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## spring.gms:

#### References:

• GAMS Development, Reformulation of Models from GAMS Library.
• GAMS Development, Reformulation of Models from MacMINLP.
• Sandgren, E, Nonlinear Integer and Discrete Programming in Mechanical Design Optimization. Journal of Mechanical Design, Trans. ASME 112 (1990), 223-229.
• Original source: GAMS model spring.gms from Gams Model Library

Point: p1
Best known point (p1): Solution value 0.85 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/27/01 14:53:07 * * Equation counts * Total E G L N X * 9 6 0 3 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 18 6 11 1 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 44 30 14 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,i4,x5,x6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,objvar; Binary Variables b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17; Integer Variables i4; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9; e1.. - (1.570796327 + 0.7853981635*i4)*x1*sqr(x2) + objvar =E= 0; e2.. - x1/x2 + x5 =E= 0; e3.. - ((4*x5 - 1)/(4*x5 - 4) + 0.615/x5) + x6 =E= 0; e4.. 2546.47908913782*x6*x5/sqr(x2) =L= 189000; e5.. - 6.95652173913044e-7*i4*x5**3/x2 + x3 =E= 0; e6.. (2.1 + 1.05*i4)*x2 + 1000*x3 =L= 14; e7.. x1 + x2 =L= 3; e8.. x2 - 0.207*b7 - 0.225*b8 - 0.244*b9 - 0.263*b10 - 0.283*b11 - 0.307*b12 - 0.331*b13 - 0.362*b14 - 0.394*b15 - 0.4375*b16 - 0.5*b17 =E= 0; e9.. b7 + b8 + b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 + b17 =E= 1; * set non default bounds x1.lo = 0.414; x2.lo = 0.207; x3.lo = 0.00178571428571429; x3.up = 0.02; i4.lo = 1; i4.up = 100; x5.lo = 1.1; \$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;