Geoscience Reference
In-Depth Information
TABLE 7.6
Lookup Tables for Encoding the Four Components of Each Equation
Data
Code
Parameter
Code
Function
Code
Operator
Code
O
i
1
None
0
None
0
+
1
D
j
2
Parameter
1
exp
1
-
2
d
ij
3
Constant
2
log
2
×
3
∑
O
i
4
1
3
ln
3
÷
4
∑
D
j
5
-1
4
4
1/
x
6
5
∑
x
2
ij
j
7
6
∑
x
ij
i
8
7
∑∑
x
y
d
ij
i
j
Source:
Harland, K. and Stillwell, J., Commuting to school: A new spatial interaction
modelling framework, in
Technologies for Migration and Population Analysis:
Spatial Interaction Data Applications
, eds. Stillwell, J.C.H., Duke-Williams, O.,
and Dennett, A., IGI Global Snippet, 2010.
TABLE 7.7
Encoded Equation for
a
Typical
SI Model
Gene
Code
1,2,0,3
kO
i
2,0,0,3
D
j
3,4,1,3
exp(
−1
d
ij
)
encoded genes together in the order that they would be encountered produces the following
encoded equation: 1,2,0,3,2,0,0,3,3,4,1,3.
One final note on encoding is as follows: many equations contain parentheses that must be
accounted for. Encoding these is simple where each opening and closing parenthesis is assigned a
specific code. However, the following rules must be followed: the gene cannot be altered and they
must form pairs.
7.8.4 c
aliBrating
the
Si M
odel
e
quationS
Each form of an equation is calibrated using the GA as an independent calibration process with
specified upper and lower limits for the parameters, but no limit is placed on the number of possible
parameters in an equation. The GA is run to optimise the fit on each model form by adjusting the
parameter values. The optimised fitness values are compared, and the fittest equations are bred
together to create new forms of the equation with genes mutated to a specified rate. The new equa-
tion forms are subsequently calibrated to assess the model fitness. This process of calibration and
equation generation is repeated until an equation is generated that surpasses a predefined fitness
threshold or the equation generation GA reaches a maximum number of generations.
