Issues of Optimization of a Genetic Algorithm for Traffic Network

Division using a Genetic Algorithm

Tomas Potuzak

Department of Computer Science and Engineering, University of West Bohemia, Univerzitni 8, Plzen, Czech Republic

Keywords: Genetic Algorithm, Traffic Network Division, Parameters Optimization.

Abstract: In this paper, we describe an approach to optimization of the genetic algorithm for division of road traffic

network, which we developed. The division of road traffic network is necessary to enable to perform the

road traffic simulation in a distributed computing environment. The optimization approach is based on a

genetic algorithm, which is employed to find best settings of the optimized genetic algorithm for road traffic

network division. Because such an optimizing genetic algorithm is expected to be extremely computation-

and time-consuming, its distributed implementation is discussed as well.

1 INTRODUCTION

Utilization of a distributed computing environment,

where combined power of multiple interconnected

computers (nodes) is utilized, is a common way how

to speed up a detailed simulation of road traffic.

Prior to the distributed simulation itself, the

simulated road traffic network must be divided into

sub-networks, which are then simulated on particular

nodes of a distributed computer. To achieve a good

speedup of the simulation, two issues should be

considered during the division – the load-balancing

of the resulting sub-networks and the minimization

of the inter-process communication.

In our previous work, we have developed a

method for division of road traffic network based on

a genetic algorithm, which considers both the

mentioned issues (Potuzak, 2011b). The method

gives good results (Potuzak, 2012). However, the

parameters of the genetic algorithm have been set

manually based on preliminary testing. Hence, it is

likely that the settings of the parameters are not

optimal and can be tuned to achieve better

performance of the division method.

In this paper, we discuss the usability of a

genetic algorithm for optimization of the parameters

of the genetic algorithm for road traffic network

division, which we developed. Because the

optimizing genetic algorithm is expected to be

extremely computation- and time-consuming, we

discuss its distributed implementation as well.

2 GENETIC ALGORITHMS

Genetic algorithms are evolutionary algorithms,

which mimic natural genetic evolution and selection

in nature in order to solve a problem. Developed by

John Holland in 1975 (Holland, 1975), they are

widely used for solving of optimization and

searching problems in many domains, including

multi-objective optimization (Farshbaf and Feizi-

Darakhshi, 2009).

2.1 Basic Notions of Genetic Algorithm

There are several basic phases and notions, which

are commonly present using a typical genetic

algorithm.

A single solution of the solved problem is

considered to be an individual (usually represented

by a vector of binary or integer values). At the start,

a set of individuals (so-called initial population) is

most often randomly generated (Menouar, 2010).

Then, the fitness function is calculated for each

individual. The fitness function represents an

objective assessment of each individual depending

on the solved problem. Then, a number of indivi-

duals with highest fitness value are selected as the

parents of a new generation. The new generation is

created using the selected individuals and the

crossover and mutation operators (Menouar, 2010).

The entire process repeats until a preset number

of generations is created or a stop condition is met.

340

Potuzak T..

Issues of Optimization of a Genetic Algorithm for Trafﬁc Network Division using a Genetic Algorithm.

DOI: 10.5220/0004141803400343

In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2012), pages 340-343

ISBN: 978-989-8565-29-7

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

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

IssuesofOptimizationofaGeneticAlgorithmforTrafficNetworkDivisionusingaGeneticAlgorithm

341

integer numbers but of different maximal size.

Hence, the bits of particular integer values will be

used in the individual directly. More specifically,

each individual will consist of 52 bits. First 20 bits

will be used for number of generations (i.e. 0 to

1 048 576 generations), 10 bits for number of

individuals in one generation (i.e. 0 to 1024 indivi-

duals), 10 bits for number of selected individuals

from each generation (i.e. 0 to 1024 individuals), 8

bits for maximal number of mutations per individual

(i.e. 0 to 256 mutations), 2 bits for type of selection

(i.e. up to 4 types of selection), and 2 bits for type of

crossover (i.e. up to 4 types of crossover). An

example is depicted in Fig. 1.

Figure 1: Example of an OGA individual.

The initial population will consist of 90

individuals (similar to the optimized genetic

algorithm for road traffic network division), which

will be randomly generated. Although a larger

number of individuals could be more appropriate,

we have to have in mind that the OGA will be

extremely time-consuming and the computation time

would increase with increasing number of

individuals in one generation.

4.3 OGA Fitness Function

The OGA fitness function will be calculated for all

individuals. For each OGA individual, the

parameters of the genetic algorithm for road traffic

network division will be set accordingly. Then, 3

road traffic networks (regular grids of 64, 256, and

1024 crossroads) will be divided into 2, 4, 8, and 16

sub-networks. So, 12 complete optimized genetic

algorithms will be used for each OGA individual to

keep the optimization as universal as possible.

The OGA fitness function will be then calculated

using the maximal achieved fitness values for each

combination of the divided network and the number

of sub-networks as:

max







OGA

(1)

where F

OGA

is the OGA fitness function,

max

F is the

maximal achieved fitness function of the optimized

genetic algorithm for ith traffic network and jth

number of sub-networks.

4.4 OGA Selection

Once the fitness value will be calculated for every

individual of the current generation, 10 individuals

with highest fitness value of the 90 individuals of the

current generation (see Fig. 2) will be selected to be

parents of next generation. This selection is the same

as the one used in the optimized genetic algorithm

for road traffic network division (Potuzak, 2012).

Figure 2: Simple truncation selection used in OGA.

4.5 OGA Crossover and Mutation

Once the parents are selected, a new generation is

produced using the crossover and mutation in the

same way as in the optimized genetic algorithm for

road traffic network division (see Fig. 3).

Figure 3: Crossover of two individuals and four mutations.

Using the crossover and mutation, a new

generation is produced. The entire process then

repeats until the preset number of generations is

reached. Since the OGA is very computation- and

time-consuming (see Section 5), the number of

created generations will be limited by the

computational power and time at our disposal.

4.6 Distributed OGA

To achieve a feasible computation time, the OGA

will be performed on a distributed computer

consisting of 24 desktop PCs. Each PC incorporates

one Intel i5-2400S Quad-Core processor at 3.1 GHz,

8 GB of RAM, and 250 GB HDD.

The calculation of the fitness value is by far the

most time-consuming part of the OGA (see

Section 4.3). Hence, the individuals of an OGA

generation will be uniformly distributed among all

available processor cores where the fitness values

will be calculated by working processes. The

selection, crossover, and mutation will be then

performed by a control process.

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5 TESTS AND RESULTS

In order to predict the feasibility of the distributed

OGA and its time requirements, we have performed

a set of tests. These tests were performed directly on

one of the computers, on which the distributed OGA

is planned to be performed (see Section 4.6). On the

computer, the DUTS Editor, which is a system

containing implementation of the optimized genetic

algorithm for road traffic network division, was

installed together with the described road traffic

networks (see Section 4.3). Then, the networks were

divided into four (one of the four numbers of sub-

networks used by the OGA – see Section 4.3) sub-

networks using from 1000 to 1 000 000 generations

of the optimized genetic algorithm.

In order to test the usability of multiple cores

simultaneously, the division was performed on one

and four cores. The results are depicted in Table 1.

Table 1: Results of the testing.

Gen. Cores

Computation time [ms]

64 crossroads 256 crossroads 1024 crossroads

1 830 3296 15310

4 859 3631 15834

1 7982 32859 139753

4 8699 35825 149127

1 79661 320038 1396286

4 86248 348558 1492700

1 805411 3063346 12309876

4 853462 3499342 14851707

As can be seen in Table 1, the simultaneous

usage of more cores increases the computation time,

but only by roughly 7 %. Hence, it is possible to

utilize all four cores simultaneously.

The time necessary for calculation of the fitness

value of an OGA individual is the sum of the times

necessary for division of particular networks into 2,

4, 8, and 16 sub-networks (i.e. four times sum of one

row of Table 1). Considering simultaneous usage of

all cores, the total time necessary for computation of

the fitness value of one OGA individual using one

core is summarized in Table 2 in the dependency on

the number of generations of the optimized genetic

algorithm for road traffic network division.

Table 2: Computation of an OGA individual fitness value.

Number of generations Computation time [ms]

1000 81296

10000 774608

100000 7710024

1000000 76818044

6 CONCLUSIONS

In this paper, we described the OGA and its possible

distributed implementation for multi-core personal

computers. Considering usage of 24 quad-core

computers (i.e. 96 cores), the predicted computation

time of the OGA ranges from 21 to 2 · 10

hours

depending on the number of generations of the OGA

and the optimized genetic algorithm. Hence, only

lower numbers of generations are feasible.

In our future work, we will focus on implemen-

tation of the distributed OGA and its testing.

ACKNOWLEDGEMENTS

Author wishes to thank to Jakub Smid for the

inspiration for the main idea of this paper.

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