Set Product(name=" "); Element j(set=product); // i / Parameter costx(name=" ", index=i); // j / Parameter norma(name=" ", index=j); // i j / Parameter prodx(name=" ", index=(i,j)); // i / Variable x(name=" ", index=i); // / Objective cost(name=" ", type=minimize); cost = sum(costx[i]*x[i], i); // j / sum(prodx[i,j]*x[i], i) >= norma[j]; // i 0 <= x[i] <= 5; // solve(); //

22 20 2 x[i].val.print(); cost.val.print(); 2.5 /, / / prod j = prodx i, j x i, j Product i OilField j / Expression prod(name=" ", index=j); // prod[j] = sum(prodx[i,j]*x[i], i); // Expression name, index Variable name index prod[j] =... Expression sum(prodx[i,j]*x[i], i) >= norma[j]; prod[j] prod[j] prod[j] >= norma[j]; prod[j] prod[j].val.print(); / [ ]=12 [ ]=24

23 Variable x(name=" ", index=i); IntegerVariable x(name=" ", index=i); IntegerVariable solve() [ ]=15 [ ]=26 [0]=2 [1]=3 = IntegerVariable 2.7 print() simple_printf() simple_printf() C++ C++ C++ simple_printf() print() simple_ printf() x[i].val.print();

24 22 2 simple_printf(" %d = %d\n", i, x[i]); 0 = 2 1 = 3 simple_printf() simple_printf(, 1, 2,...) C++ printf() 2.8 showsystem() showsystem() showsystem() solve() showsystem(); solve(); showsystem() 1-1 (sample.smp:26): 6* [0]+ [1] >= (sample.smp:26): 4* [0]+6* [1] >= (sample.smp:29): 0 <= [0] <= (sample.smp:29): 0 <= [1] <= 5 objective (sample.smp:23 name=" "): 180* [0]+160* [1] (minimize) 1-1, 1-2 prod[j] >= norma[j]; 2-1, <= x[i] <= 5; objective

25 cost = sum(costx[i]*x[i], i); showsystem() 2.9 / ; // name= " minimize maximize " name type name type <= >= < > = ==

27 3 Windows UNIX Linux Numerical Optimizer Windows UNIX Linux Numerical Optimizer/ Nuorium Windows Visual Analytics Platform Numerical Optimizer Windows 3.1 Windows Windows Numerical Optimizer/ Nuorium Visual Analytics Platform Nuorium 1. Windows MSI Solutions Nuorium 2 Nuorium foo.smp foo.smp // Set S, T; Element i(set=s), j(set=t); // Parameter c(name="c", index=j); Parameter cu(name="cu", index=i); 2 Windows7 MSI Solutions NUOPT Nuorium

28 26 3 Parameter cl(name="cl", index=i); Parameter A(name="A", index=(i,j)); Parameter bu(name="bu", index=j); Parameter bl(name="bl", index=j); // Variable x(name="x", index=j); // Objective f(name=" ", type=minimize); f = sum(c[j] * x[j], j); // cu[i] >= sum(a[i,j] * x[j], j) >= cl[i]; bu[j] >= x[j] >= bl[j]; 2. dat data.dat data.dat c = [1] -3 [2] 1; cu = [1] 1000 [2] 1000 [3] 1000; cl = [1] -1 [2] -2 [3] 2;

29 3.1 Windows 27 A = [1,1] -1 [1,2] 0.1 [2,1] -0.2 [2,2] -1 [3,1] 2 [3,2] 1 ; bu = [1] 1 [2] 2; bl = [1] 0 [2] 0; 3. foo.smp Numerical Optimizer Nuorium

30 Numerical Optimizer Windows MSI Solutions 3 NUOPT Windows Numerical Optimizer Nuorium Nuorium 4. foo.smp data.dat 3 Windows7 MSI Solutions NUOPT

3.1 Windows 29 foo.exe > mknuopt foo.smp > foo.exe data.dat 3.1.3 Visual Analytics Platform 1.

31 3.1 Windows 29 foo.exe > mknuopt foo.smp > foo.exe data.dat Visual Analytics Platform 1. Visual Analytics Platform Numerical Optimizer Numerical Optimizer NUOPT OK

32 Nuorium Nuorium 4. Windows MSI Solutions VAP Visual Analytics Platform foo.smp data.dat

33 3.1 Windows

34 UNIX Linux 1..smp foo.smp

35 3.2 UNIX Linux 33 foo.smp // Set S, T; Element i(set=s), j(set=t); // Parameter c(name="c", index=j); Parameter cu(name="cu", index=i); Parameter cl(name="cl", index=i); Parameter A(name="A", index=(i,j)); Parameter bu(name="bu", index=j); Parameter bl(name="bl", index=j); // Variable x(name="x", index=j); // Objective f(name=" ", type=minimize); f = sum(c[j] * x[j], j); // cu[i] >= sum(a[i,j] * x[j], j) >= cl[i]; bu[j] >= x[j] >= bl[j]; 2..dat data.dat data.dat c = [1] -3 [2] 1; cu = [1] 1000 [2] 1000 [3] 1000; cl = [1] -1 [2] -2 [3] 2; A = [1,1] -1 [1,2] 0.1 [2,1] -0.2 [2,2] -1 [3,1] 2 [3,2] 1 ;

36 34 3 bu = [1] 1 [2] 2; bl = [1] 0 [2] 0; 3. foo.smp data.dat foo prompt% mknuopt foo.smp prompt%./foo data.dat [List of Data Files] <reading data_file: data.dat> [Expand Constraints and Objectives] foo.smp:18:info: (1/3) name=" " foo.smp:21:info: (2/3) name="" foo.smp:22:info: (3/3) name="" [About Numerical Optimizer] MSI Numerical Optimizer xx.x.x (NLP/LP/IP/SDP module) <with Netlib BLAS>, Copyright (C) 1991 NTT DATA Mathematical Systems Inc. [Problem and Algorithm] PROBLEM_NAME foo NUMBER_OF_VARIABLES 2 NUMBER_OF_FUNCTIONS 4 PROBLEM_TYPE MINIMIZATION METHOD HIGHER_ORDER [Progress] <preprocess begin>...<preprocess end> <iteration begin> res=1.4e e e e-08 <iteration end>

37 3.2 UNIX Linux 35 [Result] STATUS OPTIMAL VALUE_OF_OBJECTIVE -3 ITERATION_COUNT 12 FUNC_EVAL_COUNT 15 FACTORIZATION_COUNT 13 RESIDUAL e-08 ELAPSED_TIME(sec.) 0.03 SOLUTION_FILE foo.sol

39 <=... 7, 23 >= == D dat... 10, 28, 30, 33, 34 E Expression I index...13, 14, 18, 20 IntegerVariable M minimize... 7, 23 N name...7, 9, 10, 12, 20, 23 Numerical Optimizer...1 3, 25, 27 Nuorium... 1, 2, 25, 28, 30 P Parameter print... 13, 21, 22 S showsystem...22, 23 SIMPLE... 1, 6 9, 11 15, 17, 18, 20, 21, 23, 25, 32 solve... 8, 22 sum...17, 18 T type... 7, 23 V Visual Analytics Platform W Windows... 2, , , 7, , 18, , 3,

40 38...7, 13, 15, 17, 18, 22, , 3, 6, 11, , 17, 18, 20, 22, , 17, 18, 22, , 14, 15, 18, 28, 30, 33, , 5 7, 9 15, 18, , 3, 5, 7, 9 12, 15, 16, 18, 22, , 8 11, 14, 22, 23, 25, 26, 28,

1 1 2 3 3 5 3.1 1...................................... 5 3.1.1........................................ 5 3.1.2 SIMPLE...............................

Numerical Optimizer SIMPLE/Excel 連係マニュアル V18 株式会社 NTTデータ数理システム 2016 年 3 月 1 1 2 3 3 5 3.1 1...................................... 5 3.1.1........................................ 5 3.1.2 SIMPLE...............................