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Instance: batch0812

Formats ams gms mod nl osil
Primal Bounds
2687026.78400000 p1 ( gdx sol )
(infeas: 4e-12)
Dual Bounds
2687026.78400000 (ALPHAECP)
2687004.90000000 (ANTIGONE)
2687026.78400000 (BARON)
2687026.78400000 (BONMIN)
2687020.11400000 (COUENNE)
2687026.78400000 (LINDO)
2687026.78400000 (SCIP)
References You, Fengqi and Grossmann, I E, Mixed-Integer Nonlinear Programming Models for the Optimal Design of Multi-product Batch Plant, 2009.
Source convex2.gms from minlp.org model 48
Application Multi-Product Batch Plant Design
Added to library 24 Sep 2013
Problem type MBNLP
#Variables 100
#Binary Variables 60
#Integer Variables 0
#Nonlinear Variables 40
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type nonlinear
Objective curvature convex
#Nonzeros in Objective 24
#Nonlinear Nonzeros in Objective 24
#Constraints 217
#Linear Constraints 216
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 1
Operands in Gen. Nonlin. Functions exp
Constraints curvature convex
#Nonzeros in Jacobian 520
#Nonlinear Nonzeros in Jacobian 16
#Nonzeros in (Upper-Left) Hessian of Lagrangian 80
#Nonzeros in Diagonal of Hessian of Lagrangian 40
#Blocks in Hessian of Lagrangian 20
Minimal blocksize in Hessian of Lagrangian 2
Maximal blocksize in Hessian of Lagrangian 2
Average blocksize in Hessian of Lagrangian 2.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 4.2e+04
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*        218       25      192        1        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        101       41       60        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*        545      505       40        0
*
*  Solve m using MINLP minimizing objvar;


Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19
          ,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36
          ,x37,x38,x39,x40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
          ,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
          ,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
          ,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,objvar;

Positive Variables  x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12;

Binary Variables  b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53,b54,b55
          ,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70,b71,b72
          ,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87,b88,b89
          ,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
          ,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
          ,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218;


e1.. -(250*exp(x1 + 0.6*x13) + 550*exp(x2 + 0.6*x14) + 250*exp(x3 + 0.6*x15) + 
     1000*exp(x4 + 0.6*x16) + 300*exp(x5 + 0.6*x17) + 800*exp(x6 + 0.6*x18) + 
     200*exp(x7 + 0.6*x19) + 1200*exp(x8 + 0.6*x20) + 250*exp(x9 + 0.6*x21) + 
     250*exp(x10 + 0.6*x22) + 450*exp(x11 + 0.6*x23) + 700*exp(x12 + 0.6*x24))
      + objvar =E= 0;

e2..    x13 - x25 =G= 2.06686275947298;

e3..    x14 - x25 =G= 0.693147180559945;

e4..    x15 - x25 =G= 1.64865862558738;

e5..    x16 - x25 =G= 1.58923520511658;

e6..    x17 - x25 =G= 1.80828877117927;

e7..    x18 - x25 =G= 1.43508452528932;

e8..    x19 - x25 =G= 1.02961941718116;

e9..    x20 - x25 =G= 1.19392246847243;

e10..    x21 - x25 =G= 1.41098697371026;

e11..    x22 - x25 =G= 1.33500106673234;

e12..    x23 - x25 =G= 1.02961941718116;

e13..    x24 - x25 =G= 1.3609765531356;

e14..    x13 - x26 =G= -0.356674943938732;

e15..    x14 - x26 =G= -0.22314355131421;

e16..    x15 - x26 =G= -0.105360515657826;

e17..    x16 - x26 =G= 1.22377543162212;

e18..    x17 - x26 =G= 0.741937344729377;

e19..    x18 - x26 =G= 0.916290731874155;

e20..    x19 - x26 =G= 1.19392246847243;

e21..    x20 - x26 =G= 1.09861228866811;

e22..    x21 - x26 =G= 0.993251773010283;

e23..    x22 - x26 =G= 0.8754687373539;

e24..    x23 - x26 =G= 0.78845736036427;

e25..    x24 - x26 =G= 1.1314021114911;

e26..    x13 - x27 =G= -0.356674943938732;

e27..    x14 - x27 =G= 0.955511445027436;

e28..    x15 - x27 =G= 0.470003629245736;

e29..    x16 - x27 =G= 1.28093384546206;

e30..    x17 - x27 =G= 1.16315080980568;

e31..    x18 - x27 =G= 1.06471073699243;

e32..    x19 - x27 =G= 0.955511445027436;

e33..    x20 - x27 =G= 0.78845736036427;

e34..    x21 - x27 =G= 1.52605630349505;

e35..    x22 - x27 =G= 1.45861502269952;

e36..    x23 - x27 =G= 1.43508452528932;

e37..    x24 - x27 =G= 1.52605630349505;

e38..    x13 - x28 =G= 1.54756250871601;

e39..    x14 - x28 =G= 0.832909122935104;

e40..    x15 - x28 =G= 0.470003629245736;

e41..    x16 - x28 =G= 0.993251773010283;

e42..    x17 - x28 =G= 0.182321556793955;

e43..    x18 - x28 =G= 0.916290731874155;

e44..    x19 - x28 =G= 0.405465108108164;

e45..    x20 - x28 =G= 0.405465108108164;

e46..    x21 - x28 =G= 0.262364264467491;

e47..    x22 - x28 =G= 0.53062825106217;

e48..    x23 - x28 =G= 0.405465108108164;

e49..    x24 - x28 =G= 0.587786664902119;

e50..    x13 - x29 =G= 0.182321556793955;

e51..    x14 - x29 =G= 1.28093384546206;

e52..    x15 - x29 =G= 0.8754687373539;

e53..    x16 - x29 =G= 1.50407739677627;

e54..    x17 - x29 =G= 0.470003629245736;

e55..    x18 - x29 =G= 0.741937344729377;

e56..    x19 - x29 =G= 0.8754687373539;

e57..    x20 - x29 =G= 0.993251773010283;

e58..    x21 - x29 =G= 1.02961941718116;

e59..    x22 - x29 =G= 1.25276296849537;

e60..    x23 - x29 =G= 1.25276296849537;

e61..    x24 - x29 =G= 1.45861502269952;

e62..    x13 - x30 =G= -0.356674943938732;

e63..    x14 - x30 =G= 0.8754687373539;

e64..    x15 - x30 =G= 1.1314021114911;

e65..    x16 - x30 =G= 0.78845736036427;

e66..    x17 - x30 =G= 1.30833281965018;

e67..    x18 - x30 =G= 1.56861591791385;

e68..    x19 - x30 =G= 1.50407739677627;

e69..    x20 - x30 =G= 1.64865862558738;

e70..    x21 - x30 =G= 1.85629799036563;

e71..    x22 - x30 =G= 1.7404661748405;

e72..    x23 - x30 =G= 1.85629799036563;

e73..    x24 - x30 =G= 1.91692261218206;

e74..    x13 - x31 =G= 0.832909122935104;

e75..    x14 - x31 =G= 1.54756250871601;

e76..    x15 - x31 =G= 1.64865862558738;

e77..    x16 - x31 =G= 1.25276296849537;

e78..    x17 - x31 =G= 1.06471073699243;

e79..    x18 - x31 =G= 1.28093384546206;

e80..    x19 - x31 =G= 1.19392246847243;

e81..    x20 - x31 =G= 1.16315080980568;

e82..    x21 - x31 =G= 1.41098697371026;

e83..    x22 - x31 =G= 1.30833281965018;

e84..    x23 - x31 =G= 1.22377543162212;

e85..    x24 - x31 =G= 1.30833281965018;

e86..    x13 - x32 =G= -0.916290731874155;

e87..    x14 - x32 =G= -0.105360515657826;

e88..    x15 - x32 =G= 0.0953101798043249;

e89..    x16 - x32 =G= 0.336472236621213;

e90..    x17 - x32 =G= 0.470003629245736;

e91..    x18 - x32 =G= 0.78845736036427;

e92..    x19 - x32 =G= 0.693147180559945;

e93..    x20 - x32 =G= 0.587786664902119;

e94..    x21 - x32 =G= 0.587786664902119;

e95..    x22 - x32 =G= 0.470003629245736;

e96..    x23 - x32 =G= 0.587786664902119;

e97..    x24 - x32 =G= 0.693147180559945;

e98..    x1 + x33 =G= 1.85629799036563;

e99..    x2 + x33 =G= 1.54756250871601;

e100..    x3 + x33 =G= 2.11625551480255;

e101..    x4 + x33 =G= 1.3609765531356;

e102..    x5 + x33 =G= 0.741937344729377;

e103..    x6 + x33 =G= 0.182321556793955;

e104..    x7 + x33 =G= -0.22314355131421;

e105..    x8 + x33 =G= 0.78845736036427;

e106..    x9 + x33 =G= 0.182321556793955;

e107..    x10 + x33 =G= 0.916290731874155;

e108..    x11 + x33 =G= 1.22377543162212;

e109..    x12 + x33 =G= 1.33500106673234;

e110..    x1 + x34 =G= 1.91692261218206;

e111..    x2 + x34 =G= 1.85629799036563;

e112..    x3 + x34 =G= 1.87180217690159;

e113..    x4 + x34 =G= 1.48160454092422;

e114..    x5 + x34 =G= 0.832909122935104;

e115..    x6 + x34 =G= 1.16315080980568;

e116..    x7 + x34 =G= -0.916290731874155;

e117..    x8 + x34 =G= -1.6094379124341;

e118..    x9 + x34 =G= -0.693147180559945;

e119..    x10 + x34 =G= 1.19392246847243;

e120..    x11 + x34 =G= -0.510825623765991;

e121..    x12 + x34 =G= 0.182321556793955;

e122..    x1 + x35 =G= 0;

e123..    x2 + x35 =G= 1.84054963339749;

e124..    x3 + x35 =G= 1.68639895357023;

e125..    x4 + x35 =G= 2.47653840011748;

e126..    x5 + x35 =G= 1.7404661748405;

e127..    x6 + x35 =G= 1.82454929205105;

e128..    x7 + x35 =G= 0.0953101798043249;

e129..    x8 + x35 =G= -0.510825623765991;

e130..    x9 + x35 =G= 0.182321556793955;

e131..    x10 + x35 =G= 1.45861502269952;

e132..    x11 + x35 =G= 1.02961941718116;

e133..    x12 + x35 =G= 1.64865862558738;

e134..    x1 + x36 =G= 1.16315080980568;

e135..    x2 + x36 =G= 1.09861228866811;

e136..    x3 + x36 =G= 1.25276296849537;

e137..    x4 + x36 =G= 1.19392246847243;

e138..    x5 + x36 =G= 1.02961941718116;

e139..    x6 + x36 =G= 1.22377543162212;

e140..    x7 + x36 =G= 0.53062825106217;

e141..    x8 + x36 =G= -0.105360515657826;

e142..    x9 + x36 =G= 0.78845736036427;

e143..    x10 + x36 =G= 0.765467842139571;

e144..    x11 + x36 =G= 0.587786664902119;

e145..    x12 + x36 =G= 0.916290731874155;

e146..    x1 + x37 =G= 0.741937344729377;

e147..    x2 + x37 =G= 0.916290731874155;

e148..    x3 + x37 =G= 1.43508452528932;

e149..    x4 + x37 =G= 1.28093384546206;

e150..    x5 + x37 =G= 1.7404661748405;

e151..    x6 + x37 =G= 0.78845736036427;

e152..    x7 + x37 =G= 0.182321556793955;

e153..    x8 + x37 =G= -0.510825623765991;

e154..    x9 + x37 =G= 0.139761942375159;

e155..    x10 + x37 =G= 1.1314021114911;

e156..    x11 + x37 =G= 1.43508452528932;

e157..    x12 + x37 =G= 0.470003629245736;

e158..    x1 + x38 =G= 0.0953101798043249;

e159..    x2 + x38 =G= -0.22314355131421;

e160..    x3 + x38 =G= -0.916290731874155;

e161..    x4 + x38 =G= 0.0953101798043249;

e162..    x5 + x38 =G= 0.587786664902119;

e163..    x6 + x38 =G= 0.916290731874155;

e164..    x7 + x38 =G= -0.693147180559945;

e165..    x8 + x38 =G= 0.262364264467491;

e166..    x9 + x38 =G= 0.336472236621213;

e167..    x10 + x38 =G= 1.44691898293633;

e168..    x11 + x38 =G= 0.993251773010283;

e169..    x12 + x38 =G= -0.105360515657826;

e170..    x1 + x39 =G= 1.43508452528932;

e171..    x2 + x39 =G= 1.38629436111989;

e172..    x3 + x39 =G= 0.78845736036427;

e173..    x4 + x39 =G= -0.693147180559945;

e174..    x5 + x39 =G= 1.22377543162212;

e175..    x6 + x39 =G= 0.78845736036427;

e176..    x7 + x39 =G= 0.336472236621213;

e177..    x8 + x39 =G= -0.105360515657826;

e178..    x9 + x39 =G= 0.741937344729377;

e179..    x10 + x39 =G= 1.48160454092422;

e180..    x11 + x39 =G= 0.78845736036427;

e181..    x12 + x39 =G= 1.16315080980568;

e182..    x1 + x40 =G= 0.993251773010283;

e183..    x2 + x40 =G= 1.45861502269952;

e184..    x3 + x40 =G= 0.641853886172395;

e185..    x4 + x40 =G= 0.693147180559945;

e186..    x5 + x40 =G= 0.53062825106217;

e187..    x6 + x40 =G= -0.356674943938732;

e188..    x7 + x40 =G= -1.20397280432594;

e189..    x8 + x40 =G= -1.6094379124341;

e190..    x9 + x40 =G= 0.470003629245736;

e191..    x10 + x40 =G= 1.25276296849537;

e192..    x11 + x40 =G= 1.22377543162212;

e193..    x12 + x40 =G= 0.741937344729377;

e194.. 485000*exp(x33 - x25) + 297000*exp(x34 - x26) + 320000*exp(x35 - x27) + 
       283000*exp(x36 - x28) + 363000*exp(x37 - x29) + 265000*exp(x38 - x30) + 
       288000*exp(x39 - x31) + 145000*exp(x40 - x32) =L= 6000;

e195..    x1 - 0.693147180559945*b53 - 1.09861228866811*b65
        - 1.38629436111989*b77 - 1.6094379124341*b89 =E= 0;

e196..    x2 - 0.693147180559945*b54 - 1.09861228866811*b66
        - 1.38629436111989*b78 - 1.6094379124341*b90 =E= 0;

e197..    x3 - 0.693147180559945*b55 - 1.09861228866811*b67
        - 1.38629436111989*b79 - 1.6094379124341*b91 =E= 0;

e198..    x4 - 0.693147180559945*b56 - 1.09861228866811*b68
        - 1.38629436111989*b80 - 1.6094379124341*b92 =E= 0;

e199..    x5 - 0.693147180559945*b57 - 1.09861228866811*b69
        - 1.38629436111989*b81 - 1.6094379124341*b93 =E= 0;

e200..    x6 - 0.693147180559945*b58 - 1.09861228866811*b70
        - 1.38629436111989*b82 - 1.6094379124341*b94 =E= 0;

e201..    x7 - 0.693147180559945*b59 - 1.09861228866811*b71
        - 1.38629436111989*b83 - 1.6094379124341*b95 =E= 0;

e202..    x8 - 0.693147180559945*b60 - 1.09861228866811*b72
        - 1.38629436111989*b84 - 1.6094379124341*b96 =E= 0;

e203..    x9 - 0.693147180559945*b61 - 1.09861228866811*b73
        - 1.38629436111989*b85 - 1.6094379124341*b97 =E= 0;

e204..    x10 - 0.693147180559945*b62 - 1.09861228866811*b74
        - 1.38629436111989*b86 - 1.6094379124341*b98 =E= 0;

e205..    x11 - 0.693147180559945*b63 - 1.09861228866811*b75
        - 1.38629436111989*b87 - 1.6094379124341*b99 =E= 0;

e206..    x12 - 0.693147180559945*b64 - 1.09861228866811*b76
        - 1.38629436111989*b88 - 1.6094379124341*b100 =E= 0;

e207..    b41 + b53 + b65 + b77 + b89 =E= 1;

e208..    b42 + b54 + b66 + b78 + b90 =E= 1;

e209..    b43 + b55 + b67 + b79 + b91 =E= 1;

e210..    b44 + b56 + b68 + b80 + b92 =E= 1;

e211..    b45 + b57 + b69 + b81 + b93 =E= 1;

e212..    b46 + b58 + b70 + b82 + b94 =E= 1;

e213..    b47 + b59 + b71 + b83 + b95 =E= 1;

e214..    b48 + b60 + b72 + b84 + b96 =E= 1;

e215..    b49 + b61 + b73 + b85 + b97 =E= 1;

e216..    b50 + b62 + b74 + b86 + b98 =E= 1;

e217..    b51 + b63 + b75 + b87 + b99 =E= 1;

e218..    b52 + b64 + b76 + b88 + b100 =E= 1;

* set non-default bounds
x1.up = 1.6094379124341;
x2.up = 1.6094379124341;
x3.up = 1.6094379124341;
x4.up = 1.6094379124341;
x5.up = 1.6094379124341;
x6.up = 1.6094379124341;
x7.up = 1.6094379124341;
x8.up = 1.6094379124341;
x9.up = 1.6094379124341;
x10.up = 1.6094379124341;
x11.up = 1.6094379124341;
x12.up = 1.6094379124341;
x13.lo = 5.7037824746562; x13.up = 8.00636756765025;
x14.lo = 5.7037824746562; x14.up = 8.00636756765025;
x15.lo = 5.7037824746562; x15.up = 8.00636756765025;
x16.lo = 5.7037824746562; x16.up = 8.00636756765025;
x17.lo = 5.7037824746562; x17.up = 8.00636756765025;
x18.lo = 5.7037824746562; x18.up = 8.00636756765025;
x19.lo = 5.7037824746562; x19.up = 8.00636756765025;
x20.lo = 5.7037824746562; x20.up = 8.00636756765025;
x21.lo = 5.7037824746562; x21.up = 8.00636756765025;
x22.lo = 5.7037824746562; x22.up = 8.00636756765025;
x23.lo = 5.7037824746562; x23.up = 8.00636756765025;
x24.lo = 5.7037824746562; x24.up = 8.00636756765025;
x25.lo = 4.89920702407788; x25.up = 5.93950480817727;
x26.lo = 4.2094573693226; x26.up = 6.78259213602813;
x27.lo = 4.8436620142491; x27.up = 6.4803112641552;
x28.lo = 3.49701248447645; x28.up = 6.45880505893423;
x29.lo = 4.2336716274432; x29.up = 6.50229017087397;
x30.lo = 3.62545142726039; x30.up = 6.08944495546819;
x31.lo = 3.74336763939801; x31.up = 6.35770894206286;
x32.lo = 3.03415138345794; x32.up = 7.21791020728598;
x33.lo = 0.506817602368452; x33.up = 2.11625551480255;
x34.lo = 0.307484699747961; x34.up = 1.91692261218206;
x35.lo = 0.867100487683383; x35.up = 2.47653840011748;
x36.lo = -0.356674943938732; x36.up = 1.25276296849537;
x37.lo = 0.131028262406404; x37.up = 1.7404661748405;
x38.lo = -0.162518929497775; x38.up = 1.44691898293633;
x39.lo = -0.127833371509885; x39.up = 1.48160454092422;
x40.lo = -0.150822889734584; x40.up = 1.45861502269952;

* set non-default levels
x36.l = -0.356674943938732;
x38.l = -0.162518929497775;
x39.l = -0.127833371509885;
x40.l = -0.150822889734584;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set MINLP $set MINLP MINLP
Solve m using %MINLP% minimizing objvar;


Last updated: 2018-05-28 Git hash: ac4a64c1
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