```MODEL: ! Find alternative primal optimal extreme point solutions (EnumrXtrmC.lng) or all feasible extreme points. (See parameter AltOpt) to a Linear Program, and report the average of all of them. All the solutions found can be written to the file: \temp\AltOpt.txt (see parameter TOFILE) An MPS copy of a specific model can be sent to \temp\AltOpt.mps by setting GENMPS = 1. One can switch to different problems by commenting/uncommenting the various models, essentially by changing a semi-colon to a space, and changing a trailing space to a semi-colon. Method: It is computationally expensive/complicated to enumerate every distinct alternative optimal solution. The approach used here is to (pseudo) randomly choose a large number of random objectives/directions and then minimize this objective subject to: the solution is feasible and is optimal for the original objective. Duplicate solutions are discarded. If enough random directions are generated, then all alternative primal optimal extreme points, or feasible extreme points will be generated. Note, in 2 dimensions, the (pseudo) random directions approach can enumerate all extreme points in finite steps by considering for every pair of already found extreme points (xpt(i), ypt(i)) and (xpt( j), ypt( j)) and choosing the objective: (ypt(i)-ypt(j))*x + (xpt(i) - xpt( j)*y, (and its negation). If there is a point between i and j, this direction will find it. You can stop the search when for every i and j there is no new point to be found between them. This idea can be generalized to 3 or more dimensions, but it becomes a combinatorial challenge. ; ! Keywords: Alternative optima, Average solution, Basic solution, Corner point, Enumeration, Extreme point, K-Best solutions, LINGO, Monte Carlo, Polytope; SETS: ROW: RHS, TYPER; COL: OBJ, X, SUB, OBJPTRB, SLB, TYPEC; NONZ( ROW, COL): COEF; SLIST : PT2; SXC( SLIST, COL): XSV; ENDSETSDATA: ! Here are a number of cases; GENMPS = 1;! 1 : send an MPS copy of current model to \temp\AltOpt.mps ; TOFILE = 0;! 1 : send solutions to file \temp\AltOpt.txt; ! We can read the data from a currently open( only one) spreadsheet with range names matching LINGO names; !CExcel NDXP = @OLE() ;!CExcel NSLIST = @OLE();!CExcel SLIST = 1..NSLIST; !CExcel ROW = @OLE(); !CExcel RHS = @OLE();!CExcel TYPER = @OLE();!CExcel COL= @OLE(); !CExcel OBJ= @OLE(); !CExcel SUB = @OLE();!CExcel NONZ, COEF = @OLE(); ! This polytope has 21 extreme points; !CBinExp NDXP = 200;!CBinExp NSLIST = 30;!CBinExp SLIST = 1..NSLIST;!CBinExp AltOpt = 0;!CBinExp COL, OBJ, SLB, SUB, TYPEC = z1 0 0 1 3 z2 0 0 1 3 z3 0 0 1 3 z4 0 0 1 3 z5 0 0 1 3 ; !CBinExp ROW, RHS, TYPER = CON 20 1 CUT1 1 1 Cut2 2 1 Cut3 2 1 Cut4 2 1 ; !CBinExp NONZ, COEF = CON Z1 1 COn Z2 2 CON z3 4 CON z4 8 CON z5 16 CUT1 Z4 1 CUT1 Z5 1 CUT2 z2 1 CUT2 z3 1 CUT2 Z5 1 CUT3 z1 1 CUT3 z3 1 CUT3 Z5 1 ; ! Case Murty: Example based on "A Problem in Enumerating Extreme Points, and an efficient Algorithm," by Katta G. Murty, Dept Ind. and Opns Eng. U. Michigan, March 2007. (There appear to be 6 distinct primal solutions); !CBinExp;NDXP = 100!CBinExp;NSLIST = 60!CBinExp;SLIST = 1..NSLIST!CBinExp;AltOpt = 1 !Find all extreme points; ! Names of rows; !CBinExp;ROW= R01 R02 R03 R04 R05 R06 R07 R08 R09 R10 R11 R12 R13 R14 R15 !CBinExp;RHS= 1 !CBinExp;TYPER = 0!CBinExp;COL = X01 X02 X03 X04 S01 S02 S03 S04 S05 S06 S07 S08 S09 S10 S11 S12 S13 S14 S15 ; !CBinExp;OBJ= 0! Upper bounds; !CBinExp;SUB= 1 1 1 1 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5; ! Constraint coefficients, with slacks explicitly added; !CBinExp; COEF = 1 1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1, 1, -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1, 1, -1, -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1, -1, 1, 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1, -1, 1, -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1, -1, -1, 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1, -1, -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 -1, 1, 1, 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1, 1, 1, -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1, 1, -1, 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1, 1, -1, -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1, -1, 1, 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1, -1, 1, -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1, -1, -1, -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 ; ! Case Low Probability: This model has 4 corner points: ( X1, X2) = (0, 0), (1.999, 0), (0, 1.999), and (1, 1). The solution ( 1, 1) has low probability of selection; ! Number of desired extreme points tries.; !CLoProb NDXP = 2000;!CLoProb NSLIST = 10; !CLoProb SLIST = 1..NSLIST; !CLoProb AltOpt = 0;!CLoProb ROW = CON1 CON2; !CLoProb RHS = 1999 1999; !CLoProb TYPER = 1; ! Names of columns; !CLoProb COL = X1 X2; !CLoProb OBJ = 0 0; ! Upper bounds; !CLoProb SUB = 999 999; ! Names of rows; ! Matrix coefficients, including Obj and RHS; !CLoProb COEF = 1000 999 999 1000; ! Case OML6: Example from chapter 6 of Optimization Modeling with LINGO. ! It has 2 alternative optima, 10 primal distinct feasible corner points; !COLM6 NDXP = 50000;!COLM6 NSLIST = 250;!COLM6 SLIST = 1..NSLIST; !COLM6 AltOpt = 1; !Find all extreme points with profit contribution = optimal value; ! Names of rows; !COLM6 ROW= MACH CAP HOURS SHIP PROD1 PROD2 PROD3; !COLM6 RHS= 35 35 36 600 218 114 111 ; !COLM6 TYPER= 1 1 1 1 -1 -1 -1;!COLM6 COL = B34 B38 B48 B58 B42 B52 ; !COLM6 OBJ= 0; ! -15.89 -17.89 -16.5 -15.22 -17.5 -16.22 ; ! Upper bounds; !COLM6 SUB= 999 999 999 999 999 999 ; ! Constraint coefficients triples, ( Row Col Coefficient); !COLM6 NONZ COEF = MACH B34 0.11111 MACH B38 0.11111 CAP B48 0.16667 CAP B42 0.16667 HOURS B58 0.22222 HOURS B52 0.22222 SHIP B34 1 SHIP B38 1 SHIP B48 1 SHIP B58 1 SHIP B42 1 SHIP B52 1 PROD1 B34 1 PROD2 B38 1 PROD2 B48 1 PROD2 B58 1 PROD3 B42 1 PROD3 B52 1; ! Case Dyera: Example from Dyer and Proll, Math. Programming, vol. 12, 1977 in <= constraint form; ! It has 10 primal extreme points ( both alternative optima and feasible); ! Number of desired extreme point tries; !CDyera NDXP = 60;!CDyera NSLIST = 50;!CDyera SLIST = 1..NSLIST; !CDyera AltOpt = 1;!CDyera ROW= ROW1 ROW2 ROW3 ROW4 ROW5; !CDyera RHS= 5 16 3 17 10; !CDyera TYPER = 1;!CDyera COL= X1 X2 X3 ; !CDyera OBJ= 0 0 0; !CDyera SUB= 99 99 99; ! Constraint coefficients; !CDyera COEF = 3 2 -1 3 2 4 3 0 -4 2.25 4 3 1 2 1 ; ! Case PD3; ! Example: The following model has 3 alternative primal extreme point optima (X1 = 1 or X2 = 1 or X3 =1) and 3 alternative dual extreme point optima, (DP1 = 1 or DP2 = 1/2 or DP3 = 1/3) for a total of 9 alternative optimal extreme point solutions. It has 10 extreme primal feasible points; ! We consider only the primal extreme point solutions as distinct. MIN= X1 + X2 + X3, X1 + X2 + X3 >= 1, 2* X1 + 2* X2 + 2* X3 >= 2, 3* X1 + 3* X2 + 3* X3 >= 3, It reports The average interior solution is: X1 = 0.3333333333333333 X2 = 0.3333333333333333 X3 = 0.3333333333333333 !CPD3 NDXP = 50;! Number of random directions to try!CPD3 NSLIST = 20;!CPD3 SLIST = 1..NSLIST; !CPD3 AltOpt = 0; ! Names of rows; !CPD3 ROW = CON1 CON2 CON3 ; !CPD3 RHS = 1 2 3; !CPD3 TYPER = -1;!CPD3 COL = X1 X2 X3 ; ! Upper bounds; !CPD3 SUB= 999 999 999 ; !CPD3 OBJ = 1 1 1 ; ! Constraint coefficients in sparse form; !CPD3 NONZ, COEF = CON1 X1 1 CON1 X2 1 CON1 X3 1 CON2 X1 2 CON2 X2 2 CON2 X3 2 CON3 X1 3 CON3 X2 3 CON3 X3 3 ; ! Case MRP/Leontief matrix There appear to be 8 corner solutions. In an MRP/Leontief model: Each constraint is an equality, Every column has exactly one positive coefficient and it is a +1, (the output) Each column has 0 or more negative coefficients, every one of which is integer, (inputs needed) Each RHS coefficient is a nonnegative integer. (the demands) Result: An LP whose complete constraint set is an MRP set has an optimal solution that is integer. Further, if the objective coefficients are all integer, then there is an optimal solution with integral dual prices. Ref: Jeroslow, R., K. Martin, R. Rardin, J. Wang(1992), "Gainfree Leontief substitution flow problems," Mathematical Programming, 57, pp. 375-414.; !CMRP NDXP = 1800;!CMRP NSLIST = 30;!CMRP SLIST = 1..NSLIST;!CMRP AltOpt = 0;! Names of rows; !CMRP ROW = DEM1 DEM2 DEM3; !CMRP RHS = 5 3 1; ! All rows are <= !CMRP TYPER = 1 1 1; ! Columns, obj cof, LB, UB and type ( 3 means continuous); !CMRP COL, OBJ, SLB, SUB, TYPEC = P1 0 0 999 3 P2 0 0 999 3 P3 0 0 999 3; ! Matrix coef in sparse form; !CMRP NONZ COEF = DEM1 P1 1 DEM2 P1 -2 DEM3 P1 -3 DEM2 P2 1 DEM3 P2 -4 DEM3 P3 1; ! This is a simple Stable Marriage example with a number of stable solutions; !CStable4x4S NDXP = 9000;!CStable4x4S NSLIST = 300;!CStable4x4S SLIST = 1..NSLIST;!CStable4x4S AltOpt = 0;!CStable4x4S COL, OBJ, SLB, SUB, TYPEC = PTOTALA, 1, 0, 1e+030, 3 Z_BOB_AVA_, 0, 0, 1, 1 Z_BOB_BARB_, 0, 0, 1, 1 Z_BOB_CORA_, 0, 0, 1, 1 Z_BOB_DAWN_, 0, 0, 1, 1 Z_CARL_AVA_, 0, 0, 1, 1 Z_CARL_BARB_, 0, 0, 1, 1 Z_CARL_CORA_, 0, 0, 1, 1 Z_CARL_DAWN_, 0, 0, 1, 1 Z_DON_AVA_, 0, 0, 1, 1 Z_DON_BARB_, 0, 0, 1, 1 Z_DON_CORA_, 0, 0, 1, 1 Z_DON_DAWN_, 0, 0, 1, 1 Z_ADAM_AVA_, 0, 0, 1, 1 Z_ADAM_BARB_, 0, 0, 1, 1 Z_ADAM_CORA_, 0, 0, 1, 1 Z_ADAM_DAWN_, 0, 0, 1, 1 AM_ADAM_, 0, 0, 1e+030, 3 AM_BOB_, 0, 0, 1e+030, 3 AM_CARL_, 0, 0, 1e+030, 3 AM_DON_, 0, 0, 1e+030, 3 AW_AVA_, 0, 0, 1e+030, 3 AW_BARB_, 0, 0, 1e+030, 3 AW_CORA_, 0, 0, 1e+030, 3 AW_DAWN_, 0, 0, 1e+030, 3 PTOTALM, 0, 0, 1e+030, 3 PTOTALW, 0, 0, 1e+030, 3 ; !CStable4x4S ROW, RHS, TYPER = ASGM_BOB_, 1, 0 ASGM_CARL_, 1, 0 ASGM_DON_, 1, 0 ASGW_AVA_, 1, 0 ASGW_BARB_, 1, 0 ASGW_CORA_, 1, 0 ASGW_DAWN_, 1, 0 NOELOPE_ADAM_AVA_, 1, -1 NOELOPE_ADAM_BARB_, 1, -1 NOELOPE_ADAM_CORA_, 1, -1 NOELOPE_ADAM_DAWN_, 1, -1 NOELOPE_BOB_AVA_, 1, -1 NOELOPE_BOB_BARB_, 1, -1 NOELOPE_BOB_CORA_, 1, -1 NOELOPE_BOB_DAWN_, 1, -1 NOELOPE_CARL_AVA_, 1, -1 NOELOPE_CARL_BARB_, 1, -1 NOELOPE_CARL_CORA_, 1, -1 NOELOPE_CARL_DAWN_, 1, -1 NOELOPE_DON_AVA_, 1, -1 NOELOPE_DON_BARB_, 1, -1 NOELOPE_DON_CORA_, 1, -1 NOELOPE_DON_DAWN_, 1, -1 _25, 0, 0 _26, 0, 0 _27, 0, 0 _28, 0, 0 _29, 0, 0 _30, 0, 0 _31, 0, 0 _32, 0, 0 _33, 0, 0 _34, 0, 0 _35, 0, 0 ASGM_ADAM_, 1, 0 ; !CStable4x4S NONZ, COEF = _35, PTOTALA, 1 ASGM_BOB_, Z_BOB_AVA_, 1 ASGW_AVA_, Z_BOB_AVA_, 1 NOELOPE_ADAM_AVA_, Z_BOB_AVA_, 1 NOELOPE_BOB_AVA_, Z_BOB_AVA_, 1 NOELOPE_BOB_CORA_, Z_BOB_AVA_, 1 NOELOPE_BOB_DAWN_, Z_BOB_AVA_, 1 _26, Z_BOB_AVA_, -2 _29, Z_BOB_AVA_, -3 _33, Z_BOB_AVA_, -2 _34, Z_BOB_AVA_, -3 _35, Z_BOB_AVA_, -5 ASGM_BOB_, Z_BOB_BARB_, 1 ASGW_BARB_, Z_BOB_BARB_, 1 NOELOPE_BOB_AVA_, Z_BOB_BARB_, 1 NOELOPE_BOB_BARB_, Z_BOB_BARB_, 1 NOELOPE_BOB_CORA_, Z_BOB_BARB_, 1 NOELOPE_BOB_DAWN_, Z_BOB_BARB_, 1 _26, Z_BOB_BARB_, -1 _30, Z_BOB_BARB_, -4 _33, Z_BOB_BARB_, -1 _34, Z_BOB_BARB_, -4 _35, Z_BOB_BARB_, -5 ASGM_BOB_, Z_BOB_CORA_, 1 ASGW_CORA_, Z_BOB_CORA_, 1 NOELOPE_ADAM_CORA_, Z_BOB_CORA_, 1 NOELOPE_BOB_CORA_, Z_BOB_CORA_, 1 NOELOPE_CARL_CORA_, Z_BOB_CORA_, 1 NOELOPE_DON_CORA_, Z_BOB_CORA_, 1 _26, Z_BOB_CORA_, -4 _31, Z_BOB_CORA_, -1 _33, Z_BOB_CORA_, -4 _34, Z_BOB_CORA_, -1 _35, Z_BOB_CORA_, -5 ASGM_BOB_, Z_BOB_DAWN_, 1 ASGW_DAWN_, Z_BOB_DAWN_, 1 NOELOPE_BOB_CORA_, Z_BOB_DAWN_, 1 NOELOPE_BOB_DAWN_, Z_BOB_DAWN_, 1 NOELOPE_CARL_DAWN_, Z_BOB_DAWN_, 1 NOELOPE_DON_DAWN_, Z_BOB_DAWN_, 1 _26, Z_BOB_DAWN_, -3 _32, Z_BOB_DAWN_, -2 _33, Z_BOB_DAWN_, -3 _34, Z_BOB_DAWN_, -2 _35, Z_BOB_DAWN_, -5 ASGM_CARL_, Z_CARL_AVA_, 1 ASGW_AVA_, Z_CARL_AVA_, 1 NOELOPE_ADAM_AVA_, Z_CARL_AVA_, 1 NOELOPE_BOB_AVA_, Z_CARL_AVA_, 1 NOELOPE_CARL_AVA_, Z_CARL_AVA_, 1 NOELOPE_CARL_BARB_, Z_CARL_AVA_, 1 _27, Z_CARL_AVA_, -3 _29, Z_CARL_AVA_, -2 _33, Z_CARL_AVA_, -3 _34, Z_CARL_AVA_, -2 _35, Z_CARL_AVA_, -5 ASGM_CARL_, Z_CARL_BARB_, 1 ASGW_BARB_, Z_CARL_BARB_, 1 NOELOPE_ADAM_BARB_, Z_CARL_BARB_, 1 NOELOPE_BOB_BARB_, Z_CARL_BARB_, 1 NOELOPE_CARL_BARB_, Z_CARL_BARB_, 1 NOELOPE_DON_BARB_, Z_CARL_BARB_, 1 _27, Z_CARL_BARB_, -4 _30, Z_CARL_BARB_, -1 _33, Z_CARL_BARB_, -4 _34, Z_CARL_BARB_, -1 _35, Z_CARL_BARB_, -5 ASGM_CARL_, Z_CARL_CORA_, 1 ASGW_CORA_, Z_CARL_CORA_, 1 NOELOPE_CARL_AVA_, Z_CARL_CORA_, 1 NOELOPE_CARL_BARB_, Z_CARL_CORA_, 1 NOELOPE_CARL_CORA_, Z_CARL_CORA_, 1 NOELOPE_CARL_DAWN_, Z_CARL_CORA_, 1 _27, Z_CARL_CORA_, -1 _31, Z_CARL_CORA_, -4 _33, Z_CARL_CORA_, -1 _34, Z_CARL_CORA_, -4 _35, Z_CARL_CORA_, -5 ASGM_CARL_, Z_CARL_DAWN_, 1 ASGW_DAWN_, Z_CARL_DAWN_, 1 NOELOPE_CARL_AVA_, Z_CARL_DAWN_, 1 NOELOPE_CARL_BARB_, Z_CARL_DAWN_, 1 NOELOPE_CARL_DAWN_, Z_CARL_DAWN_, 1 NOELOPE_DON_DAWN_, Z_CARL_DAWN_, 1 _27, Z_CARL_DAWN_, -2 _32, Z_CARL_DAWN_, -3 _33, Z_CARL_DAWN_, -2 _34, Z_CARL_DAWN_, -3 _35, Z_CARL_DAWN_, -5 ASGM_DON_, Z_DON_AVA_, 1 ASGW_AVA_, Z_DON_AVA_, 1 NOELOPE_ADAM_AVA_, Z_DON_AVA_, 1 NOELOPE_BOB_AVA_, Z_DON_AVA_, 1 NOELOPE_CARL_AVA_, Z_DON_AVA_, 1 NOELOPE_DON_AVA_, Z_DON_AVA_, 1 _28, Z_DON_AVA_, -4 _29, Z_DON_AVA_, -1 _33, Z_DON_AVA_, -4 _34, Z_DON_AVA_, -1 _35, Z_DON_AVA_, -5 ASGM_DON_, Z_DON_BARB_, 1 ASGW_BARB_, Z_DON_BARB_, 1 NOELOPE_ADAM_BARB_, Z_DON_BARB_, 1 NOELOPE_BOB_BARB_, Z_DON_BARB_, 1 NOELOPE_DON_AVA_, Z_DON_BARB_, 1 NOELOPE_DON_BARB_, Z_DON_BARB_, 1 _28, Z_DON_BARB_, -3 _30, Z_DON_BARB_, -2 _33, Z_DON_BARB_, -3 _34, Z_DON_BARB_, -2 _35, Z_DON_BARB_, -5 ASGM_DON_, Z_DON_CORA_, 1 ASGW_CORA_, Z_DON_CORA_, 1 NOELOPE_CARL_CORA_, Z_DON_CORA_, 1 NOELOPE_DON_AVA_, Z_DON_CORA_, 1 NOELOPE_DON_BARB_, Z_DON_CORA_, 1 NOELOPE_DON_CORA_, Z_DON_CORA_, 1 _28, Z_DON_CORA_, -2 _31, Z_DON_CORA_, -3 _33, Z_DON_CORA_, -2 _34, Z_DON_CORA_, -3 _35, Z_DON_CORA_, -5 ASGM_DON_, Z_DON_DAWN_, 1 ASGW_DAWN_, Z_DON_DAWN_, 1 NOELOPE_DON_AVA_, Z_DON_DAWN_, 1 NOELOPE_DON_BARB_, Z_DON_DAWN_, 1 NOELOPE_DON_CORA_, Z_DON_DAWN_, 1 NOELOPE_DON_DAWN_, Z_DON_DAWN_, 1 _28, Z_DON_DAWN_, -1 _32, Z_DON_DAWN_, -4 _33, Z_DON_DAWN_, -1 _34, Z_DON_DAWN_, -4 _35, Z_DON_DAWN_, -5 ASGW_AVA_, Z_ADAM_AVA_, 1 NOELOPE_ADAM_AVA_, Z_ADAM_AVA_, 1 NOELOPE_ADAM_BARB_, Z_ADAM_AVA_, 1 NOELOPE_ADAM_CORA_, Z_ADAM_AVA_, 1 NOELOPE_ADAM_DAWN_, Z_ADAM_AVA_, 1 _25, Z_ADAM_AVA_, -1 _29, Z_ADAM_AVA_, -4 _33, Z_ADAM_AVA_, -1 _34, Z_ADAM_AVA_, -4 _35, Z_ADAM_AVA_, -5 ASGM_ADAM_, Z_ADAM_AVA_, 1 ASGW_BARB_, Z_ADAM_BARB_, 1 NOELOPE_ADAM_BARB_, Z_ADAM_BARB_, 1 NOELOPE_ADAM_CORA_, Z_ADAM_BARB_, 1 NOELOPE_ADAM_DAWN_, Z_ADAM_BARB_, 1 NOELOPE_BOB_BARB_, Z_ADAM_BARB_, 1 _25, Z_ADAM_BARB_, -2 _30, Z_ADAM_BARB_, -3 _33, Z_ADAM_BARB_, -2 _34, Z_ADAM_BARB_, -3 _35, Z_ADAM_BARB_, -5 ASGM_ADAM_, Z_ADAM_BARB_, 1 ASGW_CORA_, Z_ADAM_CORA_, 1 NOELOPE_ADAM_CORA_, Z_ADAM_CORA_, 1 NOELOPE_ADAM_DAWN_, Z_ADAM_CORA_, 1 NOELOPE_CARL_CORA_, Z_ADAM_CORA_, 1 NOELOPE_DON_CORA_, Z_ADAM_CORA_, 1 _25, Z_ADAM_CORA_, -3 _31, Z_ADAM_CORA_, -2 _33, Z_ADAM_CORA_, -3 _34, Z_ADAM_CORA_, -2 _35, Z_ADAM_CORA_, -5 ASGM_ADAM_, Z_ADAM_CORA_, 1 ASGW_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_BOB_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_CARL_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_DON_DAWN_, Z_ADAM_DAWN_, 1 _25, Z_ADAM_DAWN_, -4 _32, Z_ADAM_DAWN_, -1 _33, Z_ADAM_DAWN_, -4 _34, Z_ADAM_DAWN_, -1 _35, Z_ADAM_DAWN_, -5 ASGM_ADAM_, Z_ADAM_DAWN_, 1 _25, AM_ADAM_, 1 _26, AM_BOB_, 1 _27, AM_CARL_, 1 _28, AM_DON_, 1 _29, AW_AVA_, 1 _30, AW_BARB_, 1 _31, AW_CORA_, 1 _32, AW_DAWN_, 1 _33, PTOTALM, 1 _34, PTOTALW, 1 ; ! Case Stable4x4; ! This is a Stable Marriage example with a number of stable solutions, that has some inequality constraints to measure the worst treatment of any party, so the feasible region is unbounded and has lots of unbounded extreme rays; !CStable4x4 !CStable4x4 NDXP = 26086;! Number of random directions to try!CStable4x4 NSLIST = 300;!CStable4x4 SLIST = 1..NSLIST;!CStable4x4 AltOpt = 1;!CStable4x4 COL, OBJ, SLB, SUB, TYPEC = Z_BOB_ALICE, 0, 0, 1, 1 Z_BOB_BARB, 0, 0, 1, 1 Z_BOB_CARMEN, 0, 0, 1, 1 Z_BOB_DOLLY, 0, 0, 1, 1 Z_CHUCK_ALICE, 0, 0, 1, 1 Z_CHUCK_BARB, 0, 0, 1, 1 Z_CHUCK_CARMEN, 0, 0, 1, 1 Z_CHUCK_DOLLY, 0, 0, 1, 1 Z_DON_ALICE, 0, 0, 1, 1 Z_DON_BARB, 0, 0, 1, 1 Z_DON_CARMEN, 0, 0, 1, 1 Z_DON_DOLLY, 0, 0, 1, 1 Z_ADAM_ALICE, 0, 0, 1, 1 Z_ADAM_BARB, 0, 0, 1, 1 Z_ADAM_CARMEN, 0, 0, 1, 1 Z_ADAM_DOLLY, 0, 0, 1, 1 AM_ADAM, 0, 0, 1e+030, 3 PWORSTM, 0, 0, 1e+030, 3 AM_BOB, 0, 0, 1e+030, 3 AM_CHUCK, 0, 0, 1e+030, 3 AM_DON, 0, 0, 1e+030, 3 AW_ALICE, 0, 0, 1e+030, 3 PWORSTW, 0, 0, 1e+030, 3 AW_BARB, 0, 0, 1e+030, 3 AW_CARMEN, 0, 0, 1e+030, 3 AW_DOLLY, 0, 0, 1e+030, 3 PTOTALM, 0, 0, 1e+030, 3 PTOTALW, 0, 0, 1e+030, 3 PTOTALA, 0, 0, 1e+030, 3 PWORSTA, 0, 0, 1e+030, 3 ; !CStable4x4 ROW, RHS, TYPER = _2, 1, 0 _3, 1, 0 _4, 1, 0 _5, 1, 0 _6, 1, 0 _7, 1, 0 _8, 1, 0 NOELOPE_ADAM_ALICE, 1, -1 NOELOPE_ADAM_BARB, 1, -1 NOELOPE_ADAM_CARMEN, 1, -1 NOELOPE_ADAM_DOLLY, 1, -1 NOELOPE_BOB_ALICE, 1, -1 NOELOPE_BOB_BARB, 1, -1 NOELOPE_BOB_CARMEN, 1, -1 NOELOPE_BOB_DOLLY, 1, -1 NOELOPE_CHUCK_ALICE, 1, -1 NOELOPE_CHUCK_BARB, 1, -1 NOELOPE_CHUCK_CARMEN, 1, -1 NOELOPE_CHUCK_DOLLY, 1, -1 NOELOPE_DON_ALICE, 1, -1 NOELOPE_DON_BARB, 1, -1 NOELOPE_DON_CARMEN, 1, -1 NOELOPE_DON_DOLLY, 1, -1 _25, 0, 0 _26, 0, -1 _27, 0, 0 _28, 0, -1 _29, 0, 0 _30, 0, -1 _31, 0, 0 _32, 0, -1 _33, 0, 0 _34, 0, -1 _35, 0, 0 _36, 0, -1 _37, 0, 0 _38, 0, -1 _39, 0, 0 _40, 0, -1 _41, 0, 0 _42, 0, 0 _43, 0, 0 _44, 0, -1 _45, 0, -1 _1, 1, 0 ; !CStable4x4 NONZ, COEF = _2, Z_BOB_ALICE, 1 _5, Z_BOB_ALICE, 1 NOELOPE_ADAM_ALICE, Z_BOB_ALICE, 1 NOELOPE_BOB_ALICE, Z_BOB_ALICE, 1 NOELOPE_BOB_CARMEN, Z_BOB_ALICE, 1 NOELOPE_BOB_DOLLY, Z_BOB_ALICE, 1 _27, Z_BOB_ALICE, -2 _33, Z_BOB_ALICE, -3 _41, Z_BOB_ALICE, -2 _42, Z_BOB_ALICE, -3 _43, Z_BOB_ALICE, -5 _2, Z_BOB_BARB, 1 _6, Z_BOB_BARB, 1 NOELOPE_BOB_ALICE, Z_BOB_BARB, 1 NOELOPE_BOB_BARB, Z_BOB_BARB, 1 NOELOPE_BOB_CARMEN, Z_BOB_BARB, 1 NOELOPE_BOB_DOLLY, Z_BOB_BARB, 1 _27, Z_BOB_BARB, -1 _35, Z_BOB_BARB, -4 _41, Z_BOB_BARB, -1 _42, Z_BOB_BARB, -4 _43, Z_BOB_BARB, -5 _2, Z_BOB_CARMEN, 1 _7, Z_BOB_CARMEN, 1 NOELOPE_ADAM_CARMEN, Z_BOB_CARMEN, 1 NOELOPE_BOB_CARMEN, Z_BOB_CARMEN, 1 NOELOPE_CHUCK_CARMEN, Z_BOB_CARMEN, 1 NOELOPE_DON_CARMEN, Z_BOB_CARMEN, 1 _27, Z_BOB_CARMEN, -4 _37, Z_BOB_CARMEN, -1 _41, Z_BOB_CARMEN, -4 _42, Z_BOB_CARMEN, -1 _43, Z_BOB_CARMEN, -5 _2, Z_BOB_DOLLY, 1 _8, Z_BOB_DOLLY, 1 NOELOPE_BOB_CARMEN, Z_BOB_DOLLY, 1 NOELOPE_BOB_DOLLY, Z_BOB_DOLLY, 1 NOELOPE_CHUCK_DOLLY, Z_BOB_DOLLY, 1 NOELOPE_DON_DOLLY, Z_BOB_DOLLY, 1 _27, Z_BOB_DOLLY, -3 _39, Z_BOB_DOLLY, -2 _41, Z_BOB_DOLLY, -3 _42, Z_BOB_DOLLY, -2 _43, Z_BOB_DOLLY, -5 _3, Z_CHUCK_ALICE, 1 _5, Z_CHUCK_ALICE, 1 NOELOPE_ADAM_ALICE, Z_CHUCK_ALICE, 1 NOELOPE_BOB_ALICE, Z_CHUCK_ALICE, 1 NOELOPE_CHUCK_ALICE, Z_CHUCK_ALICE, 1 NOELOPE_CHUCK_BARB, Z_CHUCK_ALICE, 1 _29, Z_CHUCK_ALICE, -3 _33, Z_CHUCK_ALICE, -2 _41, Z_CHUCK_ALICE, -3 _42, Z_CHUCK_ALICE, -2 _43, Z_CHUCK_ALICE, -5 _3, Z_CHUCK_BARB, 1 _6, Z_CHUCK_BARB, 1 NOELOPE_ADAM_BARB, Z_CHUCK_BARB, 1 NOELOPE_BOB_BARB, Z_CHUCK_BARB, 1 NOELOPE_CHUCK_BARB, Z_CHUCK_BARB, 1 NOELOPE_DON_BARB, Z_CHUCK_BARB, 1 _29, Z_CHUCK_BARB, -4 _35, Z_CHUCK_BARB, -1 _41, Z_CHUCK_BARB, -4 _42, Z_CHUCK_BARB, -1 _43, Z_CHUCK_BARB, -5 _3, Z_CHUCK_CARMEN, 1 _7, Z_CHUCK_CARMEN, 1 NOELOPE_CHUCK_ALICE, Z_CHUCK_CARMEN, 1 NOELOPE_CHUCK_BARB, Z_CHUCK_CARMEN, 1 NOELOPE_CHUCK_CARMEN, Z_CHUCK_CARMEN, 1 NOELOPE_CHUCK_DOLLY, Z_CHUCK_CARMEN, 1 _29, Z_CHUCK_CARMEN, -1 _37, Z_CHUCK_CARMEN, -4 _41, Z_CHUCK_CARMEN, -1 _42, Z_CHUCK_CARMEN, -4 _43, Z_CHUCK_CARMEN, -5 _3, Z_CHUCK_DOLLY, 1 _8, Z_CHUCK_DOLLY, 1 NOELOPE_CHUCK_ALICE, Z_CHUCK_DOLLY, 1 NOELOPE_CHUCK_BARB, Z_CHUCK_DOLLY, 1 NOELOPE_CHUCK_DOLLY, Z_CHUCK_DOLLY, 1 NOELOPE_DON_DOLLY, Z_CHUCK_DOLLY, 1 _29, Z_CHUCK_DOLLY, -2 _39, Z_CHUCK_DOLLY, -3 _41, Z_CHUCK_DOLLY, -2 _42, Z_CHUCK_DOLLY, -3 _43, Z_CHUCK_DOLLY, -5 _4, Z_DON_ALICE, 1 _5, Z_DON_ALICE, 1 NOELOPE_ADAM_ALICE, Z_DON_ALICE, 1 NOELOPE_BOB_ALICE, Z_DON_ALICE, 1 NOELOPE_CHUCK_ALICE, Z_DON_ALICE, 1 NOELOPE_DON_ALICE, Z_DON_ALICE, 1 _31, Z_DON_ALICE, -4 _33, Z_DON_ALICE, -1 _41, Z_DON_ALICE, -4 _42, Z_DON_ALICE, -1 _43, Z_DON_ALICE, -5 _4, Z_DON_BARB, 1 _6, Z_DON_BARB, 1 NOELOPE_ADAM_BARB, Z_DON_BARB, 1 NOELOPE_BOB_BARB, Z_DON_BARB, 1 NOELOPE_DON_ALICE, Z_DON_BARB, 1 NOELOPE_DON_BARB, Z_DON_BARB, 1 _31, Z_DON_BARB, -3 _35, Z_DON_BARB, -2 _41, Z_DON_BARB, -3 _42, Z_DON_BARB, -2 _43, Z_DON_BARB, -5 _4, Z_DON_CARMEN, 1 _7, Z_DON_CARMEN, 1 NOELOPE_CHUCK_CARMEN, Z_DON_CARMEN, 1 NOELOPE_DON_ALICE, Z_DON_CARMEN, 1 NOELOPE_DON_BARB, Z_DON_CARMEN, 1 NOELOPE_DON_CARMEN, Z_DON_CARMEN, 1 _31, Z_DON_CARMEN, -2 _37, Z_DON_CARMEN, -3 _41, Z_DON_CARMEN, -2 _42, Z_DON_CARMEN, -3 _43, Z_DON_CARMEN, -5 _4, Z_DON_DOLLY, 1 _8, Z_DON_DOLLY, 1 NOELOPE_DON_ALICE, Z_DON_DOLLY, 1 NOELOPE_DON_BARB, Z_DON_DOLLY, 1 NOELOPE_DON_CARMEN, Z_DON_DOLLY, 1 NOELOPE_DON_DOLLY, Z_DON_DOLLY, 1 _31, Z_DON_DOLLY, -1 _39, Z_DON_DOLLY, -4 _41, Z_DON_DOLLY, -1 _42, Z_DON_DOLLY, -4 _43, Z_DON_DOLLY, -5 _5, Z_ADAM_ALICE, 1 NOELOPE_ADAM_ALICE, Z_ADAM_ALICE, 1 NOELOPE_ADAM_BARB, Z_ADAM_ALICE, 1 NOELOPE_ADAM_CARMEN, Z_ADAM_ALICE, 1 NOELOPE_ADAM_DOLLY, Z_ADAM_ALICE, 1 _25, Z_ADAM_ALICE, -1 _33, Z_ADAM_ALICE, -4 _41, Z_ADAM_ALICE, -1 _42, Z_ADAM_ALICE, -4 _43, Z_ADAM_ALICE, -5 _1, Z_ADAM_ALICE, 1 _6, Z_ADAM_BARB, 1 NOELOPE_ADAM_BARB, Z_ADAM_BARB, 1 NOELOPE_ADAM_CARMEN, Z_ADAM_BARB, 1 NOELOPE_ADAM_DOLLY, Z_ADAM_BARB, 1 NOELOPE_BOB_BARB, Z_ADAM_BARB, 1 _25, Z_ADAM_BARB, -2 _35, Z_ADAM_BARB, -3 _41, Z_ADAM_BARB, -2 _42, Z_ADAM_BARB, -3 _43, Z_ADAM_BARB, -5 _1, Z_ADAM_BARB, 1 _7, Z_ADAM_CARMEN, 1 NOELOPE_ADAM_CARMEN, Z_ADAM_CARMEN, 1 NOELOPE_ADAM_DOLLY, Z_ADAM_CARMEN, 1 NOELOPE_CHUCK_CARMEN, Z_ADAM_CARMEN, 1 NOELOPE_DON_CARMEN, Z_ADAM_CARMEN, 1 _25, Z_ADAM_CARMEN, -3 _37, Z_ADAM_CARMEN, -2 _41, Z_ADAM_CARMEN, -3 _42, Z_ADAM_CARMEN, -2 _43, Z_ADAM_CARMEN, -5 _1, Z_ADAM_CARMEN, 1 _8, Z_ADAM_DOLLY, 1 NOELOPE_ADAM_DOLLY, Z_ADAM_DOLLY, 1 NOELOPE_BOB_DOLLY, Z_ADAM_DOLLY, 1 NOELOPE_CHUCK_DOLLY, Z_ADAM_DOLLY, 1 NOELOPE_DON_DOLLY, Z_ADAM_DOLLY, 1 _25, Z_ADAM_DOLLY, -4 _39, Z_ADAM_DOLLY, -1 _41, Z_ADAM_DOLLY, -4 _42, Z_ADAM_DOLLY, -1 _43, Z_ADAM_DOLLY, -5 _1, Z_ADAM_DOLLY, 1 _25, AM_ADAM, 1 _26, AM_ADAM, -1 _26, PWORSTM, 1 _28, PWORSTM, 1 _30, PWORSTM, 1 _32, PWORSTM, 1 _44, PWORSTM, -1 _27, AM_BOB, 1 _28, AM_BOB, -1 _29, AM_CHUCK, 1 _30, AM_CHUCK, -1 _31, AM_DON, 1 _32, AM_DON, -1 _33, AW_ALICE, 1 _34, AW_ALICE, -1 _34, PWORSTW, 1 _36, PWORSTW, 1 _38, PWORSTW, 1 _40, PWORSTW, 1 _45, PWORSTW, -1 _35, AW_BARB, 1 _36, AW_BARB, -1 _37, AW_CARMEN, 1 _38, AW_CARMEN, -1 _39, AW_DOLLY, 1 _40, AW_DOLLY, -1 _41, PTOTALM, 1 _42, PTOTALW, 1 _43, PTOTALA, 1 _44, PWORSTA, 1 _45, PWORSTA, 1 ; ! This is a 10x10 simple Stable Marriage problem with 1 unique optimal solution that minimizes the total preference1 awarded and 3 feasible stable solutions, where the allocations to MAN and WOMAN are: PTOTALM = 31 PTOTALW = 28 (59) PTOTALM = 26 PTOTALW = 37 (63) PTOTALM = 23 PTOTALW = 43 (66) ; !CStable10x10 NDXP = 20;!CStable10x10 NSLIST = 300;!CStable10x10 SLIST = 1..NSLIST;!CStable10x10 AltOpt = 0; !CStable10x10 COL, OBJ, SLB, SUB, TYPEC = PTOTALA, 1, 0, 1e+030, 3 Z_BOB_ALICE_, 0, 0, 1, 1 Z_BOB_BARB_, 0, 0, 1, 1 Z_BOB_CARMEN_, 0, 0, 1, 1 Z_BOB_DAWN_, 0, 0, 1, 1 Z_BOB_EVE_, 0, 0, 1, 1 Z_BOB_FANNY_, 0, 0, 1, 1 Z_BOB_GRACE_, 0, 0, 1, 1 Z_BOB_HELEN_, 0, 0, 1, 1 Z_BOB_IRENE_, 0, 0, 1, 1 Z_BOB_JILL_, 0, 0, 1, 1 Z_CARL_ALICE_, 0, 0, 1, 1 Z_CARL_BARB_, 0, 0, 1, 1 Z_CARL_CARMEN_, 0, 0, 1, 1 Z_CARL_DAWN_, 0, 0, 1, 1 Z_CARL_EVE_, 0, 0, 1, 1 Z_CARL_FANNY_, 0, 0, 1, 1 Z_CARL_GRACE_, 0, 0, 1, 1 Z_CARL_HELEN_, 0, 0, 1, 1 Z_CARL_IRENE_, 0, 0, 1, 1 Z_CARL_JILL_, 0, 0, 1, 1 Z_DON_ALICE_, 0, 0, 1, 1 Z_DON_BARB_, 0, 0, 1, 1 Z_DON_CARMEN_, 0, 0, 1, 1 Z_DON_DAWN_, 0, 0, 1, 1 Z_DON_EVE_, 0, 0, 1, 1 Z_DON_FANNY_, 0, 0, 1, 1 Z_DON_GRACE_, 0, 0, 1, 1 Z_DON_HELEN_, 0, 0, 1, 1 Z_DON_IRENE_, 0, 0, 1, 1 Z_DON_JILL_, 0, 0, 1, 1 Z_ERIC_ALICE_, 0, 0, 1, 1 Z_ERIC_BARB_, 0, 0, 1, 1 Z_ERIC_CARMEN_, 0, 0, 1, 1 Z_ERIC_DAWN_, 0, 0, 1, 1 Z_ERIC_EVE_, 0, 0, 1, 1 Z_ERIC_FANNY_, 0, 0, 1, 1 Z_ERIC_GRACE_, 0, 0, 1, 1 Z_ERIC_HELEN_, 0, 0, 1, 1 Z_ERIC_IRENE_, 0, 0, 1, 1 Z_ERIC_JILL_, 0, 0, 1, 1 Z_FRED_ALICE_, 0, 0, 1, 1 Z_FRED_BARB_, 0, 0, 1, 1 Z_FRED_CARMEN_, 0, 0, 1, 1 Z_FRED_DAWN_, 0, 0, 1, 1 Z_FRED_EVE_, 0, 0, 1, 1 Z_FRED_FANNY_, 0, 0, 1, 1 Z_FRED_GRACE_, 0, 0, 1, 1 Z_FRED_HELEN_, 0, 0, 1, 1 Z_FRED_IRENE_, 0, 0, 1, 1 Z_FRED_JILL_, 0, 0, 1, 1 Z_GUS_ALICE_, 0, 0, 1, 1 Z_GUS_BARB_, 0, 0, 1, 1 Z_GUS_CARMEN_, 0, 0, 1, 1 Z_GUS_DAWN_, 0, 0, 1, 1 Z_GUS_EVE_, 0, 0, 1, 1 Z_GUS_FANNY_, 0, 0, 1, 1 Z_GUS_GRACE_, 0, 0, 1, 1 Z_GUS_HELEN_, 0, 0, 1, 1 Z_GUS_IRENE_, 0, 0, 1, 1 Z_GUS_JILL_, 0, 0, 1, 1 Z_HANK_ALICE_, 0, 0, 1, 1 Z_HANK_BARB_, 0, 0, 1, 1 Z_HANK_CARMEN_, 0, 0, 1, 1 Z_HANK_DAWN_, 0, 0, 1, 1 Z_HANK_EVE_, 0, 0, 1, 1 Z_HANK_FANNY_, 0, 0, 1, 1 Z_HANK_GRACE_, 0, 0, 1, 1 Z_HANK_HELEN_, 0, 0, 1, 1 Z_HANK_IRENE_, 0, 0, 1, 1 Z_HANK_JILL_, 0, 0, 1, 1 Z_IRV_ALICE_, 0, 0, 1, 1 Z_IRV_BARB_, 0, 0, 1, 1 Z_IRV_CARMEN_, 0, 0, 1, 1 Z_IRV_DAWN_, 0, 0, 1, 1 Z_IRV_EVE_, 0, 0, 1, 1 Z_IRV_FANNY_, 0, 0, 1, 1 Z_IRV_GRACE_, 0, 0, 1, 1 Z_IRV_HELEN_, 0, 0, 1, 1 Z_IRV_IRENE_, 0, 0, 1, 1 Z_IRV_JILL_, 0, 0, 1, 1 Z_JACK_ALICE_, 0, 0, 1, 1 Z_JACK_BARB_, 0, 0, 1, 1 Z_JACK_CARMEN_, 0, 0, 1, 1 Z_JACK_DAWN_, 0, 0, 1, 1 Z_JACK_EVE_, 0, 0, 1, 1 Z_JACK_FANNY_, 0, 0, 1, 1 Z_JACK_GRACE_, 0, 0, 1, 1 Z_JACK_HELEN_, 0, 0, 1, 1 Z_JACK_IRENE_, 0, 0, 1, 1 Z_JACK_JILL_, 0, 0, 1, 1 Z_ADAM_ALICE_, 0, 0, 1, 1 Z_ADAM_BARB_, 0, 0, 1, 1 Z_ADAM_CARMEN_, 0, 0, 1, 1 Z_ADAM_DAWN_, 0, 0, 1, 1 Z_ADAM_EVE_, 0, 0, 1, 1 Z_ADAM_FANNY_, 0, 0, 1, 1 Z_ADAM_GRACE_, 0, 0, 1, 1 Z_ADAM_HELEN_, 0, 0, 1, 1 Z_ADAM_IRENE_, 0, 0, 1, 1 Z_ADAM_JILL_, 0, 0, 1, 1 AM_ADAM_, 0, 0, 1e+030, 3 AM_BOB_, 0, 0, 1e+030, 3 AM_CARL_, 0, 0, 1e+030, 3 AM_DON_, 0, 0, 1e+030, 3 AM_ERIC_, 0, 0, 1e+030, 3 AM_FRED_, 0, 0, 1e+030, 3 AM_GUS_, 0, 0, 1e+030, 3 AM_HANK_, 0, 0, 1e+030, 3 AM_IRV_, 0, 0, 1e+030, 3 AM_JACK_, 0, 0, 1e+030, 3 AW_ALICE_, 0, 0, 1e+030, 3 AW_BARB_, 0, 0, 1e+030, 3 AW_CARMEN_, 0, 0, 1e+030, 3 AW_DAWN_, 0, 0, 1e+030, 3 AW_EVE_, 0, 0, 1e+030, 3 AW_FANNY_, 0, 0, 1e+030, 3 AW_GRACE_, 0, 0, 1e+030, 3 AW_HELEN_, 0, 0, 1e+030, 3 AW_IRENE_, 0, 0, 1e+030, 3 AW_JILL_, 0, 0, 1e+030, 3 PTOTALM, 0, 0, 1e+030, 3 PTOTALW, 0, 0, 1e+030, 3 ; !CStable10x10 ROW, RHS, TYPER = ASGM_BOB_, 1, 0 ASGM_CARL_, 1, 0 ASGM_DON_, 1, 0 ASGM_ERIC_, 1, 0 ASGM_FRED_, 1, 0 ASGM_GUS_, 1, 0 ASGM_HANK_, 1, 0 ASGM_IRV_, 1, 0 ASGM_JACK_, 1, 0 ASGW_ALICE_, 1, 0 ASGW_BARB_, 1, 0 ASGW_CARMEN_, 1, 0 ASGW_DAWN_, 1, 0 ASGW_EVE_, 1, 0 ASGW_FANNY_, 1, 0 ASGW_GRACE_, 1, 0 ASGW_HELEN_, 1, 0 ASGW_IRENE_, 1, 0 ASGW_JILL_, 1, 0 NOELOPE_ADAM_ALICE_, 1, -1 NOELOPE_ADAM_BARB_, 1, -1 NOELOPE_ADAM_CARMEN_, 1, -1 NOELOPE_ADAM_DAWN_, 1, -1 NOELOPE_ADAM_EVE_, 1, -1 NOELOPE_ADAM_FANNY_, 1, -1 NOELOPE_ADAM_GRACE_, 1, -1 NOELOPE_ADAM_HELEN_, 1, -1 NOELOPE_ADAM_IRENE_, 1, -1 NOELOPE_ADAM_JILL_, 1, -1 NOELOPE_BOB_ALICE_, 1, -1 NOELOPE_BOB_BARB_, 1, -1 NOELOPE_BOB_CARMEN_, 1, -1 NOELOPE_BOB_DAWN_, 1, -1 NOELOPE_BOB_EVE_, 1, -1 NOELOPE_BOB_FANNY_, 1, -1 NOELOPE_BOB_GRACE_, 1, -1 NOELOPE_BOB_HELEN_, 1, -1 NOELOPE_BOB_IRENE_, 1, -1 NOELOPE_BOB_JILL_, 1, -1 NOELOPE_CARL_ALICE_, 1, -1 NOELOPE_CARL_BARB_, 1, -1 NOELOPE_CARL_CARMEN_, 1, -1 NOELOPE_CARL_DAWN_, 1, -1 NOELOPE_CARL_EVE_, 1, -1 NOELOPE_CARL_FANNY_, 1, -1 NOELOPE_CARL_GRACE_, 1, -1 NOELOPE_CARL_HELEN_, 1, -1 NOELOPE_CARL_IRENE_, 1, -1 NOELOPE_CARL_JILL_, 1, -1 NOELOPE_DON_ALICE_, 1, -1 NOELOPE_DON_BARB_, 1, -1 NOELOPE_DON_CARMEN_, 1, -1 NOELOPE_DON_DAWN_, 1, -1 NOELOPE_DON_EVE_, 1, -1 NOELOPE_DON_FANNY_, 1, -1 NOELOPE_DON_GRACE_, 1, -1 NOELOPE_DON_HELEN_, 1, -1 NOELOPE_DON_IRENE_, 1, -1 NOELOPE_DON_JILL_, 1, -1 NOELOPE_ERIC_ALICE_, 1, -1 NOELOPE_ERIC_BARB_, 1, -1 NOELOPE_ERIC_CARMEN_, 1, -1 NOELOPE_ERIC_DAWN_, 1, -1 NOELOPE_ERIC_EVE_, 1, -1 NOELOPE_ERIC_FANNY_, 1, -1 NOELOPE_ERIC_GRACE_, 1, -1 NOELOPE_ERIC_HELEN_, 1, -1 NOELOPE_ERIC_IRENE_, 1, -1 NOELOPE_ERIC_JILL_, 1, -1 NOELOPE_FRED_ALICE_, 1, -1 NOELOPE_FRED_BARB_, 1, -1 NOELOPE_FRED_CARMEN_, 1, -1 NOELOPE_FRED_DAWN_, 1, -1 NOELOPE_FRED_EVE_, 1, -1 NOELOPE_FRED_FANNY_, 1, -1 NOELOPE_FRED_GRACE_, 1, -1 NOELOPE_FRED_HELEN_, 1, -1 NOELOPE_FRED_IRENE_, 1, -1 NOELOPE_FRED_JILL_, 1, -1 NOELOPE_GUS_ALICE_, 1, -1 NOELOPE_GUS_BARB_, 1, -1 NOELOPE_GUS_CARMEN_, 1, -1 NOELOPE_GUS_DAWN_, 1, -1 NOELOPE_GUS_EVE_, 1, -1 NOELOPE_GUS_FANNY_, 1, -1 NOELOPE_GUS_GRACE_, 1, -1 NOELOPE_GUS_HELEN_, 1, -1 NOELOPE_GUS_IRENE_, 1, -1 NOELOPE_GUS_JILL_, 1, -1 NOELOPE_HANK_ALICE_, 1, -1 NOELOPE_HANK_BARB_, 1, -1 NOELOPE_HANK_CARMEN_, 1, -1 NOELOPE_HANK_DAWN_, 1, -1 NOELOPE_HANK_EVE_, 1, -1 NOELOPE_HANK_FANNY_, 1, -1 NOELOPE_HANK_GRACE_, 1, -1 NOELOPE_HANK_HELEN_, 1, -1 NOELOPE_HANK_IRENE_, 1, -1 NOELOPE_HANK_JILL_, 1, -1 NOELOPE_IRV_ALICE_, 1, -1 NOELOPE_IRV_BARB_, 1, -1 NOELOPE_IRV_CARMEN_, 1, -1 NOELOPE_IRV_DAWN_, 1, -1 NOELOPE_IRV_EVE_, 1, -1 NOELOPE_IRV_FANNY_, 1, -1 NOELOPE_IRV_GRACE_, 1, -1 NOELOPE_IRV_HELEN_, 1, -1 NOELOPE_IRV_IRENE_, 1, -1 NOELOPE_IRV_JILL_, 1, -1 NOELOPE_JACK_ALICE_, 1, -1 NOELOPE_JACK_BARB_, 1, -1 NOELOPE_JACK_CARMEN_, 1, -1 NOELOPE_JACK_DAWN_, 1, -1 NOELOPE_JACK_EVE_, 1, -1 NOELOPE_JACK_FANNY_, 1, -1 NOELOPE_JACK_GRACE_, 1, -1 NOELOPE_JACK_HELEN_, 1, -1 NOELOPE_JACK_IRENE_, 1, -1 NOELOPE_JACK_JILL_, 1, -1 _121, 0, 0 _122, 0, 0 _123, 0, 0 _124, 0, 0 _125, 0, 0 _126, 0, 0 _127, 0, 0 _128, 0, 0 _129, 0, 0 _130, 0, 0 _131, 0, 0 _132, 0, 0 _133, 0, 0 _134, 0, 0 _135, 0, 0 _136, 0, 0 _137, 0, 0 _138, 0, 0 _139, 0, 0 _140, 0, 0 _141, 0, 0 _142, 0, 0 _143, 0, 0 ASGM_ADAM_, 1, 0 ; !CStable10x10 NONZ, COEF = _143, PTOTALA, 1 ASGM_BOB_, Z_BOB_ALICE_, 1 ASGW_ALICE_, Z_BOB_ALICE_, 1 NOELOPE_BOB_ALICE_, Z_BOB_ALICE_, 1 NOELOPE_BOB_FANNY_, Z_BOB_ALICE_, 1 _122, Z_BOB_ALICE_, -9 _131, Z_BOB_ALICE_, -10 _141, Z_BOB_ALICE_, -9 _142, Z_BOB_ALICE_, -10 _143, Z_BOB_ALICE_, -9.5 ASGM_BOB_, Z_BOB_BARB_, 1 ASGW_BARB_, Z_BOB_BARB_, 1 NOELOPE_BOB_ALICE_, Z_BOB_BARB_, 1 NOELOPE_BOB_BARB_, Z_BOB_BARB_, 1 NOELOPE_BOB_CARMEN_, Z_BOB_BARB_, 1 NOELOPE_BOB_DAWN_, Z_BOB_BARB_, 1 NOELOPE_BOB_EVE_, Z_BOB_BARB_, 1 NOELOPE_BOB_FANNY_, Z_BOB_BARB_, 1 NOELOPE_BOB_GRACE_, Z_BOB_BARB_, 1 NOELOPE_BOB_HELEN_, Z_BOB_BARB_, 1 NOELOPE_BOB_IRENE_, Z_BOB_BARB_, 1 NOELOPE_BOB_JILL_, Z_BOB_BARB_, 1 NOELOPE_CARL_BARB_, Z_BOB_BARB_, 1 NOELOPE_ERIC_BARB_, Z_BOB_BARB_, 1 NOELOPE_FRED_BARB_, Z_BOB_BARB_, 1 NOELOPE_GUS_BARB_, Z_BOB_BARB_, 1 NOELOPE_HANK_BARB_, Z_BOB_BARB_, 1 NOELOPE_IRV_BARB_, Z_BOB_BARB_, 1 NOELOPE_JACK_BARB_, Z_BOB_BARB_, 1 _122, Z_BOB_BARB_, -1 _132, Z_BOB_BARB_, -3 _141, Z_BOB_BARB_, -1 _142, Z_BOB_BARB_, -3 _143, Z_BOB_BARB_, -2 ASGM_BOB_, Z_BOB_CARMEN_, 1 ASGW_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_ALICE_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_FANNY_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_GRACE_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_HELEN_, Z_BOB_CARMEN_, 1 NOELOPE_BOB_IRENE_, Z_BOB_CARMEN_, 1 NOELOPE_CARL_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_DON_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_ERIC_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_FRED_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_GUS_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_HANK_CARMEN_, Z_BOB_CARMEN_, 1 NOELOPE_IRV_CARMEN_, Z_BOB_CARMEN_, 1 _122, Z_BOB_CARMEN_, -5 _133, Z_BOB_CARMEN_, -3 _141, Z_BOB_CARMEN_, -5 _142, Z_BOB_CARMEN_, -3 _143, Z_BOB_CARMEN_, -4 ASGM_BOB_, Z_BOB_DAWN_, 1 ASGW_DAWN_, Z_BOB_DAWN_, 1 NOELOPE_BOB_ALICE_, Z_BOB_DAWN_, 1 NOELOPE_BOB_CARMEN_, Z_BOB_DAWN_, 1 NOELOPE_BOB_DAWN_, Z_BOB_DAWN_, 1 NOELOPE_BOB_FANNY_, Z_BOB_DAWN_, 1 NOELOPE_BOB_GRACE_, Z_BOB_DAWN_, 1 NOELOPE_BOB_HELEN_, Z_BOB_DAWN_, 1 NOELOPE_BOB_IRENE_, Z_BOB_DAWN_, 1 _122, Z_BOB_DAWN_, -4 _134, Z_BOB_DAWN_, -10 _141, Z_BOB_DAWN_, -4 _142, Z_BOB_DAWN_, -10 _143, Z_BOB_DAWN_, -7 ASGM_BOB_, 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Z_BOB_FANNY_, -4 _143, Z_BOB_FANNY_, -7 ASGM_BOB_, Z_BOB_GRACE_, 1 ASGW_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_BOB_ALICE_, Z_BOB_GRACE_, 1 NOELOPE_BOB_FANNY_, Z_BOB_GRACE_, 1 NOELOPE_BOB_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_BOB_HELEN_, Z_BOB_GRACE_, 1 NOELOPE_BOB_IRENE_, Z_BOB_GRACE_, 1 NOELOPE_CARL_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_FRED_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_GUS_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_HANK_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_IRV_GRACE_, Z_BOB_GRACE_, 1 NOELOPE_JACK_GRACE_, Z_BOB_GRACE_, 1 _122, Z_BOB_GRACE_, -6 _137, Z_BOB_GRACE_, -4 _141, Z_BOB_GRACE_, -6 _142, Z_BOB_GRACE_, -4 _143, Z_BOB_GRACE_, -5 ASGM_BOB_, Z_BOB_HELEN_, 1 ASGW_HELEN_, Z_BOB_HELEN_, 1 NOELOPE_BOB_ALICE_, Z_BOB_HELEN_, 1 NOELOPE_BOB_FANNY_, Z_BOB_HELEN_, 1 NOELOPE_BOB_HELEN_, Z_BOB_HELEN_, 1 _122, Z_BOB_HELEN_, -8 _138, Z_BOB_HELEN_, -10 _141, Z_BOB_HELEN_, -8 _142, Z_BOB_HELEN_, -10 _143, Z_BOB_HELEN_, -9 ASGM_BOB_, Z_BOB_IRENE_, 1 ASGW_IRENE_, Z_BOB_IRENE_, 1 NOELOPE_BOB_ALICE_, Z_BOB_IRENE_, 1 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Z_CARL_ALICE_, 1 _123, Z_CARL_ALICE_, -10 _131, Z_CARL_ALICE_, -6 _141, Z_CARL_ALICE_, -10 _142, Z_CARL_ALICE_, -6 _143, Z_CARL_ALICE_, -8 ASGM_CARL_, Z_CARL_BARB_, 1 ASGW_BARB_, Z_CARL_BARB_, 1 NOELOPE_CARL_ALICE_, Z_CARL_BARB_, 1 NOELOPE_CARL_BARB_, Z_CARL_BARB_, 1 NOELOPE_CARL_DAWN_, Z_CARL_BARB_, 1 NOELOPE_CARL_FANNY_, Z_CARL_BARB_, 1 NOELOPE_CARL_GRACE_, Z_CARL_BARB_, 1 NOELOPE_CARL_HELEN_, Z_CARL_BARB_, 1 NOELOPE_CARL_IRENE_, Z_CARL_BARB_, 1 NOELOPE_CARL_JILL_, Z_CARL_BARB_, 1 _123, Z_CARL_BARB_, -3 _132, Z_CARL_BARB_, -10 _141, Z_CARL_BARB_, -3 _142, Z_CARL_BARB_, -10 _143, Z_CARL_BARB_, -6.5 ASGM_CARL_, Z_CARL_CARMEN_, 1 ASGW_CARMEN_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_ALICE_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_BARB_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_CARMEN_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_DAWN_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_EVE_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_FANNY_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_GRACE_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_HELEN_, Z_CARL_CARMEN_, 1 NOELOPE_CARL_IRENE_, 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NOELOPE_CARL_FANNY_, Z_CARL_EVE_, 1 NOELOPE_CARL_GRACE_, Z_CARL_EVE_, 1 NOELOPE_CARL_HELEN_, Z_CARL_EVE_, 1 NOELOPE_CARL_IRENE_, Z_CARL_EVE_, 1 NOELOPE_CARL_JILL_, Z_CARL_EVE_, 1 NOELOPE_DON_EVE_, Z_CARL_EVE_, 1 NOELOPE_ERIC_EVE_, Z_CARL_EVE_, 1 NOELOPE_FRED_EVE_, Z_CARL_EVE_, 1 NOELOPE_GUS_EVE_, Z_CARL_EVE_, 1 NOELOPE_HANK_EVE_, Z_CARL_EVE_, 1 NOELOPE_IRV_EVE_, Z_CARL_EVE_, 1 NOELOPE_JACK_EVE_, Z_CARL_EVE_, 1 _123, Z_CARL_EVE_, -2 _135, Z_CARL_EVE_, -1 _141, Z_CARL_EVE_, -2 _142, Z_CARL_EVE_, -1 _143, Z_CARL_EVE_, -1.5 ASGM_CARL_, Z_CARL_FANNY_, 1 ASGW_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_CARL_ALICE_, Z_CARL_FANNY_, 1 NOELOPE_CARL_DAWN_, Z_CARL_FANNY_, 1 NOELOPE_CARL_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_CARL_HELEN_, Z_CARL_FANNY_, 1 NOELOPE_CARL_IRENE_, Z_CARL_FANNY_, 1 NOELOPE_CARL_JILL_, Z_CARL_FANNY_, 1 NOELOPE_DON_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_ERIC_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_FRED_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_GUS_FANNY_, Z_CARL_FANNY_, 1 NOELOPE_HANK_FANNY_, Z_CARL_FANNY_, 1 _123, Z_CARL_FANNY_, -5 _136, Z_CARL_FANNY_, -5 _141, Z_CARL_FANNY_, -5 _142, Z_CARL_FANNY_, -5 _143, Z_CARL_FANNY_, -5 ASGM_CARL_, Z_CARL_GRACE_, 1 ASGW_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_CARL_ALICE_, Z_CARL_GRACE_, 1 NOELOPE_CARL_DAWN_, Z_CARL_GRACE_, 1 NOELOPE_CARL_FANNY_, Z_CARL_GRACE_, 1 NOELOPE_CARL_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_CARL_HELEN_, Z_CARL_GRACE_, 1 NOELOPE_CARL_IRENE_, Z_CARL_GRACE_, 1 NOELOPE_CARL_JILL_, Z_CARL_GRACE_, 1 NOELOPE_FRED_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_GUS_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_HANK_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_IRV_GRACE_, Z_CARL_GRACE_, 1 NOELOPE_JACK_GRACE_, Z_CARL_GRACE_, 1 _123, Z_CARL_GRACE_, -4 _137, Z_CARL_GRACE_, -5 _141, Z_CARL_GRACE_, -4 _142, Z_CARL_GRACE_, -5 _143, Z_CARL_GRACE_, -4.5 ASGM_CARL_, Z_CARL_HELEN_, 1 ASGW_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_ADAM_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_BOB_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_CARL_ALICE_, Z_CARL_HELEN_, 1 NOELOPE_CARL_DAWN_, Z_CARL_HELEN_, 1 NOELOPE_CARL_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_CARL_IRENE_, Z_CARL_HELEN_, 1 NOELOPE_CARL_JILL_, Z_CARL_HELEN_, 1 NOELOPE_DON_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_ERIC_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_FRED_HELEN_, Z_CARL_HELEN_, 1 NOELOPE_JACK_HELEN_, Z_CARL_HELEN_, 1 _123, Z_CARL_HELEN_, -6 _138, Z_CARL_HELEN_, -4 _141, Z_CARL_HELEN_, -6 _142, Z_CARL_HELEN_, -4 _143, Z_CARL_HELEN_, -5 ASGM_CARL_, Z_CARL_IRENE_, 1 ASGW_IRENE_, Z_CARL_IRENE_, 1 NOELOPE_CARL_ALICE_, Z_CARL_IRENE_, 1 NOELOPE_CARL_DAWN_, Z_CARL_IRENE_, 1 NOELOPE_CARL_IRENE_, Z_CARL_IRENE_, 1 _123, Z_CARL_IRENE_, -8 _139, Z_CARL_IRENE_, -10 _141, Z_CARL_IRENE_, -8 _142, Z_CARL_IRENE_, -10 _143, Z_CARL_IRENE_, -9 ASGM_CARL_, Z_CARL_JILL_, 1 ASGW_JILL_, Z_CARL_JILL_, 1 NOELOPE_ADAM_JILL_, Z_CARL_JILL_, 1 NOELOPE_BOB_JILL_, Z_CARL_JILL_, 1 NOELOPE_CARL_ALICE_, Z_CARL_JILL_, 1 NOELOPE_CARL_DAWN_, Z_CARL_JILL_, 1 NOELOPE_CARL_IRENE_, Z_CARL_JILL_, 1 NOELOPE_CARL_JILL_, Z_CARL_JILL_, 1 NOELOPE_DON_JILL_, Z_CARL_JILL_, 1 NOELOPE_ERIC_JILL_, Z_CARL_JILL_, 1 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NOELOPE_ADAM_IRENE_, Z_ADAM_CARMEN_, 1 NOELOPE_ADAM_JILL_, Z_ADAM_CARMEN_, 1 NOELOPE_BOB_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_CARL_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_DON_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_ERIC_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_FRED_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_GUS_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_HANK_CARMEN_, Z_ADAM_CARMEN_, 1 NOELOPE_IRV_CARMEN_, Z_ADAM_CARMEN_, 1 _121, Z_ADAM_CARMEN_, -3 _133, Z_ADAM_CARMEN_, -2 _141, Z_ADAM_CARMEN_, -3 _142, Z_ADAM_CARMEN_, -2 _143, Z_ADAM_CARMEN_, -2.5 ASGM_ADAM_, Z_ADAM_CARMEN_, 1 ASGW_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_FANNY_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_GRACE_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_HELEN_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_DAWN_, 1 NOELOPE_ADAM_JILL_, Z_ADAM_DAWN_, 1 NOELOPE_BOB_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_CARL_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_DON_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_ERIC_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_FRED_DAWN_, Z_ADAM_DAWN_, 1 NOELOPE_GUS_DAWN_, Z_ADAM_DAWN_, 1 _121, Z_ADAM_DAWN_, -4 _134, Z_ADAM_DAWN_, -4 _141, Z_ADAM_DAWN_, -4 _142, Z_ADAM_DAWN_, -4 _143, Z_ADAM_DAWN_, -4 ASGM_ADAM_, Z_ADAM_DAWN_, 1 ASGW_EVE_, Z_ADAM_EVE_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_EVE_, 1 NOELOPE_BOB_EVE_, Z_ADAM_EVE_, 1 NOELOPE_DON_EVE_, Z_ADAM_EVE_, 1 NOELOPE_ERIC_EVE_, Z_ADAM_EVE_, 1 NOELOPE_FRED_EVE_, Z_ADAM_EVE_, 1 NOELOPE_GUS_EVE_, Z_ADAM_EVE_, 1 NOELOPE_HANK_EVE_, Z_ADAM_EVE_, 1 NOELOPE_IRV_EVE_, Z_ADAM_EVE_, 1 _121, Z_ADAM_EVE_, -10 _135, Z_ADAM_EVE_, -3 _141, Z_ADAM_EVE_, -10 _142, Z_ADAM_EVE_, -3 _143, Z_ADAM_EVE_, -6.5 ASGM_ADAM_, Z_ADAM_EVE_, 1 ASGW_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_FANNY_, 1 NOELOPE_ADAM_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_FANNY_, 1 NOELOPE_BOB_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_CARL_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_DON_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_ERIC_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_FRED_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_GUS_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_HANK_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_IRV_FANNY_, Z_ADAM_FANNY_, 1 NOELOPE_JACK_FANNY_, Z_ADAM_FANNY_, 1 _121, Z_ADAM_FANNY_, -8 _136, Z_ADAM_FANNY_, -1 _141, Z_ADAM_FANNY_, -8 _142, Z_ADAM_FANNY_, -1 _143, Z_ADAM_FANNY_, -4.5 ASGM_ADAM_, Z_ADAM_FANNY_, 1 ASGW_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_FANNY_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_HELEN_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_GRACE_, 1 NOELOPE_ADAM_JILL_, Z_ADAM_GRACE_, 1 NOELOPE_BOB_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_CARL_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_FRED_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_GUS_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_HANK_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_IRV_GRACE_, Z_ADAM_GRACE_, 1 NOELOPE_JACK_GRACE_, Z_ADAM_GRACE_, 1 _121, Z_ADAM_GRACE_, -5 _137, Z_ADAM_GRACE_, -3 _141, Z_ADAM_GRACE_, -5 _142, Z_ADAM_GRACE_, -3 _143, Z_ADAM_GRACE_, -4 ASGM_ADAM_, Z_ADAM_GRACE_, 1 ASGW_HELEN_, Z_ADAM_HELEN_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_HELEN_, 1 NOELOPE_ADAM_FANNY_, Z_ADAM_HELEN_, 1 NOELOPE_ADAM_HELEN_, Z_ADAM_HELEN_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_HELEN_, 1 NOELOPE_ADAM_JILL_, Z_ADAM_HELEN_, 1 NOELOPE_BOB_HELEN_, Z_ADAM_HELEN_, 1 _121, Z_ADAM_HELEN_, -7 _138, Z_ADAM_HELEN_, -9 _141, Z_ADAM_HELEN_, -7 _142, Z_ADAM_HELEN_, -9 _143, Z_ADAM_HELEN_, -8 ASGM_ADAM_, Z_ADAM_HELEN_, 1 ASGW_IRENE_, Z_ADAM_IRENE_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_IRENE_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_IRENE_, 1 NOELOPE_BOB_IRENE_, Z_ADAM_IRENE_, 1 NOELOPE_CARL_IRENE_, Z_ADAM_IRENE_, 1 _121, Z_ADAM_IRENE_, -9 _139, Z_ADAM_IRENE_, -8 _141, Z_ADAM_IRENE_, -9 _142, Z_ADAM_IRENE_, -8 _143, Z_ADAM_IRENE_, -8.5 ASGM_ADAM_, Z_ADAM_IRENE_, 1 ASGW_JILL_, Z_ADAM_JILL_, 1 NOELOPE_ADAM_EVE_, Z_ADAM_JILL_, 1 NOELOPE_ADAM_IRENE_, Z_ADAM_JILL_, 1 NOELOPE_ADAM_JILL_, Z_ADAM_JILL_, 1 NOELOPE_BOB_JILL_, Z_ADAM_JILL_, 1 NOELOPE_JACK_JILL_, Z_ADAM_JILL_, 1 _121, Z_ADAM_JILL_, -8 _140, Z_ADAM_JILL_, -8 _141, Z_ADAM_JILL_, -8 _142, Z_ADAM_JILL_, -8 _143, Z_ADAM_JILL_, -8 ASGM_ADAM_, Z_ADAM_JILL_, 1 _121, AM_ADAM_, 1 _122, AM_BOB_, 1 _123, AM_CARL_, 1 _124, AM_DON_, 1 _125, AM_ERIC_, 1 _126, AM_FRED_, 1 _127, AM_GUS_, 1 _128, AM_HANK_, 1 _129, AM_IRV_, 1 _130, AM_JACK_, 1 _131, AW_ALICE_, 1 _132, AW_BARB_, 1 _133, AW_CARMEN_, 1 _134, AW_DAWN_, 1 _135, AW_EVE_, 1 _136, AW_FANNY_, 1 _137, AW_GRACE_, 1 _138, AW_HELEN_, 1 _139, AW_IRENE_, 1 _140, AW_JILL_, 1 _141, PTOTALM, 1 _142, PTOTALW, 1 ; ! Case Ignacio; !Sangbum Lee, Chan Phalakornkule, Michael M. Domach, Ignacio E. Grossmann (2000) "Recursive MILP model for finding all the alternate optima in LP models for metabolic networks" Computers and Chemical Engineering, Elsevier, 24, 711-716. It has 9 alternative optima extreme points, and >= 18 feasible extreme points; !CIgnac NDXP = 2600;!CIgnac NSLIST = 30;!CIgnac SLIST = 1..NSLIST;!CIgnac AltOpt = 0;!CIgnac COL, OBJ, SLB, SUB, TYPEC = R18, 1, 0, 1e+030, 3 R1, 0, 0, 1e+030, 3 R2, 0, 0, 1e+030, 3 R10, 0, -20, 20, 3 R12, 0, 0, 1e+030, 3 R7, 0, 0, 1e+030, 3 R8, 0, 0, 1e+030, 3 R14, 0, 0, 1e+030, 3 R16, 0, 0, 1e+030, 3 R31, 0, 0, 1e+030, 3 R21, 0, 0, 1e+030, 3 R19, 0, 0, 1e+030, 3 R32, 0, 0, 1e+030, 3 R24, 0, 0, 1e+030, 3 R33, 0, -20, 20, 3 R23, 0, 0, 1e+030, 3 R25, 0, 0, 1e+030, 3 R27, 0, 0, 1e+030, 3 R29, 0, 0, 1e+030, 3 R28, 0, 0, 1e+030, 3 R4, 0, 0, 1e+030, 3 R5, 0, 0, 1e+030, 3 RATP, 0, 0, 1e+030, 3 ; !CIgnac ROW, RHS, TYPER = _2, 0.08199999999999999, 0 _3, 0.02836, 0 _4, 0.5972000000000001, 0 _5, 0.28764, 0 _6, 1.1332, 0 _7, -0.7144, 0 _8, 1.1712, 0 _9, 0, 0 _10, 0.4312, 0 _11, 0, 0 _12, 0, 0 _13, 0.3588, 0 _14, 0, 0 _15, 0.1444, 0 _16, 0.05160000000000001, 0 _17, 0, 0 _29, 7.2, 0 _30, 0, 0 _31, 13.3, -1 _32, 20, 1 _33, 20, 1 _34, 20, 1 _35, 20, 1 ; !CIgnac NONZ, COEF = _5, R18, -1 _6, R18, 1 _30, R18, -1 _2, R1, 1 _5, R1, -1 _6, R1, 1 _32, R1, 1 _2, R2, -1 _12, R2, 1 _29, R2, 2 _2, R10, -1 _3, R10, 1 _3, R12, -1 _16, R12, 2 _30, R12, 1 _33, R12, 1 _3, R7, 1 _13, R7, -1 _14, R7, -1 _15, R7, 1 _3, R8, 1 _14, R8, -1 _15, R8, -1 _16, R8, 1 _4, R14, 1 _16, R14, -1 _30, R14, -3 _34, R14, 1 _4, R16, -1 _5, R16, 1 _35, R16, 1 _5, R31, -1 _7, R31, -1 _30, R31, -1 _6, R21, -1 _8, R21, 1 _30, R21, -2 _6, R19, -1 _30, R19, 2 _6, R32, 1 _17, R32, -1 _29, R32, 1 _7, R24, 1 _8, R24, -1 _9, R24, 1 _7, R33, -1 _17, R33, -1 _30, R33, -2 _8, R23, -1 _30, R23, -1 _9, R25, -1 _10, R25, 1 _29, R25, 1 _10, R27, -1 _11, R27, 1 _30, R27, -3 _11, R29, -1 _17, R29, 1 _30, R29, -1 _11, R28, -1 _12, R4, -1 _13, R4, 1 _12, R5, -1 _14, R5, 1 _30, RATP, 1 _31, RATP, 1 ; ! Case 3: Example from Dyer and Proll, Math. Programming, vol. 12, 1977 in equality constraint form; ! It has 10 feasible extreme points, all of which are optimal; !CDyer NDXP = 100;!CDyer NSLIST = 90;!CDyer SLIST = 1..NSLIST; !CDyer AltOpt = 0; !CDyer ROW= ROW1 ROW2 ROW3 ROW4 ROW5; !CDyer RHS= 5 16 3 17 10; !CDyer TYPER = 0;!CDyer COL= X1 X2 X3 X4 X5 X6 X7 X8 ; !CDyer OBJ= 0 0 0 0 0 0 0 0; !CDyer SUB= 99 99 99 99 99 99 99 99; ! Constraint coefficients; !CDyer COEF = 3 2 -1 1 0 0 0 0 3 2 4 0 1 0 0 0 3 0 -4 0 0 1 0 0 2.25 4 3 0 0 0 1 0 1 2 1 0 0 0 0 1 ; ! The Area Volume model; ! Has at least 583 feasible(and optimal) primal extreme points; !CAreaVol NDXP = 50000;!CAreaVol NSLIST = 690;!CAreaVol SLIST = 1..NSLIST;!CAreaVol AltOpt = 1;!CAreaVol COL, OBJ, SLB, SUB, TYPEC = X_A_1, 1158, 0, 1e+030, 3 X_A_2, 2503, 0, 1e+030, 3 X_A_3, 3819, 0, 1e+030, 3 X_A_4, 4849, 0, 1e+030, 3 X_A_5, 5606, 0, 1e+030, 3 X_B_1, 3819, 0, 1e+030, 3 X_B_2, 4849, 0, 1e+030, 3 X_B_3, 5606, 0, 1e+030, 3 X_B_4, 6142, 0, 1e+030, 3 X_B_5, 6262, 0, 1e+030, 3 X_C_1, 6262, 0, 1e+030, 3 X_C_2, 6506, 0, 1e+030, 3 X_C_3, 6492, 0, 1e+030, 3 X_C_4, 6264, 0, 1e+030, 3 X_C_5, 6021, 0, 1e+030, 3 P_1, 0, 0, 1e+030, 3 P_2, 0, 0, 1e+030, 3 P_3, 0, 0, 1e+030, 3 P_4, 0, 0, 1e+030, 3 P_5, 0, 0, 1e+030, 3 ; !CAreaVol ROW, RHS, TYPER = _2, 150, 1 _3, 300, 1 _4, 100, 1 _5, 402906, 0 _6, 402906, 0 _7, 402906, 0 _8, 402906, 0 _9, 402906, 0 _10, 0, 0 _11, 0, 0 _12, 0, 0 _13, 0, 0 _14, 0, 0 ; !CAreaVol NONZ, COEF = _2, X_A_1, 1 _5, X_A_1, 1158 _10, X_A_1, 1 _2, X_A_2, 1 _6, X_A_2, 2503 _11, X_A_2, 1 _2, X_A_3, 1 _7, X_A_3, 3819 _12, X_A_3, 1 _2, X_A_4, 1 _8, X_A_4, 4849 _13, X_A_4, 1 _2, X_A_5, 1 _9, X_A_5, 5606 _14, X_A_5, 1 _3, X_B_1, 1 _5, X_B_1, 3819 _10, X_B_1, 1 _3, X_B_2, 1 _6, X_B_2, 4849 _11, X_B_2, 1 _3, X_B_3, 1 _7, X_B_3, 5606 _12, X_B_3, 1 _3, X_B_4, 1 _8, X_B_4, 6142 _13, X_B_4, 1 _3, X_B_5, 1 _9, X_B_5, 6262 _14, X_B_5, 1 _4, X_C_1, 1 _5, X_C_1, 6262 _10, X_C_1, 1 _4, X_C_2, 1 _6, X_C_2, 6506 _11, X_C_2, 1 _4, X_C_3, 1 _7, X_C_3, 6492 _12, X_C_3, 1 _4, X_C_4, 1 _8, X_C_4, 6264 _13, X_C_4, 1 _4, X_C_5, 1 _9, X_C_5, 6021 _14, X_C_5, 1 _10, P_1, -1 _11, P_2, -1 _12, P_3, -1 _13, P_4, -1 _14, P_5, -1 ; ! Case Xueyu 1; ! It has 2 alternative optima corner points, 4 feasible corner points; ! Number of desired extreme points to try.; !CX1 NDXP = 20;!CX1 NSLIST = 10;!CX1 SLIST = 1..NSLIST; !CX1 AltOpt = 0; ! Names of rows; !CX1 ROW = CON1 CON2 CON3 CON4; !CX1 RHS = -6 4 8 6; !CX1 TYPER = 0;!CX1 COL = X1 X2 SLK1 SLK2 SLK3 SLK4; ! Upper bounds; !CX1 SUB= 999 999 999 999 999 999 ; !CX1 OBJ = -2 -1 0 0 0 0; ! Constraint coefficients; !CX1 COEF = -3 -2 1 0 0 0 2 -1 0 1 0 0 2 1 0 0 1 0 -1 2 0 0 0 1 ; ! Case Xueyu 2; ! It has 7 extreme points, both optimal and feasible; ! Number of desired extreme points tries.; !CX2 NDXP = 40;!CX2 NSLIST = 10;!CX2 SLIST = 1..NSLIST; !CX2 AltOpt = 1; ! Names of rows; !CX2 ROW = CON1 CON2 CON3 CON4 CON5 CON6 CON7; !CX2 RHS = -1 -4 -12 -36 -26 -3 14; !CX2 TYPER = 0;!CX2 COL = X1 X2 SLK1 SLK2 SLK3 SLK4 SLK5 SLK6 SLK7; ! Upper bounds; !CX2 SUB= 999 999 999 999 999 999 999 999 999; !CX2 OBJ = 0 0 0 0 0 0 0 0 0; ! Constraint coefficients; !CX2 COEF = 2 -1 -1 0 0 0 0 0 0 3 -2 0 -1 0 0 0 0 0 1 -2 0 0 -1 0 0 0 0 -3 -2 0 0 0 -1 0 0 0 -4 1 0 0 0 0 -1 0 0 -1 2 0 0 0 0 0 -1 0 2 4 0 0 0 0 0 0 -1 ; ! Case: Variant of Astro-Cosmo problem, 2 products. ! It has 2 alternative corner point optima, and 5 feasible corner points; ! Max = 15 A + 30 C A <= 60, C <= 50, A + 2 C <= 120, ! Number of desired extreme points tries.; !CAC1 NDXP = 10;!CAC1 NSLIST = 10;!CAC1 SLIST = 1..NSLIST; !CAC1 AltOpt = 0;! The last three variables in the tableau, cols 3-5, are the slack variables; !CAC1 ROW = ALIM CLIM LABOR; !CAC1 RHS = 60 50 120; !CAC1 TYPER = 0; ! Names of columns; !CAC1 COL = A__ C__ S_1 S_2 S_3; !CAC1 OBJ = -15 -30 0 0 0; ! Upper bounds; !CAC1 SUB = 60 50 999 999 999; ! Names of rows; ! Matrix coefficients, including Obj and RHS; !CAC1 COEF = 1 0 1 0 0 0 1 0 1 0 1 2 0 0 1 ; XSV = 0;! Fix XSV so not part of optimization; ENDDATA SUBMODEL Simple ! A weighted objective; MIN = ALPHA* OBVTRUE + (1 - ALPHA)* OBVPRTRB; @FREE( OBVTRUE);! The true objective; ! Assume objective is bounded; OBVTRUE >= -999999; OBVPRTRB >= -999999; OBVTRUE = @SUM( COL( j) : OBJ( j)* X( j)); @FREE( OBVPRTRB);! The perturbed objective; OBVPRTRB = @SUM( COL( j) : OBJPTRB( j)* X( j)); ! Allow an upper bound constraint on the true Objective value; OBVTRUE <= OBVUL; @FREE( OBVUL);! It could be negative; @FOR( ROW( I) | TYPER( I) #GT# 0: ! <= rows; @SUM( NONZ( I, J): COEF( I, J) * X( J)) <= RHS( I) ); @FOR( ROW( I) | TYPER( I) #EQ# 0:! = rows; @SUM( NONZ( I, J): COEF( I, J) * X( J)) = RHS( I) ); @FOR( ROW( I) | TYPER( I) #LT# 0: ! >= rows; @SUM( NONZ( I, J): COEF( I, J) * X( J)) >= RHS( I) ); @FOR( COL( J): ! All vars are bounded: 0 <= X( J) <= SUB( J); @BND( 0, X( J), SUB( J)) ); ENDSUBMODEL PROCEDURE SAVESOL( APPEND): ! Save this solution; ! Inputs: APPEND : 0-> start new file, 1-> append to existing file; ! Make Room; NSFND = NSFND + 1; @FOR( COL( J): @INSERT( SXC, NSFND, J)); @FOR( COL( J): XSV( NSFND, J) = X( j)); ! Send output to a file? ; @IFC( TOFILE: @WRITE(' Solution# ', NSFND, ' (Iter: ', ITER,')', @NEWLINE( 1)); @IFC( APPEND: @DIVERT( '\temp\AltOpt.txt', 'A'); @ELSE @DIVERT( '\temp\AltOpt.txt'); ); ); @WRITE(' Solution# ', NSFND, ' (Iter: ', ITER,')', @NEWLINE( 1)); @FOR( COL( j) | X( j) #GT# 0: TEMP = X( j); @WRITE(' ', COL( j),' ', TEMP, @NEWLINE( 1)); ); @WRITE( @NEWLINE( 1)); @DIVERT();! Revert to output to the screen; ENDPROCEDURE CALC: @SET( 'OROUTE', 1);! Buffer size for routing output to window; @SET( 'TERSEO', 3);! Output level (0:verb, 1:terse, 2:only errors, 3:none); @SET( 'SOLVEL', 0);! Linear solver (0:LINGO decides,1:primal,2:dual,3:barrier); @SET( 'STAWIN', 0);! Turn off status window to reduce I/O time; @SET( 'STABAR', 0);! Turn off status bar to reduce I/O time; NCOL = @SIZE( COL);! Number columns; TOLDIF = 0.0001;! Tolerance for considering two values different; ALPHA = 1;! Use original true objective; @FOR( COL( j): OBJPTRB( j) = 0);! Initially, no perturbations; OBVUL = 1E20;! Initially, no constraint on the objective value; @NULLSET( SXC);! Initially, the SXC set is empty; ! @GEN( SimpleModel); @IFC( GENMPS : @SMPS('\temp\AltOpt.mps', SimpleMODEL)); @SOLVE( SimpleModel);! Get first optimal solution; ITER = 1;! Number search directions tried; NSFND = 0;! Number of solutions found so far; ! Save this solution; SAVESOL( 0); ! @WRITE( 'The Objective value= ', OBVTRUE, @NEWLINE( 1)); ISTAT = @STATUS(); ! @WRITE( ' Solve Status= ', ISTAT, @NEWLINE( 1)); ! Restrict to just optimal solutions ?; ! @write( 'OBVUL= ', OBVUL, @NEWLINE( 1)); @IFC( AltOpt: OBVUL = OBVTRUE);!Restrict to solns that equal optimal value; ! @write( 'OBVUL= ', OBVUL, @NEWLINE( 1)); ! Switch to perturb objective; ALPHA = 0; ! How to choose next direction; MODE = 1;! 1: random, 2: flip, 3: mod, 4: flip of mod; ! Generate a perturbed objective; ! A arbitrary random starting seed; URANDV = 0.13245768; ! Estimating population size, if all solutions have equal probability of selection (which is a bad assumption, see model LoProb): N1 = number solns found so far. S2 = additional draws taken, D2 = number duplicates of N1 found in S2, NP = estimate of population size, NP = N1*S2/D2; @WHILE( ITER #LT# NDXP #AND# NSFND #LT# NSLIST: ITER = ITER + 1; ! @ifc( iter #gt# 26083: @write( '*iter= ', iter, @newline( 1))); ! Generate a direction, try to make different from previous directions; !1) Choose a random direction; @IFC( MODE #EQ# 1: @FOR( COL( j): URANDV = @RAND( URANDV);! Get next random uniform; OBJPTRB( j) = URANDV - 0.5;! Uniform in ( -0.5, +0.5); ); ); !2) (or 4 or 6) Choose opposite direction; @IFC( MODE #EQ# 2 #OR# MODE #EQ# 4 #OR# MODE #EQ# 6: @FOR( COL( j): OBJPTRB( j) = - OBJPTRB( j); ); ); !3) Choose approximately orthogonal direction, e.g. ( -0.1, +0.4) becomes (+0.4, -0.1); @IFC( MODE #EQ# 3: @FOR( COL( j): TEMP = OBJPTRB( j) + 0.5; @IFC( TEMP #GT# 0.5: TEMP = TEMP - 1.0; OBJPTRB( j) = TEMP; ); ); ); !5) Choose a probabilistic orthogonal direction, e.g., ( -0.25, 0.25) probably becomes ( 0.25, 0.25); @IFC( MODE #EQ# 4: @FOR( COL( j): URANDV = @RAND( URANDV);! Get next random uniform; @IFC( URANDV #LT# 0.5 : OBJPTRB( j) = - OBJPTRB( j)); ); ); MODE = MODE + 1;! Use different direction for next iteration; @IFC( MODE #GT# 6: MODE = 1); @IFC( iter #gt# 26083: @WRITE( '*Start solve ', iter, @NEWLINE( 1))); @IFC( iter #eq# 26085: @SMPS('\temp\Trbl26085.mps', SimpleMODEL)); @IFC( iter #eq# 26085: @WRITE( '*MPS file written ', iter, @NEWLINE( 1))); @SOLVE( SimpleMODEL); ISTAT = @STATUS(); @IFC( iter #gt# 26083: @WRITE( '*Back from solve ', iter, ' ISTAT= ', ISTAT, @NEWLINE( 1))); ! Check if we have already seen this primal solution; DIFFMIN = 99999999;! Report minimum difference found; NOTDUP = 1;! Is it a duplicate? ; IA = 0;! Loop over already found solutions; @WHILE( IA #LT# NSFND #AND# NOTDUP: IA = IA + 1; ISAME = 1;! Duplicate until found otherwise; IB = 0;! Loop over variables in solution IA; @WHILE( IB #LT# NCOL #AND# ISAME: IB = IB + 1; SDIFF = @ABS( X( IB) - XSV( IA, IB)); @IFC( SDIFF #GT# TOLDIF: DIFFMIN = @SMIN( DIFFMIN, SDIFF); ISAME = 0;! Current soln and soln IA are different; ! @WRITE(' Different from solution ', IA,' Var= ', IB, ' by ', SDIFF, @NEWLINE( 1)); ); ); @IFC( ISAME: !@WRITE( ' Duplicate of soln ', IA, @NEWLINE( 1)); NOTDUP = 0; );! Current soln and soln IA are same; ); !@WRITE(' Min diff found= ', DIFFMIN, @NEWLINE( 1)); @IFC( NOTDUP: ! We found a new primal extreme point; SAVESOL( 1); ); ); @WRITE(' Completed ', ITER, ' iterations',' No. corner solns found= ', NSFND, @NEWLINE( 1)); ! Send the average solution to the file?; @IFC( ToFile: @DIVERT( '\temp\AltOpt.txt', 'A');! Send output to file, Appending to existing contents; @WRITE( @NEWLINE( 1),' The average interior solution is:', @NEWLINE( 1)); @FOR( COL( j) : TEMP = @SUM( SLIST( i) | i #LE# NSFND: XSV( i, j))/ NSFND;! Save it; @WRITE(' ', COL( j),' ', TEMP, @NEWLINE( 1)); ); @DIVERT();! Revert to output to the screen; ); ENDCALC ```