Geoscience Reference
In-Depth Information
and each applied a common series of rules to adjust its own prices. In the main, these rules involve
the implementation of behaviour based on the price set by the neighbouring stations and their dis-
tance away. A typical rule might be
if my price is X pence cheaper or X pence more expensive than
my nearest neighbour, set my price to my neighbour's price
. The overall aim of the simulation was
to evolve a solution that resembled the processes occurring in the real system. Thus, the optimisa-
tion is not aimed at solving an equation; instead, we are interested in emerging behaviour through
exploitation of the ABM paradigm.
7.7.3 P
araMeterS
to
B
e
o
PtiMiSed
The rules operated by each petrol station agent are based on industry knowledge and implemented
after experimentation with different parameters (listed in Table 7.2). It is these eight parameters (or
what are referred to as genes in GA terminology) that the GA will optimise. These are β, λ,
costTo -
Produce
,
neighbourhood
,
ixedCosts
,
overprice
,
changeInProit
and
undercut
. Early experimenta-
tion revealed that all of these parameters exert some influence over the performance of the model.
The values associated with each parameter are continuous, and a range of allowed values will be
assigned to each parameter based on values obtained through prior experimentation. Clearly, the
ranges have to be sensible if the GA is to operate successfully since the populations will be ini-
tialised and reproduce using the values within these ranges. The range of values that will be used is
summarised in Table 7.2.
7.7.4 o
PtiMal
S
olution
S
Pace
One of the key factors in the success of GAs is finding the correct balance between the amount of
exploration and exploitation needed (Flake 2001). Several studies have concentrated on developing
optimal parameter settings for GAs (see De Jong 1975; Grefenstette 1986; Schaffer et al. 1989).
Each study presents a different set of optimal parameters showing that these optimal values vary
for the problem under consideration. For example, suggested values for population size range from
50 to 100 (De Jong 1975), 20 to 30 (Schaffer et al. 1989) and 30 (Grefenstette 1986). These values
are obviously dependent on the problem under investigation. Selection, mutation and recombination
methods were selected after reviewing the literature and initial experimentation using the model.
The methods selected are summarised in Table 7.3.
7.7.5 S
tatiStical
M
eaSure
of
f
itneSS
The SRMSE was used to determine the fitness of each string of variables or chromosomes. Originally
put forward by Knudsen and Fotheringham (1986), it is given by
TABLE 7.2
Definition and Range of Allowed Values Assigned to Each Parameter in the GA
Variable
Meaning
Range of Values
β
Coefficient controlling distance
0.000003-0.003
λ
Coefficient controlling price
0.001-1.5
costToProduce
The amount per litre that it costs the station to produce and sell the petrol
60.0-70.0 p
FixedCosts
The amount the petrol station has to pay per day to keep running
100-10,000.0 p
ChangeInProfit
The level of profit under which the station will not change its strategy
2,000-5,000 p
Undercut
The amount by which a station can be cheaper than its neighbour
0.1-5.0 p
Overprice
The amount by which a station can be more expensive than its neighbour
0.1-5.0 p
Neighbourhood
The distance that petrol stations treat as their neighbourhood
1,000-10,000 m
