Geoscience Reference
In-Depth Information
TABLE 7.4
Comparison of Parameter Values Derived Using
Modeller-Driven Experimentation and the GA
Parameter
Modeller-Derived Value
GA Value
SD (5 GA Runs)
β
0.0003
0.0002
2.04 × 10
−4
λ
0.7
0.4
0.176
fixedCosts (£)
80.00
12.73
15.9
costToProduce (p)
66.00
65.75
2.27
changeInProfit (p)
40.00
1.0
22.8
Overprice (p)
5
4.4
0.73
Undercut (p)
1
0.8
1.12
Neighbourhood (km)
5.0
3.6
1.21
Note:
SD is standard deviation.
The
costToProduce
and
fixedCosts
parameters are closely linked. Profit will decrease as a result
of an increase in either or both of these parameters. The GA optimal value for
costToProduce
almost matched the modeller-derived value. However, the GA values were not tightly clustered
(Figure 7.5d) with an SD of 2.27 p, again suggesting that a reasonable solution can be obtained from
a range of values. The GA predicted value for
fixedCosts
(£12.73) is considerably smaller than the
value derived by the modeller (£80). However, in Figure 7.5c, the best solutions for the
fixedCosts
are not tightly clustered - they span a £20 range. This suggests that this parameter does not have as
great an effect on the overall solution.
The application of a GA provides interesting insights into the system under consideration. The
parameters produced by the GA are not constrained to agree with the modeller-driven parameters;
they are merely chosen to minimise the SRMSE of the model. The results provide reassurance that
the model is behaving in a realistic manner and the assumptions made in deriving the parameter
values were reasonable. Overall, the GA parameters produced a lower error than the modeller-
derived parameters. Some of the parameters produced tight clusters suggesting that the GA found
the optimal values (e.g.
costToProduce
). However, the results of other parameters were rather
more dispersed; this suggests that potentially there is more than one high-quality solution or
there are two similar minima. Overall, the GA provides an excellent methodology for refining the
model parameters.
It is encouraging that the modeller-derived and GA-derived parameters are closely aligned.
However, these numbers do not give any idea of whether the rule set that each petrol station agent
operates reproduces spatial variations observed within the real system. Figure 7.6 presents a
comparison of the prices produced at the end of the experimental period with the modeller-driven
and GA-parameterised model both initialised with all the stations at 71 p. Figure 7.6c shows that
the GA parameter values are recreating the rural-urban divide seen in the real data (Figure 7.6a).
For example, the petrol stations within the predominantly rural area of North Yorkshire are sus-
taining higher prices than West or South Yorkshire. The main difference lies in the magnitude
of the prices. On average, the prices produced by the GA are approximately 1-2 p lower than the
real data. This probably reflects a mild disequilibrium in the real prices, for example, as the result
of crude oil price changes.
The solution produced by the GA parameter values has improved on the model by reproducing
(through interplay of the rules) the lower prices surrounding Scarborough and Harrogate
(Figure 7.6b and c). It has also successfully identified the lower-priced areas, which are in fact
cities, within West and South Yorkshire, and the area of higher prices between Wakefield and
Ba r nsley.
