3 GA NETWORK DIVISION
The method for division of road traffic network,
which we developed, is based on a genetic
algorithm. It will be briefly described in this section.
3.1 Issues of Network Division
There are two issues, which should be considered
during the road traffic network division – the load-
balancing of the resulting sub-networks and the
minimization of the inter-process communication.
The load-balancing is necessary in order to
maximally utilize the computational power of all
nodes of the distributed computer. The minimization
of the inter-process communication, which is used
for the transfer of vehicles among the sub-networks
and for the synchronization, is necessary, since it is
much slower than the reminder of the simulation
computations.
3.2 Description of Division Method
The method for road traffic network division, which
we developed, considers both the load-balancing of
the sub-networks and the minimization of the inter-
process communication. It utilizes a less-detailed
road traffic simulation for assigning of the weights
to particular traffic lanes (Potuzak, 2011a). These
weights correspond to the numbers of vehicles
moving in particular lanes of the divided road traffic
network (Potuzak, 2012).
Once the weights are assigned, the traffic
network can be considered as a weighted graph with
traffic crossroads acting as nodes and the sets of
lanes connecting particular traffic crossroads acting
as weighted edges (with weights equal to sum of
weights of particular traffic lanes of the set). The
road traffic network (i.e. weighted graph) is then
divided using a genetic algorithm (GA) into required
number of load-balanced sub-networks with minimal
number of divided traffic lanes.
An individual of the utilized genetic algorithm
represents a single assignment of the crossroads to
particular sub-networks. The fitness function
consists of two parts – the equability representing
the load-balancing and the compactness representing
the minimization of inter-process communication.
The ratio of these two parts can be changed, but is
set to 0.75 in favour of the equability by default.
Each generation has 90 individuals, from which 10
individuals with highest fitness value are selected to
be parents of the next generation. The crossover is
performed using each combination of two parents
producing two offspring. Each offspring can be
mutated using up to five random changes. The entire
process repeats for preset number (from 1000 to
100 000) of generations (Potuzak, 2011b).
4 OPTIMIZING GA USING GA
The values of particular parameters of the genetic
algorithm were set based on preliminary testing. So,
it is possible that the settings are not optimal. Hence,
we utilize another genetic algorithm for the
optimization of the particular parameters of the
genetic algorithm for road traffic network division.
The genetic algorithm for optimization of the
parameters of the genetic algorithm for road traffic
network division will be referred as optimizing
genetic algorithm or OGA further in the text.
4.1 Parameters of GA to Optimize
The most obvious parameters of the genetic
algorithm for road traffic network division, which
should be optimized, are the number of individuals
in a generation, the number of individuals selected
based on the fitness function, and the number of
generations. Another parameter, which can be
optimized, is the maximal number of mutations (i.e.
random changes), which can be applied to each
individual during the creation of a new generation.
Besides the mutation, the crossover and selection
of the parent individuals can be considered for the
optimization as well. In our genetic algorithm for
road traffic network division, only one type of
selection (simple truncation selection) and one type
of crossover (see Section 3.2) have been employed.
However, there are more types of selection and
crossover, which can be utilized as well. For
example, the fitness proportionate approach (Bäck,
1996) or the reward-based approach (Loshchilov et
al., 2011) can be used for selection. For the
crossover, one-point or two point segment approach
or the uniform crossover can be utilized (Ahmed,
2010).
The parameter, which will not be optimized, is
the ratio in the fitness function (see Section 3.2) due
to its direct influence on the quality of the road
traffic network division.
4.2 OGA Individual Representation
The representation of an individual of the OGA must
incorporate all parameters described in previous
section. All the parameters can be expressed as
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