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CATMIX.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CATMIX
* Problem :
* *********
* Determine the optimal mixing policy of two catalysts along the
* length of a tubular plug flow reactor involving several reactions
* This is problem 14 in the COPS (Version 2) collection of
* E. Dolan and J. More'
* see "Benchmarking Optimization Software with COPS"
* Argonne National Labs Technical Report ANL/MCS-246 (2000)
* SIF input: Nick Gould, November 2000
* classification OOR2-AN-V-V
* The number of subintervals
*IE NH 100 $-PARAMETER
*IE NH 200 $-PARAMETER
*IE NH 400 $-PARAMETER
IE NH 800 $-PARAMETER
* The ODE is defined in [0,TF]
RE TF 1.0
* Initial condition for x1
RE X1_0 1.0
* Initial condition for x2
RE X2_0 0.0
* Smoothing parameter
RE ALPHA 0.0
* The uniform interval length
RI RNH NH
R/ H TF RNH
* Other useful values
IE 0 0
IE 1 1
IA NH-1 NH -1
R* ALPHAH ALPHA H
RM H/2 H 0.5
RM -H/2 H/2 -1.0
VARIABLES
DO I 0 NH
X U(I) $ Control
X X1(I) $ Catalyst 1
X X2(I) $ Catalyst 2
ND
GROUPS
* linear part of the objective: x1[nh] + x2[nh] - 1
XN OBJ X1(NH) 1.0 X2(NH) 1.0
DO I 0 NH-1
IA I+1 I 1
* linear part of constraint 0 = ode1 {i in 0..(nh-1)}: x1[i] - x1[i+1]
XE ODE1(I) X1(I) 1.0 X1(I+1) -1.0
* linear part of constraint 0 = ode2 {i in 0..(nh-1)}: x2[i] - x2[i+1]
XE ODE2(I) X2(I) 1.0 X2(I+1) -1.0
ND
CONSTANTS
X CATMIX OBJ 1.0
BOUNDS
XR CATMIX 'DEFAULT'
DO I 0 NH
XL CATMIX U(I) 0.0
XU CATMIX U(I) 1.0
ND
ZX CATMIX X1(0) X1_0
ZX CATMIX X2(0) X2_0
START POINT
DO I 0 NH
X CATMIX U(I) 0.0
X CATMIX X1(I) 1.0
X CATMIX X2(I) 0.0
ND
ELEMENT TYPE
EV DIFSQ U1 U2
IV DIFSQ U
EV P1 U
EV P1 X1 X2
IV P1 U
IV P1 X
EV P2 U X
ELEMENT USES
DO I 0 NH-1
IA I+1 I 1
XT O(I) DIFSQ
ZV O(I) U1 U(I)
ZV O(I) U2 U(I+1)
ND
DO I 0 NH
XT P1(I) P1
ZV P1(I) U U(I)
ZV P1(I) X1 X1(I)
ZV P1(I) X2 X2(I)
XT P2(I) P2
ZV P2(I) U U(I)
ZV P2(I) X X2(I)
ND
GROUP USES
* nonlinear part of the objective:
* alpha*h*sum{i in 0..nh-1} (u[i+1] - u[i])^2
DO I 0 NH-1
ZE OBJ O(I) ALPHAH
* nonlinear part of constraint 0 = ode1 {i in 0..(nh-1)}:
* (h/2)*( u[i]*( 10*x2[i]-x1[i] ) + u[i+1]*( 10*x2[i+1]-x1[i+1] ) )
ZE ODE1(I) P1(I) H/2
ZE ODE1(I) P1(I+1) H/2
* nonlinear part of constraint 0 = ode2 {i in 0..(nh-1)}:
* (h/2)*( u[i]*( x1[i]-10*x2[i]) + (u[i]-1)*x2[i] +
* u[i+1]*(x1[i+1]-10*x2[i+1]) + (u[i+1]-1)*x2[i+1] )
ZE ODE2(I) P1(I) -H/2
ZE ODE2(I) P1(I+1) -H/2
ZE ODE2(I) P2(I) H/2
ZE ODE2(I) P2(I+1) H/2
ND
OBJECT BOUND
* Solution
*LO SOLUTION -4.7748D-02 $ (NH=100)
*LO SOLUTION -4.8016D-02 $ (NH=200)
*LO SOLUTION -4.7862D-02 $ (NH=400)
*LO SOLUTION -4.7185D-02 $ (NH=800)
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CATMIX
INDIVIDUALS
T DIFSQ
R U U1 1.0 U2 -1.0
F U * U
G U U + U
H U U 2.0
T P1
R U U 1.0
R X X1 -1.0 X2 10.0
F U * X
G U X
G X U
H U X 1.0
T P2
F ( U - 1.0 ) * X
G U X
G X U - 1.0
H U X 1.0
ENDATA