synthes3.gms:
References:
- Leyffer, S, MacMINLP: AMPL Collection of Mixed Integer Nonlinear Programs.
- Floudas, C A, and Schweiger, C A, MINOPT Model Library.
- Duran, M A, and Grossmann, I E, An Outer-Approximation Algorithm for a Class of Mixed-Integer Nonlinear Programs. Mathematical Programming 36 (1986), 307-339.
- Original source: AMPL model synthes3.mod from MacMINLP
Point:
p1
Best known point (p1): Solution value 68.01 (global optimum, BARON certificate)
<![CDATA[
* MINLP written by GAMS Convert at 04/17/01 16:41:31
*
* Equation counts
* Total E G L N X
* 24 3 0 21 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 18 10 8 0 0 0 0 0
* FX 0 0 0 0 0 0 0 0
*
* Nonzero counts
* Total const NL DLL
* 91 79 12 0
*
* Solve m using MINLP minimizing objvar;
Variables x1,x2,x3,x4,x5,x6,x7,x8,x9,b10,b11,b12,b13,b14,b15,b16,b17,objvar;
Positive Variables x1,x2,x3,x4,x5,x6,x7,x8,x9;
Binary Variables b10,b11,b12,b13,b14,b15,b16,b17;
Equations e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
,e20,e21,e22,e23,e24;
e1.. (-1.5*log(1 + x5)) - log(1 + x6) - x8 =L= 0;
e2.. - log(1 + x3 + x4) =L= 0;
e3.. - x1 - x2 + x3 + 2*x4 + 0.8*x5 + 0.8*x6 - 0.5*x7 - x8 - 2*x9 =L= 0;
e4.. - x1 - x2 + 2*x4 + 0.8*x5 + 0.8*x6 - 2*x7 - x8 - 2*x9 =L= 0;
e5.. - 2*x4 - 0.8*x5 - 0.8*x6 + 2*x7 + x8 + 2*x9 =L= 0;
e6.. - 0.8*x5 - 0.8*x6 + x8 =L= 0;
e7.. - x4 + x7 + x9 =L= 0;
e8.. - 0.4*x5 - 0.4*x6 + 1.5*x8 =L= 0;
e9.. 0.16*x5 + 0.16*x6 - 1.2*x8 =L= 0;
e10.. x3 - 0.8*x4 =L= 0;
e11.. - x3 + 0.4*x4 =L= 0;
e12.. exp(x1) - 10*b10 =L= 1;
e13.. exp(0.833333*x2) - 10*b11 =L= 1;
e14.. x7 - 10*b12 =L= 0;
e15.. 0.8*x5 + 0.8*x6 - 10*b13 =L= 0;
e16.. 2*x4 - 2*x7 - 2*x9 - 10*b14 =L= 0;
e17.. x5 - 10*b15 =L= 0;
e18.. x6 - 10*b16 =L= 0;
e19.. x3 + x4 - 10*b17 =L= 0;
e20.. b10 + b11 =E= 1;
e21.. b13 + b14 =L= 1;
e22.. - b13 + b15 + b16 =E= 0;
e23.. b12 - b17 =L= 0;
e24.. - (exp(x1) - 10*x1 + exp(0.833333*x2) - 15*x2 - 65*log(1 + x3 + x4) + 15
*x3 + 80*x4 - 90*log(1 + x5) + 25*x5 - 80*log(1 + x6) + 35*x6) + 40*x7
- 15*x8 + 35*x9 - 5*b10 - 8*b11 - 6*b12 - 10*b13 - 6*b14 - 7*b15 - 4*b16
- 5*b17 + objvar =E= 120;
* set non default bounds
x1.up = 2;
x2.up = 2;
x3.up = 1;
x4.up = 2;
x5.up = 2;
x6.up = 2;
x7.up = 2;
x8.up = 1;
x9.up = 3;
$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;
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