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ex1264.gms:

References:

Point: p1 
Best known point (p1): Solution value 8.60 (global optimum, BARON certificate)


$offlisting * MINLP written by GAMS Convert at 04/17/01 16:38:06 * * Equation counts * Total E G L N X * 56 21 5 30 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 89 21 68 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 237 205 32 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,b17,b18,b19 ,b20,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,x69,x70 ,x71,x72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87 ,b88,objvar; Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x69 ,x70,x71,x72; Binary Variables b17,b18,b19,b20,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,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86 ,b87,b88; 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; e1.. - 0.1*b65 - 0.2*b66 - 0.3*b67 - 0.4*b68 - x69 - x70 - x71 - x72 + objvar =E= 0; e2.. x69*x1 + x70*x2 + x71*x3 + x72*x4 =G= 9; e3.. x69*x5 + x70*x6 + x71*x7 + x72*x8 =G= 7; e4.. x69*x9 + x70*x10 + x71*x11 + x72*x12 =G= 12; e5.. x69*x13 + x70*x14 + x71*x15 + x72*x16 =G= 11; e6.. - 330*x1 - 360*x5 - 385*x9 - 415*x13 + 1700*b65 =L= 0; e7.. - 330*x2 - 360*x6 - 385*x10 - 415*x14 + 1700*b66 =L= 0; e8.. - 330*x3 - 360*x7 - 385*x11 - 415*x15 + 1700*b67 =L= 0; e9.. - 330*x4 - 360*x8 - 385*x12 - 415*x16 + 1700*b68 =L= 0; e10.. 330*x1 + 360*x5 + 385*x9 + 415*x13 - 1900*b65 =L= 0; e11.. 330*x2 + 360*x6 + 385*x10 + 415*x14 - 1900*b66 =L= 0; e12.. 330*x3 + 360*x7 + 385*x11 + 415*x15 - 1900*b67 =L= 0; e13.. 330*x4 + 360*x8 + 385*x12 + 415*x16 - 1900*b68 =L= 0; e14.. - x1 - x5 - x9 - x13 + b65 =L= 0; e15.. - x2 - x6 - x10 - x14 + b66 =L= 0; e16.. - x3 - x7 - x11 - x15 + b67 =L= 0; e17.. - x4 - x8 - x12 - x16 + b68 =L= 0; e18.. x1 + x5 + x9 + x13 - 5*b65 =L= 0; e19.. x2 + x6 + x10 + x14 - 5*b66 =L= 0; e20.. x3 + x7 + x11 + x15 - 5*b67 =L= 0; e21.. x4 + x8 + x12 + x16 - 5*b68 =L= 0; e22.. b65 - x69 =L= 0; e23.. b66 - x70 =L= 0; e24.. b67 - x71 =L= 0; e25.. b68 - x72 =L= 0; e26.. - 15*b65 + x69 =L= 0; e27.. - 12*b66 + x70 =L= 0; e28.. - 9*b67 + x71 =L= 0; e29.. - 6*b68 + x72 =L= 0; e30.. x69 + x70 + x71 + x72 =G= 8; e31.. - b65 + b66 =L= 0; e32.. - b66 + b67 =L= 0; e33.. - b67 + b68 =L= 0; e34.. - x69 + x70 =L= 0; e35.. - x70 + x71 =L= 0; e36.. - x71 + x72 =L= 0; e37.. x1 - b17 - 2*b18 - 4*b19 =E= 0; e38.. x2 - b20 - 2*b21 - 4*b22 =E= 0; e39.. x3 - b23 - 2*b24 - 4*b25 =E= 0; e40.. x4 - b26 - 2*b27 - 4*b28 =E= 0; e41.. x5 - b29 - 2*b30 - 4*b31 =E= 0; e42.. x6 - b32 - 2*b33 - 4*b34 =E= 0; e43.. x7 - b35 - 2*b36 - 4*b37 =E= 0; e44.. x8 - b38 - 2*b39 - 4*b40 =E= 0; e45.. x9 - b41 - 2*b42 - 4*b43 =E= 0; e46.. x10 - b44 - 2*b45 - 4*b46 =E= 0; e47.. x11 - b47 - 2*b48 - 4*b49 =E= 0; e48.. x12 - b50 - 2*b51 - 4*b52 =E= 0; e49.. x13 - b53 - 2*b54 - 4*b55 =E= 0; e50.. x14 - b56 - 2*b57 - 4*b58 =E= 0; e51.. x15 - b59 - 2*b60 - 4*b61 =E= 0; e52.. x16 - b62 - 2*b63 - 4*b64 =E= 0; e53.. x69 - b73 - 2*b74 - 4*b75 - 8*b76 =E= 0; e54.. x70 - b77 - 2*b78 - 4*b79 - 8*b80 =E= 0; e55.. x71 - b81 - 2*b82 - 4*b83 - 8*b84 =E= 0; e56.. x72 - b85 - 2*b86 - 4*b87 - 8*b88 =E= 0; * set non default bounds x1.up = 5; x2.up = 5; x3.up = 5; x4.up = 5; x5.up = 5; x6.up = 5; x7.up = 5; x8.up = 5; x9.up = 5; x10.up = 5; x11.up = 5; x12.up = 5; x13.up = 5; x14.up = 5; x15.up = 5; x16.up = 5; x69.up = 15; x70.up = 12; x71.up = 9; x72.up = 6; $if set nostart $goto modeldef * set non default levels * set non default marginals $label modeldef Model m / all /; m.limrow=0; m.limcol=0; $if NOT '%gams.u1%' == '' $include '%gams.u1%' $if not set MINLP $set MINLP MINLP Solve m using %MINLP% minimizing objvar;