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## st_e40.gms:

#### Reference:

• Shin, D K, Gurdal, Z, and Griffin, O H, A penalty approach for nonlinear optimization with discrete design variables. Engineering Optimization 16 (1990), 29--42.

Point: p1
Best known point (p1): Solution value 30.41 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 08/29/02 11:38:03 * * Equation counts * Total E G L N X C * 9 5 0 4 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 5 2 0 3 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 23 17 6 0 * * Solve m using MINLP minimizing objvar; Variables i1,i2,i3,x4,objvar; Integer Variables i1,i2,i3; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9; e1.. (-0.15*i1*i2) - 0.14142135*i2*i3 - 0.1319*i1*i3 + x4 =E= 0; e2.. 1.7317*i2 + 1.03366*i3 - x4 =L= 0; e3.. 0.634*i1 + 2.828*i3 - x4 =L= 0; e4.. 0.5*i1 - 2*i2 - x4 =L= 0; e5.. - 0.5*i1 + 2*i2 - x4 =L= 0; e6.. (i1 - 1)*(i1 - 2)*(i1 - 3)*(i1 - 5)*(i1 - 8)*(i1 - 10)*(i1 - 12) =E= 0; e7.. (i2 - 1)*(i2 - 2)*(i2 - 3)*(i2 - 5)*(i2 - 8)*(i2 - 10)*(i2 - 12) =E= 0; e8.. (i3 - 1)*(i3 - 2)*(i3 - 3)*(i3 - 5)*(i3 - 8)*(i3 - 10)*(i3 - 12) =E= 0; e9.. - 2*i1 - i2 - 1.4142135*i3 + objvar =E= 0; * set non default bounds i1.lo = 1; i1.up = 12; i2.lo = 1; i2.up = 12; i3.lo = 1; i3.up = 12; \$if set nostart \$goto modeldef * set non default levels * set non default marginals * set non default priorities i1.prior = 0.1; i2.prior = 0.1; i3.prior = 0.1; \$label modeldef Model m / all /; m.limrow=0; m.limcol=0; m.prioropt = 1; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' \$if not set MINLP \$set MINLP MINLP Solve m using %MINLP% minimizing objvar;