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Instance slay10m
Determine the optimal placement of a set of units with fixed width and length such that the Euclidean distance between their center point and a predefined "safety point" is minimized.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 9928.96340000 (ALPHAECP) 129579.87680000 (ANTIGONE) 129579.88360000 (BARON) 129579.88000000 (BONMIN) 129579.88290000 (COUENNE) 129579.88380000 (CPLEX) 129579.88380000 (GUROBI) 129579.88380000 (LINDO) 129579.88380000 (SCIP) 129579.88380000 (SHOT) |
| Referencesⓘ | Sawaya, Nicolas W, Reformulations, relaxations and cutting planes for generalized disjunctive programming, PhD thesis, Carnegie Mellon University, 2006. |
| Sourceⓘ | SLay10M.gms from CMU-IBM MINLP solver project page |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 28 Sep 2013 |
| Problem typeⓘ | MBQP |
| #Variablesⓘ | 290 |
| #Binary Variablesⓘ | 180 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 20 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 110 |
| #Nonlinear Nonzeros in Objectiveⓘ | 20 |
| #Constraintsⓘ | 405 |
| #Linear Constraintsⓘ | 405 |
| #Quadratic Constraintsⓘ | 0 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | linear |
| #Nonzeros in Jacobianⓘ | 1260 |
| #Nonlinear Nonzeros in Jacobianⓘ | 0 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 20 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 20 |
| #Blocks in Hessian of Lagrangianⓘ | 20 |
| 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ⓘ | 4.0000e+02 |
| Infeasibility of initial pointⓘ | 3 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 406 46 180 180 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 291 111 180 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 1371 1351 20 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,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,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,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181
,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193,b194
,b195,b196,b197,b198,b199,b200,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,objvar;
Positive Variables 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;
Binary Variables b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35
,b36,b37,b38,b39,b40,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,b101,b102
,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115
,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128
,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141
,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154
,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167
,b168,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180
,b181,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193
,b194,b195,b196,b197,b198,b199,b200;
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;
e1.. -(150*(sqr((-4) + x1) + sqr((-10) + x11)) + 390*(sqr((-10) + x2) + sqr((-
15) + x12)) + 240*(sqr((-7) + x3) + sqr((-9) + x13)) + 70*(sqr((-3) + x4)
+ sqr((-3) + x14)) + 165*(sqr((-20) + x5) + sqr((-17) + x15)) + 100*(sqr(
(-18) + x6) + sqr((-8) + x16)) + 200*(sqr((-30) + x7) + sqr((-20) + x17))
+ 400*(sqr((-24) + x8) + sqr((-10) + x18)) + 330*(sqr((-22) + x9) + sqr((
-6) + x19)) + 220*(sqr((-11) + x10) + sqr((-12) + x20))) - 300*x201
- 240*x202 - 210*x203 - 140*x204 - 300*x205 - 250*x206 - 300*x207
- 210*x208 - 320*x209 - 100*x210 - 150*x211 - 220*x212 - 200*x213
- 300*x214 - 290*x215 - 400*x216 - 220*x217 - 120*x218 - 300*x219
- 150*x220 - 150*x221 - 100*x222 - 290*x223 - 110*x224 - 100*x225
- 120*x226 - 180*x227 - 220*x228 - 110*x229 - 100*x230 - 130*x231
- 190*x232 - 110*x233 - 160*x234 - 400*x235 - 220*x236 - 140*x237
- 120*x238 - 230*x239 - 260*x240 - 220*x241 - 310*x242 - 140*x243
- 150*x244 - 130*x245 - 300*x246 - 240*x247 - 210*x248 - 140*x249
- 300*x250 - 250*x251 - 300*x252 - 210*x253 - 320*x254 - 100*x255
- 150*x256 - 220*x257 - 200*x258 - 300*x259 - 290*x260 - 400*x261
- 220*x262 - 120*x263 - 300*x264 - 150*x265 - 150*x266 - 100*x267
- 290*x268 - 110*x269 - 100*x270 - 120*x271 - 180*x272 - 220*x273
- 110*x274 - 100*x275 - 130*x276 - 190*x277 - 110*x278 - 160*x279
- 400*x280 - 220*x281 - 140*x282 - 120*x283 - 230*x284 - 260*x285
- 220*x286 - 310*x287 - 140*x288 - 150*x289 - 130*x290 + objvar =E= 0;
e2.. - x1 + x2 + x201 =G= 0;
e3.. - x1 + x3 + x202 =G= 0;
e4.. - x1 + x4 + x203 =G= 0;
e5.. - x1 + x5 + x204 =G= 0;
e6.. - x1 + x6 + x205 =G= 0;
e7.. - x1 + x7 + x206 =G= 0;
e8.. - x1 + x8 + x207 =G= 0;
e9.. - x1 + x9 + x208 =G= 0;
e10.. - x1 + x10 + x209 =G= 0;
e11.. - x2 + x3 + x210 =G= 0;
e12.. - x2 + x4 + x211 =G= 0;
e13.. - x2 + x5 + x212 =G= 0;
e14.. - x2 + x6 + x213 =G= 0;
e15.. - x2 + x7 + x214 =G= 0;
e16.. - x2 + x8 + x215 =G= 0;
e17.. - x2 + x9 + x216 =G= 0;
e18.. - x2 + x10 + x217 =G= 0;
e19.. - x3 + x4 + x218 =G= 0;
e20.. - x3 + x5 + x219 =G= 0;
e21.. - x3 + x6 + x220 =G= 0;
e22.. - x3 + x7 + x221 =G= 0;
e23.. - x3 + x8 + x222 =G= 0;
e24.. - x3 + x9 + x223 =G= 0;
e25.. - x3 + x10 + x224 =G= 0;
e26.. - x4 + x5 + x225 =G= 0;
e27.. - x4 + x6 + x226 =G= 0;
e28.. - x4 + x7 + x227 =G= 0;
e29.. - x4 + x8 + x228 =G= 0;
e30.. - x4 + x9 + x229 =G= 0;
e31.. - x4 + x10 + x230 =G= 0;
e32.. - x5 + x6 + x231 =G= 0;
e33.. - x5 + x7 + x232 =G= 0;
e34.. - x5 + x8 + x233 =G= 0;
e35.. - x5 + x9 + x234 =G= 0;
e36.. - x5 + x10 + x235 =G= 0;
e37.. - x6 + x7 + x236 =G= 0;
e38.. - x6 + x8 + x237 =G= 0;
e39.. - x6 + x9 + x238 =G= 0;
e40.. - x6 + x10 + x239 =G= 0;
e41.. - x7 + x8 + x240 =G= 0;
e42.. - x7 + x9 + x241 =G= 0;
e43.. - x7 + x10 + x242 =G= 0;
e44.. - x8 + x9 + x243 =G= 0;
e45.. - x8 + x10 + x244 =G= 0;
e46.. - x9 + x10 + x245 =G= 0;
e47.. x1 - x2 + x201 =G= 0;
e48.. x1 - x3 + x202 =G= 0;
e49.. x1 - x4 + x203 =G= 0;
e50.. x1 - x5 + x204 =G= 0;
e51.. x1 - x6 + x205 =G= 0;
e52.. x1 - x7 + x206 =G= 0;
e53.. x1 - x8 + x207 =G= 0;
e54.. x1 - x9 + x208 =G= 0;
e55.. x1 - x10 + x209 =G= 0;
e56.. x2 - x3 + x210 =G= 0;
e57.. x2 - x4 + x211 =G= 0;
e58.. x2 - x5 + x212 =G= 0;
e59.. x2 - x6 + x213 =G= 0;
e60.. x2 - x7 + x214 =G= 0;
e61.. x2 - x8 + x215 =G= 0;
e62.. x2 - x9 + x216 =G= 0;
e63.. x2 - x10 + x217 =G= 0;
e64.. x3 - x4 + x218 =G= 0;
e65.. x3 - x5 + x219 =G= 0;
e66.. x3 - x6 + x220 =G= 0;
e67.. x3 - x7 + x221 =G= 0;
e68.. x3 - x8 + x222 =G= 0;
e69.. x3 - x9 + x223 =G= 0;
e70.. x3 - x10 + x224 =G= 0;
e71.. x4 - x5 + x225 =G= 0;
e72.. x4 - x6 + x226 =G= 0;
e73.. x4 - x7 + x227 =G= 0;
e74.. x4 - x8 + x228 =G= 0;
e75.. x4 - x9 + x229 =G= 0;
e76.. x4 - x10 + x230 =G= 0;
e77.. x5 - x6 + x231 =G= 0;
e78.. x5 - x7 + x232 =G= 0;
e79.. x5 - x8 + x233 =G= 0;
e80.. x5 - x9 + x234 =G= 0;
e81.. x5 - x10 + x235 =G= 0;
e82.. x6 - x7 + x236 =G= 0;
e83.. x6 - x8 + x237 =G= 0;
e84.. x6 - x9 + x238 =G= 0;
e85.. x6 - x10 + x239 =G= 0;
e86.. x7 - x8 + x240 =G= 0;
e87.. x7 - x9 + x241 =G= 0;
e88.. x7 - x10 + x242 =G= 0;
e89.. x8 - x9 + x243 =G= 0;
e90.. x8 - x10 + x244 =G= 0;
e91.. x9 - x10 + x245 =G= 0;
e92.. - x11 + x12 + x246 =G= 0;
e93.. - x11 + x13 + x247 =G= 0;
e94.. - x11 + x14 + x248 =G= 0;
e95.. - x11 + x15 + x249 =G= 0;
e96.. - x11 + x16 + x250 =G= 0;
e97.. - x11 + x17 + x251 =G= 0;
e98.. - x11 + x18 + x252 =G= 0;
e99.. - x11 + x19 + x253 =G= 0;
e100.. - x11 + x20 + x254 =G= 0;
e101.. - x12 + x13 + x255 =G= 0;
e102.. - x12 + x14 + x256 =G= 0;
e103.. - x12 + x15 + x257 =G= 0;
e104.. - x12 + x16 + x258 =G= 0;
e105.. - x12 + x17 + x259 =G= 0;
e106.. - x12 + x18 + x260 =G= 0;
e107.. - x12 + x19 + x261 =G= 0;
e108.. - x12 + x20 + x262 =G= 0;
e109.. - x13 + x14 + x263 =G= 0;
e110.. - x13 + x15 + x264 =G= 0;
e111.. - x13 + x16 + x265 =G= 0;
e112.. - x13 + x17 + x266 =G= 0;
e113.. - x13 + x18 + x267 =G= 0;
e114.. - x13 + x19 + x268 =G= 0;
e115.. - x13 + x20 + x269 =G= 0;
e116.. - x14 + x15 + x270 =G= 0;
e117.. - x14 + x16 + x271 =G= 0;
e118.. - x14 + x17 + x272 =G= 0;
e119.. - x14 + x18 + x273 =G= 0;
e120.. - x14 + x19 + x274 =G= 0;
e121.. - x14 + x20 + x275 =G= 0;
e122.. - x15 + x16 + x276 =G= 0;
e123.. - x15 + x17 + x277 =G= 0;
e124.. - x15 + x18 + x278 =G= 0;
e125.. - x15 + x19 + x279 =G= 0;
e126.. - x15 + x20 + x280 =G= 0;
e127.. - x16 + x17 + x281 =G= 0;
e128.. - x16 + x18 + x282 =G= 0;
e129.. - x16 + x19 + x283 =G= 0;
e130.. - x16 + x20 + x284 =G= 0;
e131.. - x17 + x18 + x285 =G= 0;
e132.. - x17 + x19 + x286 =G= 0;
e133.. - x17 + x20 + x287 =G= 0;
e134.. - x18 + x19 + x288 =G= 0;
e135.. - x18 + x20 + x289 =G= 0;
e136.. - x19 + x20 + x290 =G= 0;
e137.. x11 - x12 + x246 =G= 0;
e138.. x11 - x13 + x247 =G= 0;
e139.. x11 - x14 + x248 =G= 0;
e140.. x11 - x15 + x249 =G= 0;
e141.. x11 - x16 + x250 =G= 0;
e142.. x11 - x17 + x251 =G= 0;
e143.. x11 - x18 + x252 =G= 0;
e144.. x11 - x19 + x253 =G= 0;
e145.. x11 - x20 + x254 =G= 0;
e146.. x12 - x13 + x255 =G= 0;
e147.. x12 - x14 + x256 =G= 0;
e148.. x12 - x15 + x257 =G= 0;
e149.. x12 - x16 + x258 =G= 0;
e150.. x12 - x17 + x259 =G= 0;
e151.. x12 - x18 + x260 =G= 0;
e152.. x12 - x19 + x261 =G= 0;
e153.. x12 - x20 + x262 =G= 0;
e154.. x13 - x14 + x263 =G= 0;
e155.. x13 - x15 + x264 =G= 0;
e156.. x13 - x16 + x265 =G= 0;
e157.. x13 - x17 + x266 =G= 0;
e158.. x13 - x18 + x267 =G= 0;
e159.. x13 - x19 + x268 =G= 0;
e160.. x13 - x20 + x269 =G= 0;
e161.. x14 - x15 + x270 =G= 0;
e162.. x14 - x16 + x271 =G= 0;
e163.. x14 - x17 + x272 =G= 0;
e164.. x14 - x18 + x273 =G= 0;
e165.. x14 - x19 + x274 =G= 0;
e166.. x14 - x20 + x275 =G= 0;
e167.. x15 - x16 + x276 =G= 0;
e168.. x15 - x17 + x277 =G= 0;
e169.. x15 - x18 + x278 =G= 0;
e170.. x15 - x19 + x279 =G= 0;
e171.. x15 - x20 + x280 =G= 0;
e172.. x16 - x17 + x281 =G= 0;
e173.. x16 - x18 + x282 =G= 0;
e174.. x16 - x19 + x283 =G= 0;
e175.. x16 - x20 + x284 =G= 0;
e176.. x17 - x18 + x285 =G= 0;
e177.. x17 - x19 + x286 =G= 0;
e178.. x17 - x20 + x287 =G= 0;
e179.. x18 - x19 + x288 =G= 0;
e180.. x18 - x20 + x289 =G= 0;
e181.. x19 - x20 + x290 =G= 0;
e182.. x1 - x2 + 40*b21 =L= 34;
e183.. x1 - x3 + 40*b22 =L= 36;
e184.. x1 - x4 + 40*b23 =L= 36.5;
e185.. x1 - x5 + 40*b24 =L= 35.5;
e186.. x1 - x6 + 40*b25 =L= 35;
e187.. x1 - x7 + 40*b26 =L= 33.5;
e188.. x1 - x8 + 40*b27 =L= 35.5;
e189.. x1 - x9 + 40*b28 =L= 36.5;
e190.. x1 - x10 + 40*b29 =L= 34.5;
e191.. x2 - x3 + 40*b30 =L= 35;
e192.. x2 - x4 + 40*b31 =L= 35.5;
e193.. x2 - x5 + 40*b32 =L= 34.5;
e194.. x2 - x6 + 40*b33 =L= 34;
e195.. x2 - x7 + 40*b34 =L= 32.5;
e196.. x2 - x8 + 40*b35 =L= 34.5;
e197.. x2 - x9 + 40*b36 =L= 35.5;
e198.. x2 - x10 + 40*b37 =L= 33.5;
e199.. x3 - x4 + 40*b38 =L= 37.5;
e200.. x3 - x5 + 40*b39 =L= 36.5;
e201.. x3 - x6 + 40*b40 =L= 36;
e202.. x3 - x7 + 40*b41 =L= 34.5;
e203.. x3 - x8 + 40*b42 =L= 36.5;
e204.. x3 - x9 + 40*b43 =L= 37.5;
e205.. x3 - x10 + 40*b44 =L= 35.5;
e206.. x4 - x5 + 40*b45 =L= 37;
e207.. x4 - x6 + 40*b46 =L= 36.5;
e208.. x4 - x7 + 40*b47 =L= 35;
e209.. x4 - x8 + 40*b48 =L= 37;
e210.. x4 - x9 + 40*b49 =L= 38;
e211.. x4 - x10 + 40*b50 =L= 36;
e212.. x5 - x6 + 40*b51 =L= 35.5;
e213.. x5 - x7 + 40*b52 =L= 34;
e214.. x5 - x8 + 40*b53 =L= 36;
e215.. x5 - x9 + 40*b54 =L= 37;
e216.. x5 - x10 + 40*b55 =L= 35;
e217.. x6 - x7 + 40*b56 =L= 33.5;
e218.. x6 - x8 + 40*b57 =L= 35.5;
e219.. x6 - x9 + 40*b58 =L= 36.5;
e220.. x6 - x10 + 40*b59 =L= 34.5;
e221.. x7 - x8 + 40*b60 =L= 34;
e222.. x7 - x9 + 40*b61 =L= 35;
e223.. x7 - x10 + 40*b62 =L= 33;
e224.. x8 - x9 + 40*b63 =L= 37;
e225.. x8 - x10 + 40*b64 =L= 35;
e226.. x9 - x10 + 40*b65 =L= 36;
e227.. - x1 + x2 + 40*b66 =L= 34;
e228.. - x1 + x3 + 40*b67 =L= 36;
e229.. - x1 + x4 + 40*b68 =L= 36.5;
e230.. - x1 + x5 + 40*b69 =L= 35.5;
e231.. - x1 + x6 + 40*b70 =L= 35;
e232.. - x1 + x7 + 40*b71 =L= 33.5;
e233.. - x1 + x8 + 40*b72 =L= 35.5;
e234.. - x1 + x9 + 40*b73 =L= 36.5;
e235.. - x1 + x10 + 40*b74 =L= 34.5;
e236.. - x2 + x3 + 40*b75 =L= 35;
e237.. - x2 + x4 + 40*b76 =L= 35.5;
e238.. - x2 + x5 + 40*b77 =L= 34.5;
e239.. - x2 + x6 + 40*b78 =L= 34;
e240.. - x2 + x7 + 40*b79 =L= 32.5;
e241.. - x2 + x8 + 40*b80 =L= 34.5;
e242.. - x2 + x9 + 40*b81 =L= 35.5;
e243.. - x2 + x10 + 40*b82 =L= 33.5;
e244.. - x3 + x4 + 40*b83 =L= 37.5;
e245.. - x3 + x5 + 40*b84 =L= 36.5;
e246.. - x3 + x6 + 40*b85 =L= 36;
e247.. - x3 + x7 + 40*b86 =L= 34.5;
e248.. - x3 + x8 + 40*b87 =L= 36.5;
e249.. - x3 + x9 + 40*b88 =L= 37.5;
e250.. - x3 + x10 + 40*b89 =L= 35.5;
e251.. - x4 + x5 + 40*b90 =L= 37;
e252.. - x4 + x6 + 40*b91 =L= 36.5;
e253.. - x4 + x7 + 40*b92 =L= 35;
e254.. - x4 + x8 + 40*b93 =L= 37;
e255.. - x4 + x9 + 40*b94 =L= 38;
e256.. - x4 + x10 + 40*b95 =L= 36;
e257.. - x5 + x6 + 40*b96 =L= 35.5;
e258.. - x5 + x7 + 40*b97 =L= 34;
e259.. - x5 + x8 + 40*b98 =L= 36;
e260.. - x5 + x9 + 40*b99 =L= 37;
e261.. - x5 + x10 + 40*b100 =L= 35;
e262.. - x6 + x7 + 40*b101 =L= 33.5;
e263.. - x6 + x8 + 40*b102 =L= 35.5;
e264.. - x6 + x9 + 40*b103 =L= 36.5;
e265.. - x6 + x10 + 40*b104 =L= 34.5;
e266.. - x7 + x8 + 40*b105 =L= 34;
e267.. - x7 + x9 + 40*b106 =L= 35;
e268.. - x7 + x10 + 40*b107 =L= 33;
e269.. - x8 + x9 + 40*b108 =L= 37;
e270.. - x8 + x10 + 40*b109 =L= 35;
e271.. - x9 + x10 + 40*b110 =L= 36;
e272.. x11 - x12 + 40*b111 =L= 34.5;
e273.. x11 - x13 + 40*b112 =L= 35.5;
e274.. x11 - x14 + 40*b113 =L= 35.5;
e275.. x11 - x15 + 40*b114 =L= 35;
e276.. x11 - x16 + 40*b115 =L= 36;
e277.. x11 - x17 + 40*b116 =L= 34;
e278.. x11 - x18 + 40*b117 =L= 34;
e279.. x11 - x19 + 40*b118 =L= 34.5;
e280.. x11 - x20 + 40*b119 =L= 35.5;
e281.. x12 - x13 + 40*b120 =L= 36;
e282.. x12 - x14 + 40*b121 =L= 36;
e283.. x12 - x15 + 40*b122 =L= 35.5;
e284.. x12 - x16 + 40*b123 =L= 36.5;
e285.. x12 - x17 + 40*b124 =L= 34.5;
e286.. x12 - x18 + 40*b125 =L= 34.5;
e287.. x12 - x19 + 40*b126 =L= 35;
e288.. x12 - x20 + 40*b127 =L= 36;
e289.. x13 - x14 + 40*b128 =L= 37;
e290.. x13 - x15 + 40*b129 =L= 36.5;
e291.. x13 - x16 + 40*b130 =L= 37.5;
e292.. x13 - x17 + 40*b131 =L= 35.5;
e293.. x13 - x18 + 40*b132 =L= 35.5;
e294.. x13 - x19 + 40*b133 =L= 36;
e295.. x13 - x20 + 40*b134 =L= 37;
e296.. x14 - x15 + 40*b135 =L= 36.5;
e297.. x14 - x16 + 40*b136 =L= 37.5;
e298.. x14 - x17 + 40*b137 =L= 35.5;
e299.. x14 - x18 + 40*b138 =L= 35.5;
e300.. x14 - x19 + 40*b139 =L= 36;
e301.. x14 - x20 + 40*b140 =L= 37;
e302.. x15 - x16 + 40*b141 =L= 37;
e303.. x15 - x17 + 40*b142 =L= 35;
e304.. x15 - x18 + 40*b143 =L= 35;
e305.. x15 - x19 + 40*b144 =L= 35.5;
e306.. x15 - x20 + 40*b145 =L= 36.5;
e307.. x16 - x17 + 40*b146 =L= 36;
e308.. x16 - x18 + 40*b147 =L= 36;
e309.. x16 - x19 + 40*b148 =L= 36.5;
e310.. x16 - x20 + 40*b149 =L= 37.5;
e311.. x17 - x18 + 40*b150 =L= 34;
e312.. x17 - x19 + 40*b151 =L= 34.5;
e313.. x17 - x20 + 40*b152 =L= 35.5;
e314.. x18 - x19 + 40*b153 =L= 34.5;
e315.. x18 - x20 + 40*b154 =L= 35.5;
e316.. x19 - x20 + 40*b155 =L= 36;
e317.. - x11 + x12 + 40*b156 =L= 34.5;
e318.. - x11 + x13 + 40*b157 =L= 35.5;
e319.. - x11 + x14 + 40*b158 =L= 35.5;
e320.. - x11 + x15 + 40*b159 =L= 35;
e321.. - x11 + x16 + 40*b160 =L= 36;
e322.. - x11 + x17 + 40*b161 =L= 34;
e323.. - x11 + x18 + 40*b162 =L= 34;
e324.. - x11 + x19 + 40*b163 =L= 34.5;
e325.. - x11 + x20 + 40*b164 =L= 35.5;
e326.. - x12 + x13 + 40*b165 =L= 36;
e327.. - x12 + x14 + 40*b166 =L= 36;
e328.. - x12 + x15 + 40*b167 =L= 35.5;
e329.. - x12 + x16 + 40*b168 =L= 36.5;
e330.. - x12 + x17 + 40*b169 =L= 34.5;
e331.. - x12 + x18 + 40*b170 =L= 34.5;
e332.. - x12 + x19 + 40*b171 =L= 35;
e333.. - x12 + x20 + 40*b172 =L= 36;
e334.. - x13 + x14 + 40*b173 =L= 37;
e335.. - x13 + x15 + 40*b174 =L= 36.5;
e336.. - x13 + x16 + 40*b175 =L= 37.5;
e337.. - x13 + x17 + 40*b176 =L= 35.5;
e338.. - x13 + x18 + 40*b177 =L= 35.5;
e339.. - x13 + x19 + 40*b178 =L= 36;
e340.. - x13 + x20 + 40*b179 =L= 37;
e341.. - x14 + x15 + 40*b180 =L= 36.5;
e342.. - x14 + x16 + 40*b181 =L= 37.5;
e343.. - x14 + x17 + 40*b182 =L= 35.5;
e344.. - x14 + x18 + 40*b183 =L= 35.5;
e345.. - x14 + x19 + 40*b184 =L= 36;
e346.. - x14 + x20 + 40*b185 =L= 37;
e347.. - x15 + x16 + 40*b186 =L= 37;
e348.. - x15 + x17 + 40*b187 =L= 35;
e349.. - x15 + x18 + 40*b188 =L= 35;
e350.. - x15 + x19 + 40*b189 =L= 35.5;
e351.. - x15 + x20 + 40*b190 =L= 36.5;
e352.. - x16 + x17 + 40*b191 =L= 36;
e353.. - x16 + x18 + 40*b192 =L= 36;
e354.. - x16 + x19 + 40*b193 =L= 36.5;
e355.. - x16 + x20 + 40*b194 =L= 37.5;
e356.. - x17 + x18 + 40*b195 =L= 34;
e357.. - x17 + x19 + 40*b196 =L= 34.5;
e358.. - x17 + x20 + 40*b197 =L= 35.5;
e359.. - x18 + x19 + 40*b198 =L= 34.5;
e360.. - x18 + x20 + 40*b199 =L= 35.5;
e361.. - x19 + x20 + 40*b200 =L= 36;
e362.. b21 + b66 + b111 + b156 =E= 1;
e363.. b22 + b67 + b112 + b157 =E= 1;
e364.. b23 + b68 + b113 + b158 =E= 1;
e365.. b24 + b69 + b114 + b159 =E= 1;
e366.. b25 + b70 + b115 + b160 =E= 1;
e367.. b26 + b71 + b116 + b161 =E= 1;
e368.. b27 + b72 + b117 + b162 =E= 1;
e369.. b28 + b73 + b118 + b163 =E= 1;
e370.. b29 + b74 + b119 + b164 =E= 1;
e371.. b30 + b75 + b120 + b165 =E= 1;
e372.. b31 + b76 + b121 + b166 =E= 1;
e373.. b32 + b77 + b122 + b167 =E= 1;
e374.. b33 + b78 + b123 + b168 =E= 1;
e375.. b34 + b79 + b124 + b169 =E= 1;
e376.. b35 + b80 + b125 + b170 =E= 1;
e377.. b36 + b81 + b126 + b171 =E= 1;
e378.. b37 + b82 + b127 + b172 =E= 1;
e379.. b38 + b83 + b128 + b173 =E= 1;
e380.. b39 + b84 + b129 + b174 =E= 1;
e381.. b40 + b85 + b130 + b175 =E= 1;
e382.. b41 + b86 + b131 + b176 =E= 1;
e383.. b42 + b87 + b132 + b177 =E= 1;
e384.. b43 + b88 + b133 + b178 =E= 1;
e385.. b44 + b89 + b134 + b179 =E= 1;
e386.. b45 + b90 + b135 + b180 =E= 1;
e387.. b46 + b91 + b136 + b181 =E= 1;
e388.. b47 + b92 + b137 + b182 =E= 1;
e389.. b48 + b93 + b138 + b183 =E= 1;
e390.. b49 + b94 + b139 + b184 =E= 1;
e391.. b50 + b95 + b140 + b185 =E= 1;
e392.. b51 + b96 + b141 + b186 =E= 1;
e393.. b52 + b97 + b142 + b187 =E= 1;
e394.. b53 + b98 + b143 + b188 =E= 1;
e395.. b54 + b99 + b144 + b189 =E= 1;
e396.. b55 + b100 + b145 + b190 =E= 1;
e397.. b56 + b101 + b146 + b191 =E= 1;
e398.. b57 + b102 + b147 + b192 =E= 1;
e399.. b58 + b103 + b148 + b193 =E= 1;
e400.. b59 + b104 + b149 + b194 =E= 1;
e401.. b60 + b105 + b150 + b195 =E= 1;
e402.. b61 + b106 + b151 + b196 =E= 1;
e403.. b62 + b107 + b152 + b197 =E= 1;
e404.. b63 + b108 + b153 + b198 =E= 1;
e405.. b64 + b109 + b154 + b199 =E= 1;
e406.. b65 + b110 + b155 + b200 =E= 1;
* set non-default bounds
x1.lo = 2.5; x1.up = 37.5;
x2.lo = 3.5; x2.up = 36.5;
x3.lo = 1.5; x3.up = 38.5;
x4.lo = 1; x4.up = 39;
x5.lo = 2; x5.up = 38;
x6.lo = 2.5; x6.up = 37.5;
x7.lo = 4; x7.up = 36;
x8.lo = 2; x8.up = 38;
x9.lo = 1; x9.up = 39;
x10.lo = 3; x10.up = 37;
x11.lo = 3; x11.up = 37;
x12.lo = 2.5; x12.up = 37.5;
x13.lo = 1.5; x13.up = 38.5;
x14.lo = 1.5; x14.up = 38.5;
x15.lo = 2; x15.up = 38;
x16.lo = 1; x16.up = 39;
x17.lo = 3; x17.up = 37;
x18.lo = 3; x18.up = 37;
x19.lo = 2.5; x19.up = 37.5;
x20.lo = 1.5; x20.up = 38.5;
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: 2025-08-07 Git hash: e62cedfc