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## tln7.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 trimlon7.dat from MacMINLP

Points: p1  p2
Best known point (p2): Solution value 15.00

\$offlisting * MINLP written by GAMS Convert at 04/19/01 16:58:15 * * Equation counts * Total E G L N X * 43 1 0 42 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 64 1 7 56 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 288 190 98 0 * * Solve m using MINLP minimizing objvar; Variables b1,b2,b3,b4,b5,b6,b7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19 ,i20,i21,i22,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36 ,i37,i38,i39,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53 ,i54,i55,i56,i57,i58,i59,i60,i61,i62,i63,objvar; Binary Variables b1,b2,b3,b4,b5,b6,b7; Integer Variables i8,i9,i10,i11,i12,i13,i14,i15,i16,i17,i18,i19,i20,i21,i22 ,i23,i24,i25,i26,i27,i28,i29,i30,i31,i32,i33,i34,i35,i36,i37,i38,i39 ,i40,i41,i42,i43,i44,i45,i46,i47,i48,i49,i50,i51,i52,i53,i54,i55,i56 ,i57,i58,i59,i60,i61,i62,i63; 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; e1.. - 0.1*b1 - 0.2*b2 - 0.3*b3 - 0.4*b4 - 0.5*b5 - 0.6*b6 - 0.7*b7 - i8 - i9 - i10 - i11 - i12 - i13 - i14 + objvar =E= 0; e2.. 550*i15 + 630*i22 + 685*i29 + 720*i36 + 760*i43 + 810*i50 + 850*i57 =L= 3400; e3.. 550*i16 + 630*i23 + 685*i30 + 720*i37 + 760*i44 + 810*i51 + 850*i58 =L= 3400; e4.. 550*i17 + 630*i24 + 685*i31 + 720*i38 + 760*i45 + 810*i52 + 850*i59 =L= 3400; e5.. 550*i18 + 630*i25 + 685*i32 + 720*i39 + 760*i46 + 810*i53 + 850*i60 =L= 3400; e6.. 550*i19 + 630*i26 + 685*i33 + 720*i40 + 760*i47 + 810*i54 + 850*i61 =L= 3400; e7.. 550*i20 + 630*i27 + 685*i34 + 720*i41 + 760*i48 + 810*i55 + 850*i62 =L= 3400; e8.. 550*i21 + 630*i28 + 685*i35 + 720*i42 + 760*i49 + 810*i56 + 850*i63 =L= 3400; e9.. - 550*i15 - 630*i22 - 685*i29 - 720*i36 - 760*i43 - 810*i50 - 850*i57 =L= -3200; e10.. - 550*i16 - 630*i23 - 685*i30 - 720*i37 - 760*i44 - 810*i51 - 850*i58 =L= -3200; e11.. - 550*i17 - 630*i24 - 685*i31 - 720*i38 - 760*i45 - 810*i52 - 850*i59 =L= -3200; e12.. - 550*i18 - 630*i25 - 685*i32 - 720*i39 - 760*i46 - 810*i53 - 850*i60 =L= -3200; e13.. - 550*i19 - 630*i26 - 685*i33 - 720*i40 - 760*i47 - 810*i54 - 850*i61 =L= -3200; e14.. - 550*i20 - 630*i27 - 685*i34 - 720*i41 - 760*i48 - 810*i55 - 850*i62 =L= -3200; e15.. - 550*i21 - 630*i28 - 685*i35 - 720*i42 - 760*i49 - 810*i56 - 850*i63 =L= -3200; e16.. i15 + i22 + i29 + i36 + i43 + i50 + i57 =L= 6; e17.. i16 + i23 + i30 + i37 + i44 + i51 + i58 =L= 6; e18.. i17 + i24 + i31 + i38 + i45 + i52 + i59 =L= 6; e19.. i18 + i25 + i32 + i39 + i46 + i53 + i60 =L= 6; e20.. i19 + i26 + i33 + i40 + i47 + i54 + i61 =L= 6; e21.. i20 + i27 + i34 + i41 + i48 + i55 + i62 =L= 6; e22.. i21 + i28 + i35 + i42 + i49 + i56 + i63 =L= 6; e23.. b1 - i8 =L= 0; e24.. b2 - i9 =L= 0; e25.. b3 - i10 =L= 0; e26.. b4 - i11 =L= 0; e27.. b5 - i12 =L= 0; e28.. b6 - i13 =L= 0; e29.. b7 - i14 =L= 0; e30.. - 15*b1 + i8 =L= 0; e31.. - 15*b2 + i9 =L= 0; e32.. - 15*b3 + i10 =L= 0; e33.. - 15*b4 + i11 =L= 0; e34.. - 15*b5 + i12 =L= 0; e35.. - 15*b6 + i13 =L= 0; e36.. - 15*b7 + i14 =L= 0; e37.. - (i8*i15 + i9*i16 + i10*i17 + i11*i18 + i12*i19 + i13*i20 + i14*i21) =L= -8; e38.. - (i8*i22 + i9*i23 + i10*i24 + i11*i25 + i12*i26 + i13*i27 + i14*i28) =L= -11; e39.. - (i8*i29 + i9*i30 + i10*i31 + i11*i32 + i12*i33 + i13*i34 + i14*i35) =L= -15; e40.. - (i8*i36 + i9*i37 + i10*i38 + i11*i39 + i12*i40 + i13*i41 + i14*i42) =L= -5; e41.. - (i8*i43 + i9*i44 + i10*i45 + i11*i46 + i12*i47 + i13*i48 + i14*i49) =L= -8; e42.. - (i8*i50 + i9*i51 + i10*i52 + i11*i53 + i12*i54 + i13*i55 + i14*i56) =L= -12; e43.. - (i8*i57 + i9*i58 + i10*i59 + i11*i60 + i12*i61 + i13*i62 + i14*i63) =L= -6; * set non default bounds i8.up = 15; i9.up = 15; i10.up = 15; i11.up = 15; i12.up = 15; i13.up = 15; i14.up = 15; i15.up = 6; i16.up = 6; i17.up = 6; i18.up = 6; i19.up = 6; i20.up = 6; i21.up = 6; i22.up = 6; i23.up = 6; i24.up = 6; i25.up = 6; i26.up = 6; i27.up = 6; i28.up = 6; i29.up = 6; i30.up = 6; i31.up = 6; i32.up = 6; i33.up = 6; i34.up = 6; i35.up = 6; i36.up = 6; i37.up = 6; i38.up = 6; i39.up = 6; i40.up = 6; i41.up = 6; i42.up = 6; i43.up = 6; i44.up = 6; i45.up = 6; i46.up = 6; i47.up = 6; i48.up = 6; i49.up = 6; i50.up = 6; i51.up = 6; i52.up = 6; i53.up = 6; i54.up = 6; i55.up = 6; i56.up = 6; i57.up = 6; i58.up = 6; i59.up = 6; i60.up = 6; i61.up = 6; i62.up = 6; i63.up = 6; \$if set nostart \$goto modeldef * set non default levels i8.l = 1; i9.l = 1; i10.l = 1; i11.l = 1; i12.l = 1; i13.l = 1; i14.l = 1; i15.l = 1; i16.l = 1; i17.l = 1; i18.l = 1; i19.l = 1; i20.l = 1; i21.l = 1; i22.l = 1; i23.l = 1; i24.l = 1; i25.l = 1; i26.l = 1; i27.l = 1; i28.l = 1; i29.l = 1; i30.l = 1; i31.l = 1; i32.l = 1; i33.l = 1; i34.l = 1; i35.l = 1; i36.l = 1; i37.l = 1; i38.l = 1; i39.l = 1; i40.l = 1; i41.l = 1; i42.l = 1; i43.l = 1; i44.l = 1; i45.l = 1; i46.l = 1; i47.l = 1; i48.l = 1; i49.l = 1; i50.l = 1; i51.l = 1; i52.l = 1; i53.l = 1; i54.l = 1; i55.l = 1; i56.l = 1; i57.l = 1; i58.l = 1; i59.l = 1; i60.l = 1; i61.l = 1; i62.l = 1; i63.l = 1; * 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;