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## ex1263a.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 ex12.6.3.gms from Floudas e.a. Test Problems

Point: p1
Best known point (p1): Solution value 19.60 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:38:04 * * Equation counts * Total E G L N X * 36 1 5 30 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 25 1 4 20 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 153 121 32 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,b17,b18,b19 ,b20,i21,i22,i23,i24,objvar; Binary Variables b17,b18,b19,b20; Integer Variables i1,i2,i3,i4,i5,i6,i7,i8,i9,i10,i11,i12,i13,i14,i15,i16,i21 ,i22,i23,i24; 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; e1.. - 0.1*b17 - 0.2*b18 - 0.3*b19 - 0.4*b20 - i21 - i22 - i23 - i24 + objvar =E= 0; e2.. i21*i1 + i22*i2 + i23*i3 + i24*i4 =G= 15; e3.. i21*i5 + i22*i6 + i23*i7 + i24*i8 =G= 28; e4.. i21*i9 + i22*i10 + i23*i11 + i24*i12 =G= 21; e5.. i21*i13 + i22*i14 + i23*i15 + i24*i16 =G= 30; e6.. - 290*i1 - 315*i5 - 350*i9 - 455*i13 + 1750*b17 =L= 0; e7.. - 290*i2 - 315*i6 - 350*i10 - 455*i14 + 1750*b18 =L= 0; e8.. - 290*i3 - 315*i7 - 350*i11 - 455*i15 + 1750*b19 =L= 0; e9.. - 290*i4 - 315*i8 - 350*i12 - 455*i16 + 1750*b20 =L= 0; e10.. 290*i1 + 315*i5 + 350*i9 + 455*i13 - 1850*b17 =L= 0; e11.. 290*i2 + 315*i6 + 350*i10 + 455*i14 - 1850*b18 =L= 0; e12.. 290*i3 + 315*i7 + 350*i11 + 455*i15 - 1850*b19 =L= 0; e13.. 290*i4 + 315*i8 + 350*i12 + 455*i16 - 1850*b20 =L= 0; e14.. - i1 - i5 - i9 - i13 + b17 =L= 0; e15.. - i2 - i6 - i10 - i14 + b18 =L= 0; e16.. - i3 - i7 - i11 - i15 + b19 =L= 0; e17.. - i4 - i8 - i12 - i16 + b20 =L= 0; e18.. i1 + i5 + i9 + i13 - 5*b17 =L= 0; e19.. i2 + i6 + i10 + i14 - 5*b18 =L= 0; e20.. i3 + i7 + i11 + i15 - 5*b19 =L= 0; e21.. i4 + i8 + i12 + i16 - 5*b20 =L= 0; e22.. b17 - i21 =L= 0; e23.. b18 - i22 =L= 0; e24.. b19 - i23 =L= 0; e25.. b20 - i24 =L= 0; e26.. - 30*b17 + i21 =L= 0; e27.. - 30*b18 + i22 =L= 0; e28.. - 30*b19 + i23 =L= 0; e29.. - 30*b20 + i24 =L= 0; e30.. i21 + i22 + i23 + i24 =G= 19; e31.. - b17 + b18 =L= 0; e32.. - b18 + b19 =L= 0; e33.. - b19 + b20 =L= 0; e34.. - i21 + i22 =L= 0; e35.. - i22 + i23 =L= 0; e36.. - i23 + i24 =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; i21.up = 30; i22.up = 30; i23.up = 30; i24.up = 30; \$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;