Geoscience Reference
In-Depth Information
7.7 EXAMPLE 1: OPTIMISING MODEL PARAMETERS
In this section, a simple optimisation problem is presented, that is, how can we find the
fittest
(optimal) values for the set of parameters that are used within a simple rule set operated by an
agent-based model (ABM)? The parameters that form the core of the rule set (and as such produce
fit solutions) can be determined through experimentation, analysis of existing data or recommenda-
tions from the literature. However, these approaches all contain a degree of subjectivity. Using a GA
allows both a vast number of potential parameter combinations to be searched and it lends some
objectivity to the final choice of parameters.
7.7.1 M
odel
An ABM was developed to simulate the spatial and temporal variations in petrol prices observed
over Yorkshire in northern England, where each agent in the model is a petrol station. Underlying
the ABM is an SI model which is comprised of two parts:
ˆ
m
m
m
S
=
δ
exp
−
β
d
−
λ
p
(
1
+
ε
)
(7.1)
ij
j
ij
j
ˆ
S
m
m
ij
m
S
=
HF
∑
ij
i
(7.2)
ˆ
m
S
ij
j
where
S
ij
m
is the amount of fuel
m
sold by garage
j
to ward
i
δ
j
m
is 1 where garage
j
sells fuel
m
and 0 otherwise
d
ij
is the distance between ward
i
and garage
j
p
j
m
is the price of fuel
m
at garage
j
H
i
is the number of households within the ward
i
F
m
is the amount of fuel of type
m
required per car per day
ε is a stochastic term
Equation 7.1 calculates the relative amount of fuel sold by each petrol station to the population
of each ward (UK census area of ~100-30,000 people). The amount sold to a given ward decays
exponentially with the distance between the ward centroid and the station and also with a rise
in price. This exponential fall-off is traditional in SI models and well matched in many retailing
examples (Birkin et al. 1996). Equation 7.2 ensures that the total volume of fuel sold to each
ward equals the demand
H
i
F
m
and gives the actual amount of fuel sold in each ward. Note
that in this example,
m
was limited to one fuel type, that is, unleaded petrol. The two coefficients,
λ
and β, are usually determined by calibrating the model with real data. More details of the
ABM and the calibration process can be found in Heppenstall (2004) and Heppenstall et al.
(2005, 2006).
7.7.2 r
ule
S
etS
An individual petrol station was represented using the object-orientated language of Java. Each petrol
station agent was supplied with knowledge of the price of petrol at all other stations. Other variables
supplied to the petrol station agents included production costs and the number of customers within
their neighbourhood, defined as a fixed-radius circular-distance around the petrol station. Each
petrol station agent was able to view the prices of neighbouring stations (thus sharing information),
