tp070.apm

Model tp070
  ! Source version 1

  Parameters
    e1 = -1     ! from PROB.FOR
    e2 =  1     ! from H+S
    d1 =  7.658 ! from PROB.FOR
    d2 =  7.685 ! from H+S, seems to be a typo
    e  = e1     ! my quite clear decision from data below
    d  = d1     ! my quite clear decision from data below
    yobs[ 1] = 0.00189
    yobs[ 2] = 0.1038
    yobs[ 3] = 0.268
    yobs[ 4] = 0.506
    yobs[ 5] = 0.577
    yobs[ 6] = 0.604
    yobs[ 7] = 0.725
    yobs[ 8] = 0.898
    yobs[ 9] = 0.947
    yobs[10] = 0.845
    yobs[11] = 0.702
    yobs[12] = 0.528
    yobs[13] = 0.385
    yobs[14] = 0.257
    yobs[15] = 0.159
    yobs[16] = 0.0869
    yobs[17] = 0.0453
    yobs[18] = 0.01509
    yobs[19] = 0.00189
    c[1] = 0.1
    c[2] = 1
    c[3:19] = c[2:18] + 1
    s[0] = 0
  End Parameters

  Variables
    x[1] = 2,    >= 0.00001, <= 100
    x[2] = 4,    >= 0.00001, <= 100
    x[3] = 0.04, >= 0.00001, <=   1
    x[4] = 2,    >= 0.00001, <= 100
    obj
  End Variables

  Intermediates
    b = x[3] + (1 - x[3])*x[4]
    ycal[1:19] = (1 + 1/(12*x[2]))^e *            &
                 x[3]*b^x[2] *                    &
                 (x[2]/6.2832)^(1/2) *            &
                 (c[1:19]/d)^(x[2] - 1) *         &
                 exp(x[2] - b*c[1:19]*x[2]/7.658) &
               + (1 + 1/(12*x[1]))^e *            &
                 (1 - x[3]) *                     &
                 (b/x[4])^x[1] *                  &
                 (x[1]/6.2832)^(1/2) *            &
                 (c[1:19]/7.658)^(x[1] - 1) *     &
                 exp(x[1] - b*c[1:19]*x[1]/(7.658*x[4]))
    s[1:19] = s[0:18] + (yobs[1:19] - ycal[1:19])^2
    mf = s[19]
  End Intermediates

  Equations
    b >= 0

    obj = mf

    ! best known objective = 0.007498463574427645
    ! begin of best known solution
    ! x[1] = 12.27697912756719
    ! x[2] =  4.631748162745852
    ! x[3] =  0.3128646302166193
    ! x[4] =  2.029282825337289
    ! end of best known solution

    ! e = e1, d = d1 ! best known objective = 0.007498463574427645
    ! e = e1, d = d1 ! begin of best known solution
    ! e = e1, d = d1 ! x[1] = 12.27697912756719
    ! e = e1, d = d1 ! x[2] =  4.631748162745852
    ! e = e1, d = d1 ! x[3] =  0.3128646302166193
    ! e = e1, d = d1 ! x[4] =  2.029282825337289
    ! e = e1, d = d1 ! end of best known solution

    ! e = e1, d = d2 ! best known objective = 0.007261547474631637
    ! e = e1, d = d2 ! begin of best known solution
    ! e = e1, d = d2 ! x[1] = 12.13773384939642
    ! e = e1, d = d2 ! x[2] =  4.82102598947378
    ! e = e1, d = d2 ! x[3] =  0.3031189915355265
    ! e = e1, d = d2 ! x[4] =  2.065299221807952
    ! e = e1, d = d2 ! end of best known solution

    ! e = e2, d = d1 ! best known objective = 0.0105735495312881
    ! e = e2, d = d1 ! begin of best known solution
    ! e = e2, d = d1 ! x[1] = 12.02765526345873
    ! e = e2, d = d1 ! x[2] =  4.634279639662956
    ! e = e2, d = d1 ! x[3] =  0.3022728725783973
    ! e = e2, d = d1 ! x[4] =  2.073537805595134
    ! e = e2, d = d1 ! end of best known solution

    ! e = e2, d = d2 ! best known objective = 0.009401973254465482
    ! e = e2, d = d2 ! begin of best known solution
    ! e = e2, d = d2 ! x[1] = 11.96577794613915
    ! e = e2, d = d2 ! x[2] =  4.769875049754542
    ! e = e2, d = d2 ! x[3] =  0.2981702392381668
    ! e = e2, d = d2 ! x[4] =  2.091469742396469
    ! e = e2, d = d2 ! end of best known solution

  End Equations
End Model