Evolutionary Algorithms - GeoComputation - page 153

TABLE 7.3
Summary of the Methods and Parameters Used within the GA

Parameter/Method Value Selected on the Basis of

Population initialisation Random Literature

Number of generations 100 Experimentation

Population size 100 Experimentation

Selection Linear ranking Literature

Selection pressure 2.0 Literature

Recombination Intermediate recombination Literature

Recombination value 0.25 Literature

Mutation Chance of mutation 1/8 (since there

are 8 parameters to optimise)

Literature

Number of mutations per generation 3.0 Experimentation

Convergence factor 0.99 Experimentation

∑ −

t 2 /

( yyn )

i i

(7.3)

y

where
y t is the predicted value of the dependent variable at petrol station i
y i is the measured value at station i
n is the total number of stations
y is the mean value of the y i

While y t and y i could be compared at each time step during the simulation, in this example, they are
only calculated on the last day of the simulation.

7.7.6 c oMPariSon of P araMeter V alueS
Table 7.4 details the optimal parameters derived by modeller-driven experimentation (based on
early experimentation and numerical exploration) and the optimal parameters suggested by the GA.
The GA was run five times to give an indication of the spread of values produced. Figure 7.5 shows
this spread as a function of the SRMSE for each parameter.
The GA values for β and λ were both reasonably close to the parameters derived by modeller-
driven experimentation. As evident from Figure 7.5a and b, neither of these values produced definite
clusters; this is supported by the standard deviation (SD) in Table 7.4. This implies that reason-
able solutions can be produced from a wide range of values and do not exert influence on the
other variables.
The GA gave the neighbourhood parameter a slightly smaller value than the modeller-derived
values (Figure 7.5h). The overprice parameter was well clustered and in good agreement with the
modeller-derived value (Figure 7.5g). The undercut value (Figure 7.5h) was also quite tightly clus-
tered. There is a large difference between the GA predicted value (£1) and the modeller-derived
value (£40) for the changeInProfit (Figure 7.5e). There is also a very large SD (£22.80) for the
parameter indicating a large degree of uncertainty in the optimal value. The system modelled here
is highly complex with many non-linear processes contributing to price setting at each station. One
of the interesting findings here was the control over the stability of the system that this parameter
appeared to exert.