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## ex1266a.gms:

#### References:

• GAMS Development, Reformulation of Models from Handbook of Test Problems in Local and Global Optimization.
• 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: MINLP Model of Chapter 12 ex12.6.6.gms from Floudas e.a. Test Problems

Point: p1
Best known point (p1): Solution value 16.30 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:38:32 * * Equation counts * Total E G L N X * 54 1 7 46 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 49 1 6 42 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 302 230 72 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,i5,i6,i7,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 ,b37,b38,b39,b40,b41,b42,i43,i44,i45,i46,i47,i48,objvar; Binary Variables b37,b38,b39,b40,b41,b42; Integer Variables i1,i2,i3,i4,i5,i6,i7,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,i43,i44,i45,i46,i47,i48; 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; e1.. - 0.1*b37 - 0.2*b38 - 0.3*b39 - 0.4*b40 - 0.5*b41 - i43 - i44 - i45 - i46 - i47 - i48 + objvar =E= 0; e2.. i43*i1 + i44*i2 + i45*i3 + i46*i4 + i47*i5 + i48*i6 =G= 8; e3.. i43*i7 + i44*i8 + i45*i9 + i46*i10 + i47*i11 + i48*i12 =G= 16; e4.. i43*i13 + i44*i14 + i45*i15 + i46*i16 + i47*i17 + i48*i18 =G= 12; e5.. i43*i19 + i44*i20 + i45*i21 + i46*i22 + i47*i23 + i48*i24 =G= 7; e6.. i43*i25 + i44*i26 + i45*i27 + i46*i28 + i47*i29 + i48*i30 =G= 14; e7.. i43*i31 + i44*i32 + i45*i33 + i46*i34 + i47*i35 + i48*i36 =G= 16; e8.. - 330*i1 - 360*i7 - 380*i13 - 430*i19 - 490*i25 - 530*i31 + 2100*b37 =L= 0; e9.. - 330*i2 - 360*i8 - 380*i14 - 430*i20 - 490*i26 - 530*i32 + 2100*b38 =L= 0; e10.. - 330*i3 - 360*i9 - 380*i15 - 430*i21 - 490*i27 - 530*i33 + 2100*b39 =L= 0; e11.. - 330*i4 - 360*i10 - 380*i16 - 430*i22 - 490*i28 - 530*i34 + 2100*b40 =L= 0; e12.. - 330*i5 - 360*i11 - 380*i17 - 430*i23 - 490*i29 - 530*i35 + 2100*b41 =L= 0; e13.. - 330*i6 - 360*i12 - 380*i18 - 430*i24 - 490*i30 - 530*i36 + 2100*b42 =L= 0; e14.. 330*i1 + 360*i7 + 380*i13 + 430*i19 + 490*i25 + 530*i31 - 2200*b37 =L= 0; e15.. 330*i2 + 360*i8 + 380*i14 + 430*i20 + 490*i26 + 530*i32 - 2200*b38 =L= 0; e16.. 330*i3 + 360*i9 + 380*i15 + 430*i21 + 490*i27 + 530*i33 - 2200*b39 =L= 0; e17.. 330*i4 + 360*i10 + 380*i16 + 430*i22 + 490*i28 + 530*i34 - 2200*b40 =L= 0; e18.. 330*i5 + 360*i11 + 380*i17 + 430*i23 + 490*i29 + 530*i35 - 2200*b41 =L= 0; e19.. 330*i6 + 360*i12 + 380*i18 + 430*i24 + 490*i30 + 530*i36 - 2200*b42 =L= 0; e20.. - i1 - i7 - i13 - i19 - i25 - i31 + b37 =L= 0; e21.. - i2 - i8 - i14 - i20 - i26 - i32 + b38 =L= 0; e22.. - i3 - i9 - i15 - i21 - i27 - i33 + b39 =L= 0; e23.. - i4 - i10 - i16 - i22 - i28 - i34 + b40 =L= 0; e24.. - i5 - i11 - i17 - i23 - i29 - i35 + b41 =L= 0; e25.. - i6 - i12 - i18 - i24 - i30 - i36 + b42 =L= 0; e26.. i1 + i7 + i13 + i19 + i25 + i31 - 5*b37 =L= 0; e27.. i2 + i8 + i14 + i20 + i26 + i32 - 5*b38 =L= 0; e28.. i3 + i9 + i15 + i21 + i27 + i33 - 5*b39 =L= 0; e29.. i4 + i10 + i16 + i22 + i28 + i34 - 5*b40 =L= 0; e30.. i5 + i11 + i17 + i23 + i29 + i35 - 5*b41 =L= 0; e31.. i6 + i12 + i18 + i24 + i30 + i36 - 5*b42 =L= 0; e32.. b37 - i43 =L= 0; e33.. b38 - i44 =L= 0; e34.. b39 - i45 =L= 0; e35.. b40 - i46 =L= 0; e36.. b41 - i47 =L= 0; e37.. b42 - i48 =L= 0; e38.. - 15*b37 + i43 =L= 0; e39.. - 12*b38 + i44 =L= 0; e40.. - 8*b39 + i45 =L= 0; e41.. - 7*b40 + i46 =L= 0; e42.. - 4*b41 + i47 =L= 0; e43.. - 2*b42 + i48 =L= 0; e44.. i43 + i44 + i45 + i46 + i47 + i48 =G= 16; e45.. - b37 + b38 =L= 0; e46.. - b38 + b39 =L= 0; e47.. - b39 + b40 =L= 0; e48.. - b40 + b41 =L= 0; e49.. - b41 + b42 =L= 0; e50.. - i43 + i44 =L= 0; e51.. - i44 + i45 =L= 0; e52.. - i45 + i46 =L= 0; e53.. - i46 + i47 =L= 0; e54.. - i47 + i48 =L= 0; * set non default bounds i1.up = 5; i2.up = 5; i3.up = 5; i4.up = 5; i5.up = 5; i6.up = 5; i7.up = 5; i8.up = 5; i9.up = 5; i10.up = 5; i11.up = 5; i12.up = 5; i13.up = 5; i14.up = 5; i15.up = 5; i16.up = 5; i17.up = 5; i18.up = 5; i19.up = 5; i20.up = 5; i21.up = 5; i22.up = 5; i23.up = 5; i24.up = 5; i25.up = 5; i26.up = 5; i27.up = 5; i28.up = 5; i29.up = 5; i30.up = 5; i31.up = 5; i32.up = 5; i33.up = 5; i34.up = 5; i35.up = 5; i36.up = 5; i43.up = 15; i44.up = 12; i45.up = 8; i46.up = 7; i47.up = 4; i48.up = 2; \$if set nostart \$goto modeldef * set non default levels i1.l = 1; i7.l = 2; i14.l = 2; i20.l = 1; i26.l = 2; i31.l = 1; i43.l = 8; i44.l = 7; * 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;