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ODFITS.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME ODFITS
* Problem:
* ********
* A simple Origin/Destination matrix fit using a minimum entropy
* approach. The objective is a combination of different aims, namely
* to be close to an a priori matrix for some entries, to be consistent
* with some traffic counts (for some entries) and to be small (for entries
* where nothing else is known).
* The objective function is of the form
*
* SUM m T [ ln( T / a ) - 1 ] + E SUM T [ ln ( T ) - 1 ]
* i in I i i i i i in J i i
*
* + g SUM q F [ ln( F / c ) - 1 ]
* i in K i i i i
*
* with the constraints that all Ti and Fi be positive and that
*
* F = SUM p T
* i j ij j
*
* where the pij represent path weights from an a priori assignment.
* Source: a modification of an example in
* L.G. Willumsen,
* "Origin-Destination Matrix: static estimation"
* in "Concise Encyclopedia of Traffic and Transportation Systems"
* (M. Papageorgiou, ed.), Pergamon Press, 1991.
* M. Bierlaire, private communication, 1991.
* SIF input: Ph Toint, Dec 1991.
* classification OLR2-MN-10-6
* Number of available traffic counts
IE ARCS 6
* The traffic counts values (in veh.) [ ci ]
RE TC1 100.0
RE TC2 500.0
RE TC3 400.0
RE TC4 1100.0
RE TC5 600.0
RE TC6 700.0
* quality of the traffic counts [ qi ]
RE QLT1 1.0
RE QLT2 1.0
RE QLT3 1.0
RE QLT4 1.0
RE QLT5 1.0
RE QLT6 1.0
* Path weights resulting from the assignment phase [ pij ]
RE P131 1.0
RE P132 0.0
RE P133 0.0
RE P134 0.0
RE P135 0.0
RE P136 0.0
RE P141 0.0
RE P142 1.0
RE P143 0.0
RE P144 1.0
RE P145 0.0
RE P146 0.0
RE P231 0.0
RE P232 0.0
RE P233 1.0
RE P234 1.0
RE P235 1.0
RE P236 0.0
RE P241 0.0
RE P242 0.0
RE P243 0.0
RE P244 1.0
RE P245 1.0
RE P246 1.0
* A priori known values for some entries [ ai ]
RE APV13 90.0
RE APV14 450.0
RE APV23 360.0
* A priori known coefficients and their inverse [ mi ]
RE MU13 0.5
RE MU14 0.5
RE MU23 0.5
RD 1/MU13 MU13 1.0
RD 1/MU14 MU14 1.0
RD 1/MU23 MU23 1.0
* [ g ]
RE GAMMA 1.5
* entropic coefficient [ E ] and its inverse
RE ENTROP 0.2
RD 1/ENTR ENTROP 1.0
* usefull parameters
IE 1 1
DO I 1 ARCS
AD 1/QLT(I) QLT(I) 1.0
A* G/QLT(I) 1/QLT(I) GAMMA
OD I
VARIABLES
* entries with a priori known value [ in I ]
T13
T14
T23
* entries with no information [ in J ]
T24
* arc flows acorresponding to traffic counts [ in K ]
DO I 1 ARCS
X F(I)
OD I
GROUPS
* fit for entries with a priori known values
N AP13 T13 -1.0
ZN AP13 'SCALE' 1/MU13
N AP14 T14 -1.0
ZN AP14 'SCALE' 1/MU14
N AP23 T23 -1.0
ZN AP23 'SCALE' 1/MU23
* fit for entries without information
N AP24 T24 -1.0
ZN AP24 'SCALE' 1/ENTR
* fit for arc flows corresponding to traffic counts
DO I 1 ARCS
XN CP(I) F(I) -1.0
ZN CP(I) 'SCALE' G/QLT(I)
OD I
* constraints expressing arc flows as the sum of their flows to
* the destinations, weighted by the assignment phase coefficients
DO I 1 ARCS
XE C(I) F(I) -1.0
ZE C(I) T13 P13(I)
ZE C(I) T14 P14(I)
ZE C(I) T23 P23(I)
ZE C(I) T24 P24(I)
OD I
BOUNDS
LO ODFITS 'DEFAULT' 0.1
START POINT
* start from the a priori known values for variables where this is known
ZV ODFITS T13 APV13
ZV ODFITS T14 APV14
ZV ODFITS T23 APV23
* start from 1.0 for variables corresponding to entries about which
* nothing is known
XV ODFITS T24 1.0
* start from the traffic count values for the corresponding arc flows,
DO I 1 ARCS
ZV ODFITS F(I) TC(I)
OD I
ELEMENT TYPE
* element = x * ln( x / den )
EV XLOGX X
EP XLOGX DEN
ELEMENT USES
* entries with apriori known values
XT TFIT13 XLOGX
ZV TFIT13 X T13
ZP TFIT13 DEN APV13
XT TFIT23 XLOGX
ZV TFIT23 X T23
ZP TFIT23 DEN APV23
XT TFIT14 XLOGX
ZV TFIT14 X T14
ZP TFIT14 DEN APV14
* entries without information
XT TFIT24 XLOGX
ZV TFIT24 X T24
XP TFIT24 DEN 1.0
* arc flows corresponding to traffic counts
DO I 1 ARCS
XT CFIT(I) XLOGX
ZV CFIT(I) X F(I)
ZP CFIT(I) DEN TC(I)
OD I
GROUP USES
* fit entries with a priori known values
E AP13 TFIT13
E AP14 TFIT14
E AP23 TFIT23
* fit entries without information
E AP24 TFIT24
* fit arc flows to corresponding traffic counts
DO I 1 ARCS
XE CP(I) CFIT(I)
OD I
OBJECT BOUND
* Solution
*LO ODFITS -2380.026775
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS ODFITS
TEMPORARIES
R LOGX
M LOG
INDIVIDUALS
T XLOGX
A LOGX LOG( X / DEN )
F X * LOGX
G X 1.0 + LOGX
H X X 1.0 / X
ENDATA