MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance squfl010-040

Separable quadratic uncapacitated facility location problem.
A set of customers, each having unit demand, has to be satisfied by open facilities. The objective is to minimize the sum of the fixed cost for operating facilities and the shipping cost which is proportional to the square of the quantity delivered to each customer.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
312.11391560 p1 ( gdx sol )
(infeas: 2e-16)
259.01140090 p2 ( gdx sol )
(infeas: 1e-15)
240.59852620 p3 ( gdx sol )
(infeas: 1e-12)
Other points (infeas > 1e-08)  
Dual Bounds
-576.90649990 (ALPHAECP)
240.59485050 (ANTIGONE)
240.59852590 (BARON)
240.59852600 (BONMIN)
240.59834470 (COUENNE)
240.59852620 (CPLEX)
240.59852620 (GUROBI)
240.59852620 (LINDO)
240.59852400 (SCIP)
240.59852620 (SHOT)
References Günlük, Oktay, Lee, Jon, and Weismantel, Robert, MINLP Strengthening for Separable Convex Quadratic Transportation-Cost UFL, Tech. Rep. RC24213, IBM Research, 2007.
Günlük, Oktay and Linderoth, Jeff T, Perspective reformulations of mixed integer nonlinear programs with indicator variables, Mathematical Programming, 124:1-2, 2010, 183-205.
Günlük, Oktay and Linderoth, Jeff T, Perspective Reformulation and Applications. In Lee, Jon and Leyffer, Sven, Eds, Mixed Integer Nonlinear Programming, Springer, 2012, 61-89.
Application Facility Location
Added to library 24 Feb 2014
Problem type MBQP
#Variables 410
#Binary Variables 10
#Integer Variables 0
#Nonlinear Variables 400
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 410
#Nonlinear Nonzeros in Objective 400
#Constraints 440
#Linear Constraints 440
#Quadratic Constraints 0
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature linear
#Nonzeros in Jacobian 1200
#Nonlinear Nonzeros in Jacobian 0
#Nonzeros in (Upper-Left) Hessian of Lagrangian 400
#Nonzeros in Diagonal of Hessian of Lagrangian 400
#Blocks in Hessian of Lagrangian 400
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0000e+00
Maximal coefficient 9.6000e+01
Infeasibility of initial point 1
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
*        441       41        0      400        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        411      401       10        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*       1611     1211      400        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,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53
          ,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69,x70
          ,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86,x87
          ,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102,x103
          ,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115,x116
          ,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128,x129
          ,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141,x142
          ,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154,x155
          ,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167,x168
          ,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179,x180,x181
          ,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192,x193,x194
          ,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205,x206,x207
          ,x208,x209,x210,x211,x212,x213,x214,x215,x216,x217,x218,x219,x220
          ,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231,x232,x233
          ,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244,x245,x246
          ,x247,x248,x249,x250,x251,x252,x253,x254,x255,x256,x257,x258,x259
          ,x260,x261,x262,x263,x264,x265,x266,x267,x268,x269,x270,x271,x272
          ,x273,x274,x275,x276,x277,x278,x279,x280,x281,x282,x283,x284,x285
          ,x286,x287,x288,x289,x290,x291,x292,x293,x294,x295,x296,x297,x298
          ,x299,x300,x301,x302,x303,x304,x305,x306,x307,x308,x309,x310,x311
          ,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322,x323,x324
          ,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335,x336,x337
          ,x338,x339,x340,x341,x342,x343,x344,x345,x346,x347,x348,x349,x350
          ,x351,x352,x353,x354,x355,x356,x357,x358,x359,x360,x361,x362,x363
          ,x364,x365,x366,x367,x368,x369,x370,x371,x372,x373,x374,x375,x376
          ,x377,x378,x379,x380,x381,x382,x383,x384,x385,x386,x387,x388,x389
          ,x390,x391,x392,x393,x394,x395,x396,x397,x398,x399,x400,b401,b402
          ,b403,b404,b405,b406,b407,b408,b409,b410,objvar;

Positive 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,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
          ,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68
          ,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85
          ,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101
          ,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114
          ,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127
          ,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140
          ,x141,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153
          ,x154,x155,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166
          ,x167,x168,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179
          ,x180,x181,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192
          ,x193,x194,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205
          ,x206,x207,x208,x209,x210,x211,x212,x213,x214,x215,x216,x217,x218
          ,x219,x220,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231
          ,x232,x233,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244
          ,x245,x246,x247,x248,x249,x250,x251,x252,x253,x254,x255,x256,x257
          ,x258,x259,x260,x261,x262,x263,x264,x265,x266,x267,x268,x269,x270
          ,x271,x272,x273,x274,x275,x276,x277,x278,x279,x280,x281,x282,x283
          ,x284,x285,x286,x287,x288,x289,x290,x291,x292,x293,x294,x295,x296
          ,x297,x298,x299,x300,x301,x302,x303,x304,x305,x306,x307,x308,x309
          ,x310,x311,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322
          ,x323,x324,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335
          ,x336,x337,x338,x339,x340,x341,x342,x343,x344,x345,x346,x347,x348
          ,x349,x350,x351,x352,x353,x354,x355,x356,x357,x358,x359,x360,x361
          ,x362,x363,x364,x365,x366,x367,x368,x369,x370,x371,x372,x373,x374
          ,x375,x376,x377,x378,x379,x380,x381,x382,x383,x384,x385,x386,x387
          ,x388,x389,x390,x391,x392,x393,x394,x395,x396,x397,x398,x399,x400;

Binary Variables  b401,b402,b403,b404,b405,b406,b407,b408,b409,b410;

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,e219,e220
          ,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
          ,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
          ,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
          ,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
          ,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
          ,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
          ,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
          ,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
          ,e325,e326,e327,e328,e329,e330,e331,e332,e333,e334,e335,e336,e337
          ,e338,e339,e340,e341,e342,e343,e344,e345,e346,e347,e348,e349,e350
          ,e351,e352,e353,e354,e355,e356,e357,e358,e359,e360,e361,e362,e363
          ,e364,e365,e366,e367,e368,e369,e370,e371,e372,e373,e374,e375,e376
          ,e377,e378,e379,e380,e381,e382,e383,e384,e385,e386,e387,e388,e389
          ,e390,e391,e392,e393,e394,e395,e396,e397,e398,e399,e400,e401,e402
          ,e403,e404,e405,e406,e407,e408,e409,e410,e411,e412,e413,e414,e415
          ,e416,e417,e418,e419,e420,e421,e422,e423,e424,e425,e426,e427,e428
          ,e429,e430,e431,e432,e433,e434,e435,e436,e437,e438,e439,e440,e441;


e1.. -(22.6381215938389*x1*x1 + 17.4766742929333*x2*x2 + 25.4187922554943*x3*x3
      + 27.1035680108328*x4*x4 + 23.5265920480145*x5*x5 + 15.0632062277023*x6*
     x6 + 20.9421663198548*x7*x7 + 26.8892056897746*x8*x8 + 20.0917422875622*x9
     *x9 + 22.0772847970411*x10*x10 + 27.2388846140546*x11*x11 + 
     9.91963706190005*x12*x12 + 19.7178101724914*x13*x13 + 24.8309507278873*x14
     *x14 + 8.9002697856764*x15*x15 + 16.6041126627463*x16*x16 + 
     20.9076060331827*x17*x17 + 16.4388004434191*x18*x18 + 16.5182812638846*x19
     *x19 + 9.88089720278549*x20*x20 + 12.1667353823901*x21*x21 + 
     24.3980080339173*x22*x22 + 5.89692650301416*x23*x23 + 27.3832431206695*x24
     *x24 + 25.1917920228286*x25*x25 + 22.2371740468545*x26*x26 + 
     18.6146514682277*x27*x27 + 16.2386002137011*x28*x28 + 11.7825630607253*x29
     *x29 + 16.4103192237971*x30*x30 + 14.0196662324014*x31*x31 + 
     27.5888902829072*x32*x32 + 32.1142581799004*x33*x33 + 21.8448948139885*x34
     *x34 + 15.6688171723033*x35*x35 + 10.5878182197044*x36*x36 + 
     21.2659919405636*x37*x37 + 19.9399176135982*x38*x38 + 20.4104873074429*x39
     *x39 + 13.8610580105744*x40*x40 + 45.1831182079448*x41*x41 + 
     41.8922529723062*x42*x42 + 25.9983886435708*x43*x43 + 18.4146205683989*x44
     *x44 + 44.4508052690104*x45*x45 + 43.222614022418*x46*x46 + 
     7.83087186917261*x47*x47 + 44.0974324424632*x48*x48 + 24.1032080114607*x49
     *x49 + 21.3901261474851*x50*x50 + 14.2786694069753*x51*x51 + 
     19.6496550606165*x52*x52 + 37.1545124093958*x53*x53 + 48.6880643503487*x54
     *x54 + 37.4288246723691*x55*x55 + 21.1065932390664*x56*x56 + 
     8.59743563059761*x57*x57 + 43.7082794462957*x58*x58 + 26.9893113680541*x59
     *x59 + 38.4147587357678*x60*x60 + 27.6431119850894*x61*x61 + 
     27.2081707885029*x62*x62 + 26.180086548645*x63*x63 + 23.4793052891068*x64*
     x64 + 8.05600976794875*x65*x65 + 43.6070455642507*x66*x66 + 
     45.5814383894113*x67*x67 + 24.8259847424505*x68*x68 + 40.3429322999097*x69
     *x69 + 34.7333648360789*x70*x70 + 39.6370142018807*x71*x71 + 
     15.7319707168115*x72*x72 + 10.2078177848558*x73*x73 + 33.6787428698496*x74
     *x74 + 40.2454233156587*x75*x75 + 36.634811099167*x76*x76 + 22.27676876787
     *x77*x77 + 26.5232783828231*x78*x78 + 43.5517742892559*x79*x79 + 
     41.5350353466256*x80*x80 + 41.8335888980131*x81*x81 + 48.5376172984876*x82
     *x82 + 38.3466968942412*x83*x83 + 8.41612312434711*x84*x84 + 
     52.7549779687686*x85*x85 + 47.0825798478005*x86*x86 + 17.3796675041212*x87
     *x87 + 38.1234862605185*x88*x88 + 35.3396889090277*x89*x89 + 
     14.4643524524883*x90*x90 + 5.34829959943684*x91*x91 + 22.2653351256225*x92
     *x92 + 46.2454200528829*x93*x93 + 55.8374582944024*x94*x94 + 
     40.6308664485861*x95*x95 + 31.4335072617773*x96*x96 + 13.4112067223631*x97
     *x97 + 48.5696936037444*x98*x98 + 36.8993023115838*x99*x99 + 
     40.9836123190193*x100*x100 + 25.6312719069291*x101*x101 + 39.2062655130486
     *x102*x102 + 27.5420044062431*x103*x103 + 13.2995411207383*x104*x104 + 
     8.46899828859079*x105*x105 + 39.825353158153*x106*x106 + 50.7145370144725*
     x107*x107 + 20.9305616681182*x108*x108 + 43.0974611923811*x109*x109 + 
     31.2589828634291*x110*x110 + 39.0004467733683*x111*x111 + 5.85207457485276
     *x112*x112 + 4.05707679016365*x113*x113 + 27.4118952163913*x114*x114 + 
     46.7403642600311*x115*x115 + 42.1857296019859*x116*x116 + 33.9770380372982
     *x117*x117 + 37.4815569098476*x118*x118 + 40.7766875146816*x119*x119 + 
     42.3432110912681*x120*x120 + 41.8096676388354*x121*x121 + 18.5696808935251
     *x122*x122 + 7.58990279485765*x123*x123 + 37.8694515922791*x124*x124 + 
     17.7230764563209*x125*x125 + 25.4760814821429*x126*x126 + 21.7375222978638
     *x127*x127 + 46.2693611273112*x128*x128 + 4.54660149955549*x129*x129 + 
     35.4495510183106*x130*x130 + 35.7984880582191*x131*x131 + 21.901140187113*
     x132*x132 + 10.0418757457177*x133*x133 + 23.3064810423527*x134*x134 + 
     23.3941126275948*x135*x135 + 7.47045385542959*x136*x136 + 25.5396143114494
     *x137*x137 + 23.6714747719547*x138*x138 + 2.96080784760476*x139*x139 + 
     25.3193751498536*x140*x140 + 30.0182424556163*x141*x141 + 5.83084524853944
     *x142*x142 + 23.6514987581814*x143*x143 + 40.5072826571826*x144*x144 + 
     30.4312990116754*x145*x145 + 41.5896374550884*x146*x146 + 24.501600970022*
     x147*x147 + 32.2666564456072*x148*x148 + 26.024154868957*x149*x149 + 
     35.6018006285022*x150*x150 + 32.7659324359211*x151*x151 + 36.8394615362202
     *x152*x152 + 36.7889144303202*x153*x153 + 40.0508174481167*x154*x154 + 
     17.6775070488635*x155*x155 + 17.579862644958*x156*x156 + 6.86014064091719*
     x157*x157 + 2.07714802960749*x158*x158 + 39.5431633780402*x159*x159 + 
     30.9129885122014*x160*x160 + 53.7186648061791*x161*x161 + 34.3820347456099
     *x162*x162 + 8.45720703763966*x163*x163 + 39.0462093345896*x164*x164 + 
     32.8211593848664*x165*x165 + 40.7771865823617*x166*x166 + 20.6422254432407
     *x167*x167 + 56.3016199376175*x168*x168 + 12.2817800194979*x169*x169 + 
     39.2313614019054*x170*x170 + 35.6110459801796*x171*x171 + 28.8191322549938
     *x172*x172 + 25.4018036358971*x173*x173 + 38.7666408171936*x174*x174 + 
     37.6390516445844*x175*x175 + 14.7674823830956*x176*x176 + 25.5404894453816
     *x177*x177 + 39.3018592559483*x178*x178 + 17.3036764948037*x179*x179 + 
     39.4235548336344*x180*x180 + 38.6270585541198*x181*x181 + 10.4664070033472
     *x182*x182 + 33.421447798866*x183*x183 + 43.2253499251171*x184*x184 + 
     29.0353047005975*x185*x185 + 52.9939023039257*x186*x186 + 40.257102945243*
     x187*x187 + 38.860600314683*x188*x188 + 40.5310486179103*x189*x189 + 
     45.4664216368371*x190*x190 + 45.3664020287264*x191*x191 + 36.9853554415264
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     29.2837944824625*x275*x275 + 27.1625585907911*x276*x276 + 7.2350848701947*
     x277*x277 + 11.9047505480768*x278*x278 + 42.6513971007399*x279*x279 + 
     36.89043170665*x280*x280 + 6.64903572985773*x281*x281 + 36.3350815872672*
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     43.7434810880439*x285*x285 + 27.8630451485851*x286*x286 + 36.8692783297684
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     *x307*x307 + 17.3256727590746*x308*x308 + 23.1352262436616*x309*x309 + 
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     27.2510415470059*x325*x325 + 34.1223028388969*x326*x326 + 17.5567214281191
     *x327*x327 + 50.3743988099625*x328*x328 + 5.6590918620866*x329*x329 + 
     34.9780577982336*x330*x330 + 32.778655850946*x331*x331 + 23.3213666648354*
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     30.9395752881326*x335*x335 + 8.25314573977791*x336*x336 + 22.282009707736*
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     *x342*x342 + 27.3378028092636*x343*x343 + 39.4220274031084*x344*x344 + 
     26.5179831202782*x345*x345 + 46.73622174105*x346*x346 + 33.7929660091746*
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     39.5062161815598*x350*x350 + 38.8560640891196*x351*x351 + 34.0495249267681
     *x352*x352 + 31.8172613223881*x353*x353 + 42.5075613284177*x354*x354 + 
     27.0453220696648*x355*x355 + 26.1304188859277*x356*x356 + 3.69037126260968
     *x357*x357 + 7.63043300249988*x358*x358 + 45.1739476749785*x359*x359 + 
     37.9751942193799*x360*x360 + 20.7529705896298*x361*x361 + 14.3893321866194
     *x362*x362 + 28.0817490698092*x363*x363 + 31.4238046558608*x364*x364 + 
     21.2794747772648*x365*x365 + 10.1834356269501*x366*x366 + 25.9014119165658
     *x367*x367 + 26.4883984185792*x368*x368 + 22.9076512770755*x369*x369 + 
     25.997089184782*x370*x370 + 31.8823915967004*x371*x371 + 14.8080477345421*
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     3.88397054710166*x375*x375 + 20.0589377640637*x376*x376 + 25.9149998836053
     *x377*x377 + 11.9924452452965*x378*x378 + 18.6176990335993*x379*x379 + 
     5.02472422177832*x380*x380 + 14.8008188904632*x381*x381 + 26.7875251230091
     *x382*x382 + 9.67687108012286*x383*x383 + 31.1767205303097*x384*x384 + 
     30.1406979856964*x385*x385 + 20.8511059740515*x386*x386 + 14.2363298453376
     *x387*x387 + 19.5722735572342*x388*x388 + 6.80248295322444*x389*x389 + 
     16.9867420360034*x390*x390 + 11.5518321715263*x391*x391 + 32.1358835441953
     *x392*x392 + 37.0226994405158*x393*x393 + 23.4627429415224*x394*x394 + 
     12.7078688009999*x395*x395 + 7.58658819030826*x396*x396 + 24.4312631498729
     *x397*x397 + 22.2514570586902*x398*x398 + 18.4755526211779*x399*x399 + 
     9.86807133301415*x400*x400) - 62*b401 - 3*b402 - 68*b403 - 19*b404
      - 9*b405 - 18*b406 - 48*b407 - 44*b408 - 96*b409 - 25*b410 + objvar =E= 0
     ;

e2..    x1 - b401 =L= 0;

e3..    x2 - b401 =L= 0;

e4..    x3 - b401 =L= 0;

e5..    x4 - b401 =L= 0;

e6..    x5 - b401 =L= 0;

e7..    x6 - b401 =L= 0;

e8..    x7 - b401 =L= 0;

e9..    x8 - b401 =L= 0;

e10..    x9 - b401 =L= 0;

e11..    x10 - b401 =L= 0;

e12..    x11 - b401 =L= 0;

e13..    x12 - b401 =L= 0;

e14..    x13 - b401 =L= 0;

e15..    x14 - b401 =L= 0;

e16..    x15 - b401 =L= 0;

e17..    x16 - b401 =L= 0;

e18..    x17 - b401 =L= 0;

e19..    x18 - b401 =L= 0;

e20..    x19 - b401 =L= 0;

e21..    x20 - b401 =L= 0;

e22..    x21 - b401 =L= 0;

e23..    x22 - b401 =L= 0;

e24..    x23 - b401 =L= 0;

e25..    x24 - b401 =L= 0;

e26..    x25 - b401 =L= 0;

e27..    x26 - b401 =L= 0;

e28..    x27 - b401 =L= 0;

e29..    x28 - b401 =L= 0;

e30..    x29 - b401 =L= 0;

e31..    x30 - b401 =L= 0;

e32..    x31 - b401 =L= 0;

e33..    x32 - b401 =L= 0;

e34..    x33 - b401 =L= 0;

e35..    x34 - b401 =L= 0;

e36..    x35 - b401 =L= 0;

e37..    x36 - b401 =L= 0;

e38..    x37 - b401 =L= 0;

e39..    x38 - b401 =L= 0;

e40..    x39 - b401 =L= 0;

e41..    x40 - b401 =L= 0;

e42..    x41 - b402 =L= 0;

e43..    x42 - b402 =L= 0;

e44..    x43 - b402 =L= 0;

e45..    x44 - b402 =L= 0;

e46..    x45 - b402 =L= 0;

e47..    x46 - b402 =L= 0;

e48..    x47 - b402 =L= 0;

e49..    x48 - b402 =L= 0;

e50..    x49 - b402 =L= 0;

e51..    x50 - b402 =L= 0;

e52..    x51 - b402 =L= 0;

e53..    x52 - b402 =L= 0;

e54..    x53 - b402 =L= 0;

e55..    x54 - b402 =L= 0;

e56..    x55 - b402 =L= 0;

e57..    x56 - b402 =L= 0;

e58..    x57 - b402 =L= 0;

e59..    x58 - b402 =L= 0;

e60..    x59 - b402 =L= 0;

e61..    x60 - b402 =L= 0;

e62..    x61 - b402 =L= 0;

e63..    x62 - b402 =L= 0;

e64..    x63 - b402 =L= 0;

e65..    x64 - b402 =L= 0;

e66..    x65 - b402 =L= 0;

e67..    x66 - b402 =L= 0;

e68..    x67 - b402 =L= 0;

e69..    x68 - b402 =L= 0;

e70..    x69 - b402 =L= 0;

e71..    x70 - b402 =L= 0;

e72..    x71 - b402 =L= 0;

e73..    x72 - b402 =L= 0;

e74..    x73 - b402 =L= 0;

e75..    x74 - b402 =L= 0;

e76..    x75 - b402 =L= 0;

e77..    x76 - b402 =L= 0;

e78..    x77 - b402 =L= 0;

e79..    x78 - b402 =L= 0;

e80..    x79 - b402 =L= 0;

e81..    x80 - b402 =L= 0;

e82..    x81 - b403 =L= 0;

e83..    x82 - b403 =L= 0;

e84..    x83 - b403 =L= 0;

e85..    x84 - b403 =L= 0;

e86..    x85 - b403 =L= 0;

e87..    x86 - b403 =L= 0;

e88..    x87 - b403 =L= 0;

e89..    x88 - b403 =L= 0;

e90..    x89 - b403 =L= 0;

e91..    x90 - b403 =L= 0;

e92..    x91 - b403 =L= 0;

e93..    x92 - b403 =L= 0;

e94..    x93 - b403 =L= 0;

e95..    x94 - b403 =L= 0;

e96..    x95 - b403 =L= 0;

e97..    x96 - b403 =L= 0;

e98..    x97 - b403 =L= 0;

e99..    x98 - b403 =L= 0;

e100..    x99 - b403 =L= 0;

e101..    x100 - b403 =L= 0;

e102..    x101 - b403 =L= 0;

e103..    x102 - b403 =L= 0;

e104..    x103 - b403 =L= 0;

e105..    x104 - b403 =L= 0;

e106..    x105 - b403 =L= 0;

e107..    x106 - b403 =L= 0;

e108..    x107 - b403 =L= 0;

e109..    x108 - b403 =L= 0;

e110..    x109 - b403 =L= 0;

e111..    x110 - b403 =L= 0;

e112..    x111 - b403 =L= 0;

e113..    x112 - b403 =L= 0;

e114..    x113 - b403 =L= 0;

e115..    x114 - b403 =L= 0;

e116..    x115 - b403 =L= 0;

e117..    x116 - b403 =L= 0;

e118..    x117 - b403 =L= 0;

e119..    x118 - b403 =L= 0;

e120..    x119 - b403 =L= 0;

e121..    x120 - b403 =L= 0;

e122..    x121 - b404 =L= 0;

e123..    x122 - b404 =L= 0;

e124..    x123 - b404 =L= 0;

e125..    x124 - b404 =L= 0;

e126..    x125 - b404 =L= 0;

e127..    x126 - b404 =L= 0;

e128..    x127 - b404 =L= 0;

e129..    x128 - b404 =L= 0;

e130..    x129 - b404 =L= 0;

e131..    x130 - b404 =L= 0;

e132..    x131 - b404 =L= 0;

e133..    x132 - b404 =L= 0;

e134..    x133 - b404 =L= 0;

e135..    x134 - b404 =L= 0;

e136..    x135 - b404 =L= 0;

e137..    x136 - b404 =L= 0;

e138..    x137 - b404 =L= 0;

e139..    x138 - b404 =L= 0;

e140..    x139 - b404 =L= 0;

e141..    x140 - b404 =L= 0;

e142..    x141 - b404 =L= 0;

e143..    x142 - b404 =L= 0;

e144..    x143 - b404 =L= 0;

e145..    x144 - b404 =L= 0;

e146..    x145 - b404 =L= 0;

e147..    x146 - b404 =L= 0;

e148..    x147 - b404 =L= 0;

e149..    x148 - b404 =L= 0;

e150..    x149 - b404 =L= 0;

e151..    x150 - b404 =L= 0;

e152..    x151 - b404 =L= 0;

e153..    x152 - b404 =L= 0;

e154..    x153 - b404 =L= 0;

e155..    x154 - b404 =L= 0;

e156..    x155 - b404 =L= 0;

e157..    x156 - b404 =L= 0;

e158..    x157 - b404 =L= 0;

e159..    x158 - b404 =L= 0;

e160..    x159 - b404 =L= 0;

e161..    x160 - b404 =L= 0;

e162..    x161 - b405 =L= 0;

e163..    x162 - b405 =L= 0;

e164..    x163 - b405 =L= 0;

e165..    x164 - b405 =L= 0;

e166..    x165 - b405 =L= 0;

e167..    x166 - b405 =L= 0;

e168..    x167 - b405 =L= 0;

e169..    x168 - b405 =L= 0;

e170..    x169 - b405 =L= 0;

e171..    x170 - b405 =L= 0;

e172..    x171 - b405 =L= 0;

e173..    x172 - b405 =L= 0;

e174..    x173 - b405 =L= 0;

e175..    x174 - b405 =L= 0;

e176..    x175 - b405 =L= 0;

e177..    x176 - b405 =L= 0;

e178..    x177 - b405 =L= 0;

e179..    x178 - b405 =L= 0;

e180..    x179 - b405 =L= 0;

e181..    x180 - b405 =L= 0;

e182..    x181 - b405 =L= 0;

e183..    x182 - b405 =L= 0;

e184..    x183 - b405 =L= 0;

e185..    x184 - b405 =L= 0;

e186..    x185 - b405 =L= 0;

e187..    x186 - b405 =L= 0;

e188..    x187 - b405 =L= 0;

e189..    x188 - b405 =L= 0;

e190..    x189 - b405 =L= 0;

e191..    x190 - b405 =L= 0;

e192..    x191 - b405 =L= 0;

e193..    x192 - b405 =L= 0;

e194..    x193 - b405 =L= 0;

e195..    x194 - b405 =L= 0;

e196..    x195 - b405 =L= 0;

e197..    x196 - b405 =L= 0;

e198..    x197 - b405 =L= 0;

e199..    x198 - b405 =L= 0;

e200..    x199 - b405 =L= 0;

e201..    x200 - b405 =L= 0;

e202..    x201 - b406 =L= 0;

e203..    x202 - b406 =L= 0;

e204..    x203 - b406 =L= 0;

e205..    x204 - b406 =L= 0;

e206..    x205 - b406 =L= 0;

e207..    x206 - b406 =L= 0;

e208..    x207 - b406 =L= 0;

e209..    x208 - b406 =L= 0;

e210..    x209 - b406 =L= 0;

e211..    x210 - b406 =L= 0;

e212..    x211 - b406 =L= 0;

e213..    x212 - b406 =L= 0;

e214..    x213 - b406 =L= 0;

e215..    x214 - b406 =L= 0;

e216..    x215 - b406 =L= 0;

e217..    x216 - b406 =L= 0;

e218..    x217 - b406 =L= 0;

e219..    x218 - b406 =L= 0;

e220..    x219 - b406 =L= 0;

e221..    x220 - b406 =L= 0;

e222..    x221 - b406 =L= 0;

e223..    x222 - b406 =L= 0;

e224..    x223 - b406 =L= 0;

e225..    x224 - b406 =L= 0;

e226..    x225 - b406 =L= 0;

e227..    x226 - b406 =L= 0;

e228..    x227 - b406 =L= 0;

e229..    x228 - b406 =L= 0;

e230..    x229 - b406 =L= 0;

e231..    x230 - b406 =L= 0;

e232..    x231 - b406 =L= 0;

e233..    x232 - b406 =L= 0;

e234..    x233 - b406 =L= 0;

e235..    x234 - b406 =L= 0;

e236..    x235 - b406 =L= 0;

e237..    x236 - b406 =L= 0;

e238..    x237 - b406 =L= 0;

e239..    x238 - b406 =L= 0;

e240..    x239 - b406 =L= 0;

e241..    x240 - b406 =L= 0;

e242..    x241 - b407 =L= 0;

e243..    x242 - b407 =L= 0;

e244..    x243 - b407 =L= 0;

e245..    x244 - b407 =L= 0;

e246..    x245 - b407 =L= 0;

e247..    x246 - b407 =L= 0;

e248..    x247 - b407 =L= 0;

e249..    x248 - b407 =L= 0;

e250..    x249 - b407 =L= 0;

e251..    x250 - b407 =L= 0;

e252..    x251 - b407 =L= 0;

e253..    x252 - b407 =L= 0;

e254..    x253 - b407 =L= 0;

e255..    x254 - b407 =L= 0;

e256..    x255 - b407 =L= 0;

e257..    x256 - b407 =L= 0;

e258..    x257 - b407 =L= 0;

e259..    x258 - b407 =L= 0;

e260..    x259 - b407 =L= 0;

e261..    x260 - b407 =L= 0;

e262..    x261 - b407 =L= 0;

e263..    x262 - b407 =L= 0;

e264..    x263 - b407 =L= 0;

e265..    x264 - b407 =L= 0;

e266..    x265 - b407 =L= 0;

e267..    x266 - b407 =L= 0;

e268..    x267 - b407 =L= 0;

e269..    x268 - b407 =L= 0;

e270..    x269 - b407 =L= 0;

e271..    x270 - b407 =L= 0;

e272..    x271 - b407 =L= 0;

e273..    x272 - b407 =L= 0;

e274..    x273 - b407 =L= 0;

e275..    x274 - b407 =L= 0;

e276..    x275 - b407 =L= 0;

e277..    x276 - b407 =L= 0;

e278..    x277 - b407 =L= 0;

e279..    x278 - b407 =L= 0;

e280..    x279 - b407 =L= 0;

e281..    x280 - b407 =L= 0;

e282..    x281 - b408 =L= 0;

e283..    x282 - b408 =L= 0;

e284..    x283 - b408 =L= 0;

e285..    x284 - b408 =L= 0;

e286..    x285 - b408 =L= 0;

e287..    x286 - b408 =L= 0;

e288..    x287 - b408 =L= 0;

e289..    x288 - b408 =L= 0;

e290..    x289 - b408 =L= 0;

e291..    x290 - b408 =L= 0;

e292..    x291 - b408 =L= 0;

e293..    x292 - b408 =L= 0;

e294..    x293 - b408 =L= 0;

e295..    x294 - b408 =L= 0;

e296..    x295 - b408 =L= 0;

e297..    x296 - b408 =L= 0;

e298..    x297 - b408 =L= 0;

e299..    x298 - b408 =L= 0;

e300..    x299 - b408 =L= 0;

e301..    x300 - b408 =L= 0;

e302..    x301 - b408 =L= 0;

e303..    x302 - b408 =L= 0;

e304..    x303 - b408 =L= 0;

e305..    x304 - b408 =L= 0;

e306..    x305 - b408 =L= 0;

e307..    x306 - b408 =L= 0;

e308..    x307 - b408 =L= 0;

e309..    x308 - b408 =L= 0;

e310..    x309 - b408 =L= 0;

e311..    x310 - b408 =L= 0;

e312..    x311 - b408 =L= 0;

e313..    x312 - b408 =L= 0;

e314..    x313 - b408 =L= 0;

e315..    x314 - b408 =L= 0;

e316..    x315 - b408 =L= 0;

e317..    x316 - b408 =L= 0;

e318..    x317 - b408 =L= 0;

e319..    x318 - b408 =L= 0;

e320..    x319 - b408 =L= 0;

e321..    x320 - b408 =L= 0;

e322..    x321 - b409 =L= 0;

e323..    x322 - b409 =L= 0;

e324..    x323 - b409 =L= 0;

e325..    x324 - b409 =L= 0;

e326..    x325 - b409 =L= 0;

e327..    x326 - b409 =L= 0;

e328..    x327 - b409 =L= 0;

e329..    x328 - b409 =L= 0;

e330..    x329 - b409 =L= 0;

e331..    x330 - b409 =L= 0;

e332..    x331 - b409 =L= 0;

e333..    x332 - b409 =L= 0;

e334..    x333 - b409 =L= 0;

e335..    x334 - b409 =L= 0;

e336..    x335 - b409 =L= 0;

e337..    x336 - b409 =L= 0;

e338..    x337 - b409 =L= 0;

e339..    x338 - b409 =L= 0;

e340..    x339 - b409 =L= 0;

e341..    x340 - b409 =L= 0;

e342..    x341 - b409 =L= 0;

e343..    x342 - b409 =L= 0;

e344..    x343 - b409 =L= 0;

e345..    x344 - b409 =L= 0;

e346..    x345 - b409 =L= 0;

e347..    x346 - b409 =L= 0;

e348..    x347 - b409 =L= 0;

e349..    x348 - b409 =L= 0;

e350..    x349 - b409 =L= 0;

e351..    x350 - b409 =L= 0;

e352..    x351 - b409 =L= 0;

e353..    x352 - b409 =L= 0;

e354..    x353 - b409 =L= 0;

e355..    x354 - b409 =L= 0;

e356..    x355 - b409 =L= 0;

e357..    x356 - b409 =L= 0;

e358..    x357 - b409 =L= 0;

e359..    x358 - b409 =L= 0;

e360..    x359 - b409 =L= 0;

e361..    x360 - b409 =L= 0;

e362..    x361 - b410 =L= 0;

e363..    x362 - b410 =L= 0;

e364..    x363 - b410 =L= 0;

e365..    x364 - b410 =L= 0;

e366..    x365 - b410 =L= 0;

e367..    x366 - b410 =L= 0;

e368..    x367 - b410 =L= 0;

e369..    x368 - b410 =L= 0;

e370..    x369 - b410 =L= 0;

e371..    x370 - b410 =L= 0;

e372..    x371 - b410 =L= 0;

e373..    x372 - b410 =L= 0;

e374..    x373 - b410 =L= 0;

e375..    x374 - b410 =L= 0;

e376..    x375 - b410 =L= 0;

e377..    x376 - b410 =L= 0;

e378..    x377 - b410 =L= 0;

e379..    x378 - b410 =L= 0;

e380..    x379 - b410 =L= 0;

e381..    x380 - b410 =L= 0;

e382..    x381 - b410 =L= 0;

e383..    x382 - b410 =L= 0;

e384..    x383 - b410 =L= 0;

e385..    x384 - b410 =L= 0;

e386..    x385 - b410 =L= 0;

e387..    x386 - b410 =L= 0;

e388..    x387 - b410 =L= 0;

e389..    x388 - b410 =L= 0;

e390..    x389 - b410 =L= 0;

e391..    x390 - b410 =L= 0;

e392..    x391 - b410 =L= 0;

e393..    x392 - b410 =L= 0;

e394..    x393 - b410 =L= 0;

e395..    x394 - b410 =L= 0;

e396..    x395 - b410 =L= 0;

e397..    x396 - b410 =L= 0;

e398..    x397 - b410 =L= 0;

e399..    x398 - b410 =L= 0;

e400..    x399 - b410 =L= 0;

e401..    x400 - b410 =L= 0;

e402..    x1 + x41 + x81 + x121 + x161 + x201 + x241 + x281 + x321 + x361 =E= 1
       ;

e403..    x2 + x42 + x82 + x122 + x162 + x202 + x242 + x282 + x322 + x362 =E= 1
       ;

e404..    x3 + x43 + x83 + x123 + x163 + x203 + x243 + x283 + x323 + x363 =E= 1
       ;

e405..    x4 + x44 + x84 + x124 + x164 + x204 + x244 + x284 + x324 + x364 =E= 1
       ;

e406..    x5 + x45 + x85 + x125 + x165 + x205 + x245 + x285 + x325 + x365 =E= 1
       ;

e407..    x6 + x46 + x86 + x126 + x166 + x206 + x246 + x286 + x326 + x366 =E= 1
       ;

e408..    x7 + x47 + x87 + x127 + x167 + x207 + x247 + x287 + x327 + x367 =E= 1
       ;

e409..    x8 + x48 + x88 + x128 + x168 + x208 + x248 + x288 + x328 + x368 =E= 1
       ;

e410..    x9 + x49 + x89 + x129 + x169 + x209 + x249 + x289 + x329 + x369 =E= 1
       ;

e411..    x10 + x50 + x90 + x130 + x170 + x210 + x250 + x290 + x330 + x370
        =E= 1;

e412..    x11 + x51 + x91 + x131 + x171 + x211 + x251 + x291 + x331 + x371
        =E= 1;

e413..    x12 + x52 + x92 + x132 + x172 + x212 + x252 + x292 + x332 + x372
        =E= 1;

e414..    x13 + x53 + x93 + x133 + x173 + x213 + x253 + x293 + x333 + x373
        =E= 1;

e415..    x14 + x54 + x94 + x134 + x174 + x214 + x254 + x294 + x334 + x374
        =E= 1;

e416..    x15 + x55 + x95 + x135 + x175 + x215 + x255 + x295 + x335 + x375
        =E= 1;

e417..    x16 + x56 + x96 + x136 + x176 + x216 + x256 + x296 + x336 + x376
        =E= 1;

e418..    x17 + x57 + x97 + x137 + x177 + x217 + x257 + x297 + x337 + x377
        =E= 1;

e419..    x18 + x58 + x98 + x138 + x178 + x218 + x258 + x298 + x338 + x378
        =E= 1;

e420..    x19 + x59 + x99 + x139 + x179 + x219 + x259 + x299 + x339 + x379
        =E= 1;

e421..    x20 + x60 + x100 + x140 + x180 + x220 + x260 + x300 + x340 + x380
        =E= 1;

e422..    x21 + x61 + x101 + x141 + x181 + x221 + x261 + x301 + x341 + x381
        =E= 1;

e423..    x22 + x62 + x102 + x142 + x182 + x222 + x262 + x302 + x342 + x382
        =E= 1;

e424..    x23 + x63 + x103 + x143 + x183 + x223 + x263 + x303 + x343 + x383
        =E= 1;

e425..    x24 + x64 + x104 + x144 + x184 + x224 + x264 + x304 + x344 + x384
        =E= 1;

e426..    x25 + x65 + x105 + x145 + x185 + x225 + x265 + x305 + x345 + x385
        =E= 1;

e427..    x26 + x66 + x106 + x146 + x186 + x226 + x266 + x306 + x346 + x386
        =E= 1;

e428..    x27 + x67 + x107 + x147 + x187 + x227 + x267 + x307 + x347 + x387
        =E= 1;

e429..    x28 + x68 + x108 + x148 + x188 + x228 + x268 + x308 + x348 + x388
        =E= 1;

e430..    x29 + x69 + x109 + x149 + x189 + x229 + x269 + x309 + x349 + x389
        =E= 1;

e431..    x30 + x70 + x110 + x150 + x190 + x230 + x270 + x310 + x350 + x390
        =E= 1;

e432..    x31 + x71 + x111 + x151 + x191 + x231 + x271 + x311 + x351 + x391
        =E= 1;

e433..    x32 + x72 + x112 + x152 + x192 + x232 + x272 + x312 + x352 + x392
        =E= 1;

e434..    x33 + x73 + x113 + x153 + x193 + x233 + x273 + x313 + x353 + x393
        =E= 1;

e435..    x34 + x74 + x114 + x154 + x194 + x234 + x274 + x314 + x354 + x394
        =E= 1;

e436..    x35 + x75 + x115 + x155 + x195 + x235 + x275 + x315 + x355 + x395
        =E= 1;

e437..    x36 + x76 + x116 + x156 + x196 + x236 + x276 + x316 + x356 + x396
        =E= 1;

e438..    x37 + x77 + x117 + x157 + x197 + x237 + x277 + x317 + x357 + x397
        =E= 1;

e439..    x38 + x78 + x118 + x158 + x198 + x238 + x278 + x318 + x358 + x398
        =E= 1;

e440..    x39 + x79 + x119 + x159 + x199 + x239 + x279 + x319 + x359 + x399
        =E= 1;

e441..    x40 + x80 + x120 + x160 + x200 + x240 + x280 + x320 + x360 + x400
        =E= 1;

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: 2022-05-24 Git hash: 1198c186
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