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## ex1224.gms:

#### References:

• Floudas, C A, Pardalos, P M, Adjiman, C S, Esposito, W R, Gumus, Z H, Harding, S T, Klepeis, J L, Meyer, C A, and Schweiger, C A, Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, 1999.
• Berman, O, and Ashrafi, N, Optimization Models for Reliability of Modular Software Systems. IEEE Transactions on Software Engineering 19, 11 (1993), 1119-1123.
• Original source: MINLP Model of Chapter 12 ex12.2.4.gms from Floudas e.a. Test Problems

Point: p1
Best known point (p1): Solution value -0.94 (global optimum, BARON certificate)

\$offlisting * MINLP written by GAMS Convert at 04/17/01 16:37:51 * * Equation counts * Total E G L N X * 8 3 0 5 0 0 * * Variable counts * x b i s1s s2s sc si * Total cont binary integer sos1 sos2 scont sint * 12 4 8 0 0 0 0 0 * FX 0 0 0 0 0 0 0 0 * * Nonzero counts * Total const NL DLL * 31 25 6 0 * * Solve m using MINLP minimizing objvar; Variables x1,x2,x3,b4,b5,b6,b7,b8,b9,b10,b11,objvar; Positive Variables x1,x2,x3; Binary Variables b4,b5,b6,b7,b8,b9,b10,b11; Equations e1,e2,e3,e4,e5,e6,e7,e8; e1.. x1*x2*x3 + objvar =E= 0; e2.. - log(1 - x1) - 2.30258509299405*b4 - 1.6094379124341*b5 - 1.89711998488588*b6 =E= 0; e3.. - log(1 - x2) - 2.99573227355399*b7 - 1.6094379124341*b8 - 1.89711998488588*b9 =E= 0; e4.. - log(1 - x3) - 3.91202300542815*b10 - 2.81341071676004*b11 =L= 0; e5.. - b4 - b5 - b6 =L= -1; e6.. - b7 - b8 - b9 =L= -1; e7.. - b10 - b11 =L= -1; e8.. 3*b4 + b5 + 2*b6 + 3*b7 + 2*b8 + b9 + 3*b10 + 2*b11 =L= 10; * set non default bounds x1.up = 0.997; x2.up = 0.9985; x3.up = 0.9988; \$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;