AN EFFICIENT INFORMATION EXCHANGE STRATEGY IN A

DISTRIBUTED COMPUTING SYSTEM

Application to the CARP

Kamel Belkhelladi

1,2

, Pierre Chauvet

1,2

and Arnaud Schaal

LISA, Universit´e d’Angers, 62, avenue Notre Dame du Lac, 49000 Angers, France

CREAM, Universit´e Catholique de l’Ouest, 44-46, rue Rabelais, 49008 Angers, France

Keywords:

Capacitated Arc Routing Problem, Information exchange strategy, Distributed computing, Agents.

Abstract:

Distributed computation models have been widely used to enhance the performance of traditional evolutionary

algorithms, and have been implemented on parallel computers to speed up the computation. In this paper,

we introduce a multi-agent model conceived as a conceptual and practical framework for distributed genetic

algorithms used both to reduce execution time and get closer to optimal solutions. Instead of using expensive

parallel computing facilities, our distributed model is implemented on easily available networked personal

computers (PCs). In order to show that the parallel co-evolution of different sub-populations may lead to an

efﬁcient search strategy, we design a new information exchange strategy based on different dynamic migration

window methods and a selective migration model. To evaluate the proposed approach, different kinds of

experiments have been conducted on an extended set of Capacitated Arc Routing Problem(CARP). Obtained

results are useful for optimization practitioners and show the efﬁciency of our approach.

1 INTRODUCTION

Genetic Algorithms, a special class of Evolutionary

Algorithms (EAs), are proven to be successful in a

wild range of applications, especially in cases of op-

timization. In order to solve more difﬁcult problems,

two inherent features of EAs, premature convergence

and computation time must be improved. To over-

come the two problems, the idea of parallelizing EAs

has been proposed by different researchers, and it

has been proven to be a promising method (Cant`u-

Paz, 2000). Conceptually, the parallelism is to di-

vide a big population in a sequential EA into multiple

smaller sub-populations that are distributed to sepa-

rate processors and can then be evaluated simultane-

ously. According to the sub-population size, the par-

allel EAs are categorized into two types: coarse-grain

and ﬁne-grain, and they are usually implemented on

distributed memory and massively parallel comput-

ers, respectively. All though parallel computers can

speed up EAs, they are not easily available and it is

very expensive to upgrade their processing power and

memory. A promising alternative without expensive

hardware facilities is to construct the parallel evolu-

tionary computation (EC) framework on a set of net-

worked personal computers.

To make the parallel EAs more realistic, we pro-

pose in this paper a mobile agent-based methodol-

ogy to support parallelism on networked computers

in a ﬂexible and adaptive way. In addition, we de-

sign a new information exchange strategy. The idea

is that an EA periodically selects some promising in-

dividuals from each sub-population and sends them

to other sub-populations, according to certain criteria.

To evaluate the proposed approach, different kinds of

experiments have been conducted on an extended set

of Capacitated Arc Routing Problem (CARP) and the

obtained results show the promise and efﬁciency of

our approach.

2 THE CARP

The Capacitated Arc Routing Problem (CARP) is a

vehicle routing problem raised by applications like ur-

ban waste collection, snow plowing, sweeping, grit-

ting, etc. It is deﬁned on an undirected network

G=(V,E), with a set V of n nodes and a set E of m

edges. A ﬂeet of identical vehicles with capacity W is

based at a depot node s. Each edge e can be traversed

342

Belkhelladi K., Chauvet P. and Schaal A. (2008).

AN EFFICIENT INFORMATION EXCHANGE STRATEGY IN A DISTRIBUTED COMPUTING SYSTEM - Application to the CARP.

In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - ICSO, pages 342-346

DOI: 10.5220/0001497103420346

 SciTePress

any number of times, each time with a cost c

, and

has a non-negativedemand q

. All costs and demands

are integers. The τ edges with non-zero demands are

called required edges or tasks and require service by a

vehicle. The goal is to determine a set of vehicle trips

of minimum total cost, such that each trip starts and

ends at the depot, each required edge is serviced by

one single trip, and the total demand handled by any

vehicle does not exceed W.

Since the CARP is NP-hard, large scale instances

must be solved in practice using heuristics. Among

fast constructive methods, one can cite Path-Scanning

(Golden et al., 1983) and Ulusoy’s splitting technique

(Ulusoy, 1985). Available meta-heuristics are very

recent and include tabu search methods (Belenguer

and Benavent, 2003; Hertz et al., 2000), guided local

search (Beullens et al., 2003) and genetic algorithm

(Lacomme et al., 2001). All these heuristics algo-

rithms can be evaluated through lower bounds (Am-

berg and Voß, 2002).

3 AGENT-BASED APPROACH

The DGA-MAS

developed in this work uses several

components of the genetic algorithm algorithm pro-

posed by (Lacomme et al., 2001) for the CARP. The

common parts are described below:

Solution Encoding: The network is coded as a sym-

metric digraph, in which each edge is replaced by two

opposite arcs. A chromosome is an ordered list of the

τ tasks, in which each task may appear as one of two

directions. The implicit shortest paths are assumed

between successive tasks. The chromosome does not

include trip delimiters and can be viewed as a giant

trip for an incapacitated vehicle. A procedure Split

optimally partitions (subject to the sequence) the gi-

ant trip into feasible trips. The ﬁtness function of the

genetic algorithm (GA) is the total cost of the result-

ing CARP solution.

Initialization: The global population P of chro-

mosomes is initialized with the solutions of the

two CARP heuristics cited in introduction (PS and

UH)(Golden et al., 1983; Ulusoy, 1985), completed

by random permutations. The distributed genetic

algorithm (DGA) forbids clones (identical chromo-

somes).

Selection and Crossover: At each iteration, two par-

ents are selected by a biased roulette wheel (Gold-

berg, 1989). Three crossovers were deﬁned for

the giant trip representation, LOX (Linear Order

Crossover), a modiﬁed version of the classical order

Distributed Genetic Algorithm using Multi-agent Sys-

tem

crossover OX and X1 (crossing in a point).

Mutation: Several mutation operators have been pro-

posed for the CARP, such as inversion, insertion, dis-

placement (MOVE), and reciprocal exchange muta-

tion (SWAP). Reciprocal exchange mutation selects

two positions at random and swaps the tasks on these

positions.

Several researchers are trying to compare the per-

formance of using coarse-grain and ﬁne-grain mod-

els to parallelize genetic algorithms. Some prefer

ﬁne-grain models but others favor coarse-grain ones

(Cant`u-Paz, 2000). As our goal is to develop a

distributed genetic framework without using a pow-

erful connection machine, we choose to implement

a coarse-grain model on a set of networked PCs.

By using the concept of coarse-grained paralleliza-

tion, the population is divided into a few large sub-

populations. These sub-populations evolve indepen-

dently and concurrently on different processors. After

a predeﬁned period of time, some selected individuals

are exchanged via a migration process.

Our distributed genetic algorithms with multiple

sub-populations uses the master-slave (Luque et al.,

2005) multi-agent model for the CARP. The inter-

connection topology is logically a star, with the mas-

ter in the center. Our new migration process is

based on different dynamic migration window meth-

ods (Kim, 2002) and the selective migration model

(Eldos, 2006).

In the master-slave multi-agent model, the master

agent maintains the lists of partial results that are sent

from slaves. At ﬁrst, the master agent generates the

population and divides them into sub-populations. It

sends them to slave agents. The slaves execute a con-

ventional genetic algorithm on their sub-population:

ﬁtness evaluation, selection, crossover, mutation and

periodically return their best partial results to the mas-

ter agent. Pseudo-code of the conventional genetic

algorithm is shown in section 3.1. The subroutine Mi-

gration is an extension to a general coarse-grained

model. The master stores the partial results in lists.

Then, the master agent searches the lists and selects

two slaves that have bad partial results and sends the

migration window size to selected slaves. The se-

lected slaves exchange individuals according to the

migration window methods. However, in the pro-

posed model, individuals are screened and examined

at both the source and the destination to qualify for

migration. The source gives or denies a visa based on

local qualiﬁcation criteria and the destination grants

or denies a residency based on local qualiﬁcation cri-

teria. The simplest form of qualiﬁcation criteria is

through the individual’s relative ﬁtness. Every in-

dividual in a very sub-population is ranked locally;

AN EFFICIENT INFORMATION EXCHANGE STRATEGY IN A DISTRIBUTED COMPUTING SYSTEM -

Application to the CARP

343

an individual qualiﬁes for a visa at the source sub-

population if its rank is within a range, typically the

middle class. On the destination sub-population, an

immigrant is accepted as a new member of the popu-

lation if its rank is better than a threshold set by that

receiving sub-population.

3.1 The Algorithm

The Pseudo-code of the algorithm in each slave Agent

is described as below:

initialize the population, P

while generation < max_generation begin

evaluate P

select P1’ from P using roulette

wheel selection

select parents randomly from P1’

apply genetic operators to create

the rest of the new population, P2’

merge P1’ and P2’ to P’

replace P with P’

if an interval of K generations is reached

Migration

end

generation = generation + 1

end

subroutine Migration

begin

Pick a random number (1 - pop_size)

to nominate

an immigrant X

If the rank of X is within limits then

Send X to the Master

Mark X as "dead" to be killed

end

If an immigrant Y is received then

If the rank of Y exceeds threshold

Add to the population

Update Fitness and Ranking

Pick a random number (1 - pop_size)

to nominate a victim V

Discard the victim V

end

4 EXPERIMENTS AND RESULTS

Following our computational experiments and the

agent’s methodology, we conducted two series of ex-

periments to compare the corresponding performance

for genetic computation with and without individ-

ual’s exchange. The ﬁrst series examines whether the

parallel implementation can improve search quality.

The second series of experiments evaluates the per-

formance of using Multi-agent and the individuals ex-

change strategies in order to exploit the computational

power of multiple machines.

Both the pure Parallel Genetic Algorithm (PGA)

and the Distributed Genetic Algorithm (DGA-MAS),

including the multi-agent strategies, are implemented

on a network of PCs, connected with a 100Mbit/sec

Ethernet. In the experiments, we arranged eight net-

worked computers running Suse Linux operating sys-

tem as a distributed computing environment to sup-

port our Multi-agent system.

One computer played the role of ”master” and

ran the multi-agent platform. Once the platform was

activated, the master agent instantiated other agents

(slave agents) and sent each one towards a machine

in the network. Each machine in this framework

had a slave agent to take care of the computation for

each sub-population. Also, the master agent allowed

activation of the communication phase described in

Section 3 for exchanging individuals among sub-

populations.

In the experiments, we use three crossover types

(LOX, OX, X1) and two mutation types (MOVE,

SWAP). Sevenvalues for crossover rate are used rang-

ing from 0.2 to 0.7 in increments of 0.1. Also, seven

mutation rates are allowed varying from 0.1 to 0.4

in increments of 0.05. Our results are obtained with

small sub-populations of 30 solutions. Clones (iden-

tical solutions) are forbidden in each sub-population,

to have a better dispersion of solutions and to dimin-

ish the risk of premature convergence. The number

of generations is ﬁxed to 5000 for all slave agents.

The migration interval is 500 generations. Whenever

migration occurs, the dynamic migration window size

varies at random from 1 to θ. The θ value is generated

at random within 20% of the sub-population size. The

threshold value is ﬁxed to the mean ﬁtness of the sub-

population.

These tests are done on a standard set of undi-

rected instances in which all edges are required. Table

1 contain 23 instances from (DeArmon, 1981) with 7

to 27 nodes and 11 to 55 edges. All these ﬁles can be

obtained at http://www.uv.es/∼belengue/carp.html.

In the Table 1, Pb gives the instance number and

N,M the numbers of nodes and edges. LBB is a lower

bound from (Belenguer and Benavent, 2003). TS is

the result of Carpet (Hertz et al., 2000) with the pa-

rameter setting yielding the best results on average

(the same setting for all instances). Best gives the

best solution published, generally obtained by Car-

pet with various parameter settings. GA is the so-

lution of GA from (Lacomme et al., 2001). Our re-

sults are shown in the pure parallel genetic algorithm

(PGA) and the distributed genetic algorithm includ-

ing the Multi-agent strategy (DGA) columns.

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

344

Table 1: Results of the DGA-MAS on DeArmon’s instances

vs best known results.

Pb N M LBB Best TS GA PGA DGA

1 12 22 316 316 316 316 316 316

2 12 26 339 339 339 339 339 339

3 12 22 275 275 275 275 275 275

4 11 19 287 287 287 287 287 287

5 13 26 377 377 377 377 377 377

6 12 22 298 298 298 298 298 298

7 12 22 325 325 325 325 325 325

8 27 46 344 348 352 350 355 344

9 27 51 303 311 317 303 323 305

10 12 25 275 275 275 275 275 275

11 22 45 395 395 395 395 403 395

12 13 23 448 458 458 458 462 452

13 10 28 536 544 544 540 544 540

14 7 21 100 100 100 100 100 100

15 7 21 58 58 58 58 58 58

16 8 28 127 127 127 127 129 127

17 8 28 91 91 91 91 91 91

18 9 36 164 164 164 164 164 164

19 11 11 55 55 55 55 58 55

20 11 22 121 121 121 121 123 121

21 11 33 156 156 156 156 158 157

22 11 44 200 200 200 200 203 200

23 11 55 233 233 233 235 237 233

5 DISCUSSION

We can observe that DGA-MAS obtained solutions as

good as our PGA. Furthermore, within 48% of the

solved problems, DGA-MAS outperformed our PGA

implementation of evolutionary system by a mean ad-

vantage of 0.98% in term of solution cost. DGA-MAS

is very efﬁcient: on all instances, it is at least as good

as Carpet. On the 23 DeArmon’s instances, it out-

performs Carpet 4 times, improves 4 best known so-

lutions with one to optimality, and reaches LBB 20

times. The average deviation to LBB is roughly di-

vided by 3 compared to Carpet and becomes 0.19%.

Moreover, the mean speed up factor for the execution

times between DGA-MAS and PGA is approximately

1.7, in spite of overhead communication time spent in

DGA-MAS. Hence, the mean execution time spent to

ﬁnd a solution using PGA and DGA-MAS are respec-

tively 40.3 and 24.5 seconds.

6 CONCLUSIONS

In this paper, we have proposed DGA-MAS, an efﬁ-

cient distributed genetic algorithm which combines

the two advantages of parallelism: the computational

power and co-evolution. We implemented an infor-

mation exchange strategy based on the dynamic mi-

gration window methods that control the size and the

frequency of migration and the selective migration

model for the choice of individuals to migrate. Re-

sults conﬁrm the positive impact of using MAS

strat-

egy in regard to the pure parallel GA. They also point

out that such strategies are, at a minimum, as good as

the best known methods.

In future work, we will improve the performance

of our information exchange system by the addition

of intelligent modules, thus allowing the study of the

exchange semantics of the requests for improving in-

formation. We will test also our framework on other

NP-complete problems such as planning and schedul-

ing problems.

REFERENCES

Amberg, A. and Voß, S. (2002). A hierarchical relax-

ations lower bound for the capacitated arc routing

problem. In HICSS ’02: Proceedings of the 35th An-

nual Hawaii International Conference on System Sci-

ences (HICSS’02)-Volume 3, pages 83–84, Washing-

ton, DC, USA. IEEE Computer Society.

Belenguer, J. and Benavent, E. (2003). A cutting plane al-

gorithm for the capacitated arc routing problem. Com-

put. Oper. Res., 30(5):705–728.

Beullens, P., Muyldermans, L., Cattrysse, D., and Oudheus-

den, D. (2003). A guided local search heuristic for the

capacitated arc routing problem. European Journal of

Operational Research, 127(3):629–643.

Cant`u-Paz, E. (2000). Efﬁcient and Accurate Parallel Ge-

netic Algorithms. Kluwer Academic Publishers, Nor-

well, MA, USA.

DeArmon, J. (1981). A Comparison of Heuristics for

the Capacitated Chinese Postman Problem. Master’s

Thesis. The University of Maryland at College Park,

MD, USA.

Eldos, T. (2006). A new migration model for distributed

genetic algorithms. In The International Conference

On Scientiﬁc Computing (CSC), pages 128–134.

Goldberg, D. (1989). Genetic Algorithms in Search, Op-

timization and Machine Learning. Addison-Wesley

Longman Publishing Co., Inc., Boston, MA, USA.

Golden, B., DeArmon, J., and Baker, E. (1983). Computa-

tional experiments with algorithms for a class of rout-

ing problems. Computers and Operations Research,

10(1):47–59.

Hertz, A., Laporte, G., and Mittaz, M. (2000). A tabu

search heuristic for the capacitated arc routing prob-

lem. Oper. Res., 48(1):129–135.

Multi-Agent System

AN EFFICIENT INFORMATION EXCHANGE STRATEGY IN A DISTRIBUTED COMPUTING SYSTEM -

Application to the CARP

345

Kim, J. (2002). Distributed genetic algorithm with mul-

tiple populations using multi-agent. In ISHPC’02:

Proceedings of the 4th International Symposium on

High Performance Computing, pages 329–334, Lon-

don, UK. Springer-Verlag.

Lacomme, P., Prins, C., and Ramdane-Ch´erif, W. (2001).

A genetic algorithm for the capacitated arc rout-

ing problem and its extensions. In Proceedings of

the EvoWorkshops on Applications of Evolutionary

Computing, pages 473–483, London, UK. Springer-

Verlag.

Luque, G., Alba, E., and Dorronsoro, B. (2005). Paral-

lel Genetic Algorithms , E. Alba (ed.), Parallel Meta-

heuristics: A New Class of Algorithms. John Wiley.

Ulusoy, G. (1985). The ﬂeet size and mix problem for

capacitated arc routing. European Journal of Oper-

ational Research, 22(3):329–337.

ICINCO 2008 - International Conference on Informatics in Control, Automation and Robotics

346