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## gear2.gms:

#### References:

• GAMS Development, GAMS Model Library.
• GAMS Development, Reformulation of Models from MacMINLP.
• Deb, K, and Goyal, M, Optimizing Engineering Designs Using a Combined Genetic Search. In Back, T, Ed, Proceedings of the Seventh International Conference on Genetic Algorithms. 1997, pp. 521-528.
• Original source: GAMS model gear.gms from Gams Model Library and AMPL model geartrain.mod from MacMINLP

Point: p1
Best known point (p1): Solution value 0.00 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:38:53 * * Equation counts * Total E G L N X * 5 5 0 0 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 29 5 24 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 33 29 4 0 * * Solve m using MINLP minimizing objvar; Variables objvar,x2,x3,x4,x5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18 ,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29; Binary Variables b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19,b20,b21 ,b22,b23,b24,b25,b26,b27,b28,b29; Equations e1,e2,e3,e4,e5; e1.. - sqr(0.14427932477276 - x2*x3/(x4*x5)) + objvar =E= 0; e2.. x2 - b6 - 2*b7 - 4*b8 - 8*b9 - 16*b10 - 32*b11 =E= 0; e3.. x3 - b12 - 2*b13 - 4*b14 - 8*b15 - 16*b16 - 32*b17 =E= 0; e4.. x4 - b18 - 2*b19 - 4*b20 - 8*b21 - 16*b22 - 32*b23 =E= 0; e5.. x5 - b24 - 2*b25 - 4*b26 - 8*b27 - 16*b28 - 32*b29 =E= 0; * set non default bounds x2.lo = 12; x2.up = 60; x3.lo = 12; x3.up = 60; x4.lo = 12; x4.up = 60; x5.lo = 12; x5.up = 60; \$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;