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## bearing.gms:

#### References:

• Siddall, J N, Optimal Engineering Design: Principles and Applications. Marcel Dekker, New York, 1982.
• 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.
• Coello Coello, C A, Treating Constraints as Objectives for Single-Objective Evolutionary Optimization. Engineering Optimization 32 (2000), 275-308.
• Original source: GAMS Model of bearing.gms from GAMS Model Library

Point: p1
Best known point: p1 with value 1.9517

* NLP written by GAMS Convert at 07/25/01 14:27:44 * * Equation counts * Total E G L N X * 13 10 1 2 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 14 14 0 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 41 13 28 0 * * Solve m using NLP minimizing objvar; Variables x1,x2,x3,x4,objvar,x6,x7,x8,x9,x10,x11,x12,x13,x14; Negative Variables x10; Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13; e1.. 10000*objvar - 10000*x7 - 10000*x8 =E= 0; e2.. - 1.42857142857143*x4*x6 + 10000*x8 =E= 0; e3.. 10*x7*x9 - 0.00968946189201592*x3*(x1**4 - x2**4) =E= 0; e4.. 143.3076*x10*x4 - 10000*x7 =E= 0; e5.. 3.1415927*x6*(0.001*x9)**3 - 6e-6*x3*x4*x13 =E= 0; e6.. 101000*x12*x13 - 1.57079635*x6*x14 =E= 0; e7.. log10(0.8 + 8.112*x3) - 10964781961.4318*x11**(-3.55) =E= 0; e8.. - 0.5*x10 + x11 =E= 560; e9.. x1 - x2 =G= 0; e10.. 0.0307*sqr(x4) - 0.3864*sqr(0.0062831854*x1*x9)*x6 =L= 0; e11.. 101000*x12 - 15707.9635*x14 =L= 0; e12.. - (log(x1) - log(x2)) + x13 =E= 0; e13.. - (sqr(x1) - sqr(x2)) + x14 =E= 0; * set non default bounds x1.lo = 1; x1.up = 16; x2.lo = 1; x2.up = 16; x3.lo = 1; x3.up = 16; x4.lo = 1; x4.up = 16; x6.lo = 1; x6.up = 1000; x7.lo = 0.0001; x8.lo = 0.0001; x9.lo = 1; x10.up = 50; x11.lo = 100; x12.lo = 1; x13.lo = 0.0001; x14.lo = 0.01; * set non default levels x1.l = 6; x2.l = 5; x3.l = 6; x4.l = 3; x6.l = 1000; x7.l = 1.6; x8.l = 0.3; x10.l = 50; x11.l = 600; * set non default marginals Model m / all /; m.limrow=0; m.limcol=0; \$if NOT '%gams.u1%' == '' \$include '%gams.u1%' Solve m using NLP minimizing objvar;