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tls2.gms:

References:

• Leyffer, S, MacMINLP: AMPL Collection of Mixed Integer Nonlinear Programs.
• Harjunkoski, I, Westerlund, T, Porn, R, and Skrifvars, H, Different Transformations for Solving Non-Convex Trim Loss Problems by MINLP. European Journal of Operational Research 105, 3 (1998), 594-603.
• Original source: AMPL model trimlon.mod and trimloss2.dat from MacMINLP

Point: p1
Best known point (p1): Solution value 5.30 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/18/01 12:09:28 * * Equation counts * Total E G L N X * 25 7 0 18 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 38 5 31 2 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 210 202 8 0 * * Solve m using MINLP minimizing objvar; Variables b1,b2,i3,i4,x5,x6,x7,x8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19 ,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36 ,b37,objvar; Binary Variables b1,b2,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21,b22 ,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36,b37; Integer Variables i3,i4; 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; e1.. - 0.1*b1 - 0.2*b2 - b9 - 2*b10 - 3*b11 - 4*b12 - 5*b13 - 6*b14 - 7*b15 - 8*b16 - b17 - 2*b18 - 3*b19 - 4*b20 - 5*b21 - 6*b22 - 7*b23 + objvar =E= 0; e2.. 460*b24 + 920*b25 + 1380*b26 + 1840*b27 + 570*b32 + 1140*b33 + 1710*b34 =L= 1900; e3.. 460*b28 + 920*b29 + 1380*b30 + 1840*b31 + 570*b35 + 1140*b36 + 1710*b37 =L= 1900; e4.. - 460*b24 - 920*b25 - 1380*b26 - 1840*b27 - 570*b32 - 1140*b33 - 1710*b34 =L= -1700; e5.. - 460*b28 - 920*b29 - 1380*b30 - 1840*b31 - 570*b35 - 1140*b36 - 1710*b37 =L= -1700; e6.. b24 + 2*b25 + 3*b26 + 4*b27 + b32 + 2*b33 + 3*b34 =L= 5; e7.. b28 + 2*b29 + 3*b30 + 4*b31 + b35 + 2*b36 + 3*b37 =L= 5; e8.. b1 - b9 - 2*b10 - 3*b11 - 4*b12 - 5*b13 - 6*b14 - 7*b15 - 8*b16 =L= 0; e9.. b2 - b17 - 2*b18 - 3*b19 - 4*b20 - 5*b21 - 6*b22 - 7*b23 =L= 0; e10.. - 8*b1 + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14 + 7*b15 + 8*b16 =L= 0; e11.. - 7*b2 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23 =L= 0; e12.. i3 - 3*b9 - 8*b10 - 15*b11 - 24*b12 - 35*b13 - 48*b14 - 63*b15 - 80*b16 =E= 1; e13.. i4 - 3*b17 - 8*b18 - 15*b19 - 24*b20 - 35*b21 - 48*b22 - 63*b23 =E= 1; e14.. b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 =L= 1; e15.. b17 + b18 + b19 + b20 + b21 + b22 + b23 =L= 1; e16.. x5 - 3*b24 - 8*b25 - 15*b26 - 24*b27 =E= 1; e17.. x6 - 3*b28 - 8*b29 - 15*b30 - 24*b31 =E= 1; e18.. x7 - 3*b32 - 8*b33 - 15*b34 =E= 1; e19.. x8 - 3*b35 - 8*b36 - 15*b37 =E= 1; e20.. b24 + b25 + b26 + b27 =L= 1; e21.. b28 + b29 + b30 + b31 =L= 1; e22.. b32 + b33 + b34 =L= 1; e23.. b35 + b36 + b37 =L= 1; e24.. - (sqrt(i3*x5) + sqrt(i4*x6)) + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14 + 7*b15 + 8*b16 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23 + b24 + 2*b25 + 3*b26 + 4*b27 + b28 + 2*b29 + 3*b30 + 4*b31 =L= -10; e25.. - (sqrt(i3*x7) + sqrt(i4*x8)) + b9 + 2*b10 + 3*b11 + 4*b12 + 5*b13 + 6*b14 + 7*b15 + 8*b16 + b17 + 2*b18 + 3*b19 + 4*b20 + 5*b21 + 6*b22 + 7*b23 + b32 + 2*b33 + 3*b34 + b35 + 2*b36 + 3*b37 =L= -9; * set non default bounds i3.lo = 1; i3.up = 100; i4.lo = 1; i4.up = 100; x5.lo = 1; x6.lo = 1; x7.lo = 1; x8.lo = 1; \$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;