### tp067v1.apm

Model tp067v1
! Source version 1
! This is the poor man's free formulation of #67, intuitive,
! without discontinuities. The poor man's one because the sense
! of #67 is to prove whether a solving software has procedure
! handling capabilities. Since up to now, procedures cannot
! directly be expressed in APM, this formulation has to be thought
! of as a workaround. This is further a free formulation because
! the obtained solution is sensible but not exact.
! See also tp067v2 and tp067v3.
! Both the auxiliaries below, x[4] and x[5], are initialized in such
! a manner that the initial point belongs to the feasible domain.
! Recall, the initial point of the original #67 is also feasible.
Parameters
ivx4 = 3048.289708675017
ivx5 = 89.19762025827802
End Parameters
Variables
x[1] = 1745, >= 10^(-5), <= 2000
x[2] = 12000, >= 10^(-5), <= 16000
x[3] = 110, >= 10^(-5), <= 120
x[4] = ivx4
x[5] = ivx5
obj
End Variables
Intermediates
y2 = x[4]
y3 = 1.22*y2 - x[1]
y6 = (x[2] + y3)/x[1]
y2c = 0.01*x[1]*(112 + 13.167*y6 - 0.6667*y6^2)
y4 = x[5]
y5 = 86.35 + 1.098*y6 - 0.038*y6^2 + 0.325*(y4 - 89)
y8 = 3*y5 - 133
y7 = 35.82 - 0.222*y8
y4c = 98000*x[3]/(y2*y7 + 1000*x[3])
c[ 1] = y2c - y2
c[ 2] = y4c - y4
c[ 3] = y2 - 0
c[ 4] = y3 - 0
c[ 5] = y4 - 85
c[ 6] = y5 - 90
c[ 7] = y6 - 3
c[ 8] = y7 - 1/100
c[ 9] = y8 - 145
c[10] = 5000 - y2
c[11] = 2000 - y3
c[12] = 93 - y4
c[13] = 95 - y5
c[14] = 12 - y6
c[15] = 4 - y7
c[16] = 162 - y8
mf = -(0.063*y2*y5 - 5.04*x[1] - 3.36*y3 - 0.035*x[2] - 10*x[3])
End Intermediates
Equations
c[1: 2] = 0
c[3:16] >= 0
obj = mf
! best known objective = -1162.02698005969
! begin of best known solution
! x[1] = 1728.371443241086
! x[2] = 16000
! x[3] = 98.13617652300942
! x[4] = 3056.042166591054
! x[5] = 90.61853974698703
! end of best known solution
End Equations
End Model

Stephan K.H. Seidl