MANAGING COMBINATORIAL OPTIMIZATION PROBLEMS

BY MEANS OF EVOLUTIONARY COMPUTATION

AND MULTI-AGENT SYSTEM

Mauricio Paletta

Centro Inv. Inf. y Tec. Comp. (CITEC), Universidad de Guayana (UNEG), Av. Atlántico, Ciudad Guayana 8050, Venezuela

Pilar Herrero

Facultad de Informática, Universidad Politécnica de Madrid (UPM), Campus de Montegancedo S/N; 28660, Madrid, Spain

Keywords: Evolutionary Program, Multi-agent System, Inter-agent Communication Protocol, JADE.

Abstract: The necessity for solving a combinatorial optimization problem is very common. Evolutionary/genetic

program could be used to deal with such situations. Unfortunately, depending on the complexity of the

problem, high computational capabilities are required, primarily in those cases in which measuring the

quality of a potential solution is very demanding. However, advances in Distributed Artificial Intelligence

(DAI), Multi-Agent Systems (MAS) to be more specific, could help users to deal with this situation by

parallelizing the evolutionary program aiming to distribute the computational capabilities required. This

paper presents an inter-agent MAS protocol for parallelizing an evolutionary program aiming to reduce the

communications requirements necessary as well as allowing a response within a reasonable period of time.

1 INTRODUCTION

Evolutionary/Genetic Programs (EPs) (Eiben et al,

2003), (Jain et al, 2007) are powerful searching

techniques used to solve Combinatorial

Optimization Problems (COPs) in many disciplines.

Depending of the complexity of the problem, EPs

could require high computational capabilities such

as CPU time, memory, etc. This problem increases

considerably if the calculation of the fitness function

for evaluating any potential solution also requires

high computational capabilities.

Parallelizing EPs has been proposed to overcome

the above problem (Andre et al, 1996), (Arenas et al,

2002), (Lee, 2007). The basic idea is to divide a big

population into multiple smaller sub-populations that

are distributed to separate processors and can then

evaluated simultaneously. Combination of EP and

MAS technologies (Ferber, 1995) is essential for

accomplishing this objective.

In order to reduce the communication necessities

required for parallelizing EPs, this paper focuses on

defining a multi-agent architecture, establishing an

interaction protocol for obtaining a suitable solution,

based on EP specifications for any specific COP.

The rest of the paper is organized as follows:

section 2 presents some work related to the scope of

this paper; section 3 describes the proposed inter-

agents protocol; section 4 shows the evaluation of

this proposal. Finally, section 5 reaches some

conclusions and future work.

2 RELATED WORK

Some examples of making evolutionary algorithms

in distributed environments can be consulted on

(Arenas et al, 2002), (Meng et al, 2007). DREAM

(Arenas et al, 2002) and G2DGA (Berntsson, 2005)

are examples of frameworks concerning

development of Peer-to-Peer distributed computing

systems. Using JADE (Bellifemine et al, 1999),

(Chmiel, 2005) as a middleware to propose a multi-

agent synchronous evolutionary system can be

reviewed on (Eiben et al, 2007), (Lee, 2007) and

(Meng et al, 2007). The newscast protocol (Jelasity

et al, 2002), which is a lazy fully distributed

information propagation protocol, is an example of a

work with the same goal but different scope.

253

Paletta M. and Herrero P. (2010).

MANAGING COMBINATORIAL OPTIMIZATION PROBLEMS BY MEANS OF EVOLUTIONARY COMPUTATION AND MULTI-AGENT SYSTEM.

In Proceedings of the 2nd International Conference on Agents and Artiﬁcial Intelligence - Agents, pages 253-256

 SciTePress

3 OVERALL INTER-AGENT

PROTOCOL

The proposed inter-agents communication protocol

occurs in a general that basically consists of two

different types of agents:

1) EPEnvAgent which: 1) informs the rest of

the agent about the EP parameters and problem

specifications; 2) takes control of the population

growth; and, 3) allows the evolution among multiple

system nodes.

2) EPAgent which represents a potential

solution to the problem as well as carry out the main

steps of evolutionary computation: selection and

variation (crossover and mutation) - to generate

descendants (new potential solutions / agents).

Other elements involved in the architecture are

the EP parameters (population size, probability of

applying genetic operators, among others), and the

problem specifications which is necessary to define

a specific COP.

Each computational node may have multiple

EPAgent (a population) but only one EPEnvAgent is

needed. The number of EPAgent in the system

(population size) may vary, as the EP evolves. An

EPAgent can be created as well as eliminated from

the system. The creation of new EPAgent is the

result of applying genetic operators, while the

disposal is due to self-destruction or suicide. Some

parameters are used to control these functions.

On the other hand, and following the FIPA ACL

specifications (FIPA, 2002), agents communicate

with each other according to the messages shown in

Figure 1. Messages are the following:

 INFORM, from EPAgent to EPEnvAgent. For

EPEnvAgent to keep some statistics of the

evolutionary process and keep track of the best

solution it has at any given time, any EPAgent uses

this message to report or inform its measure of

quality (fitness), as well as the structure that

represents the solution to the COP (chromosome).

 PROPAGATE, from EPEnvAgent to

EPEnvAgent. When an EPEnvAgent realizes that

has obtained a better individual (solution) in the

population of EPAgents, it uses this message to

transmit /propagate this information to the rest of

EPEnvAgent.

 REQUEST, from EPAgent to EPEnvAgent. In

this proposal, EP parameters may change

dynamically. An EPAgent should, from time to time,

requests by using this message the EPEnvAgent to

send back the parameters.

 INFORM, from EPEnvAgent to EPAgent. In

response to the previous message, the EPAgent is

receiving the EP parameters from the EPEnvAgent.

It is important to mention that these parameters can

change the way in which EPAgents may vary to

produce descendants (new EPAgents) or self-

destruction.

 INFORM_REF, from EPEnvAgent to

EPEnvAgent. By using this message, the main

EPEnvAgent informs all the auxiliary EPEnvAgent

changes in the EP parameters.

 PROPOSE, from EPAgent to EPEnvAgent. In

this proposal each EPAgent is responsible for

searching (selecting) a suitable partner to cross.

Through this message, the EPAgent makes a request

to find a suitable partner by sending its fitness and Id

as parameters of the message. These parameters are

needed when some other EPAgent accepts the

request and responds appropriately to the sender.

 PROPOSE, from EPEnvAgent to EPAgent. By

this message, the EPEnvAgent replicates the

proposal sent by an EPAgent for the rest of

EPAgents. They become aware of it, so that, they

can respond directly to EPAgent who made the

original request.

 ACCEPT_PROPOSAL, from EPAgent to

EPAgent. An EPAgent uses this message to respond

positively to a request from another EPAgent for

crossing with it. This happens only if it decides to

accept the proposal (based on the fitness received

from the sender agent and by using some

probabilities). The EPAgent sends its chromosome

so that the sender can use it for applying the

corresponding genetic operation.

 REQUEST_WHENEVER, from EPAgent to

EPEnvAgent. EPAgents are responsible for the

selection mechanism and for applying genetic

operators to generate new EPAgents. These new

agents must be created by the EPEnvAgent. Through

this message, the EPEnvAgent knows that a new

EPAgent must be created with the chromosome

given as a parameter of the message.

 CONFIRM, from EPEnvAgent to EPAgent.

EPEnvAgent has the control to start and stop the

evolution. When the process has to be finished, the

EPEnvAgent uses this message to give to all

EPAgents the order to self-destruct.

 CONFIRM, from EPAgent to EPEnvAgent.

Once an EP-Agent is self-destructed, either because

it received an order from the EPEnvAgent or for

effect of this evolutionary algorithm (by using some

parameters and based on the current fitness), its uses

this message to confirm his suicide.

 CONFIRM, from EPEnvAgent to

EPEnvAgent. If the receiver is the main

EPEnvAgent, then some auxiliary EPEnvAgent has

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254

decided to stop its participation in the evolution

process. On the other hand, if the receiver is an

auxiliary EPEnvAgent, then the entire evolution

process must be stopped.

EPEnvAgent EPAgent

INFORM

PROPOSE

(Fitness, Chromosome)

(Fitness, Chromosome, Agent Id)

(Fitness, Agent Id)

REQUEST

INFORM

(EP Parameters)

REQUEST_WHENEVER

(Chromosome)

ACCEPT_PROPOSAL

(Chromosome)

CONFIRM

An agent is informing

its fitness

An agent is requiring

the EP parameters

An agent is requiring another

agent for crossing with him

An agent is reporting a new

agent should be created

An agent is

confirming its suicide

The agent is

receiving the EP

Parameters

An agent is requiring for

crossing with the current agent

The EPEnv is giving

order to commit suicide

An agent accepted the

proposal sent for the

current agent

PROPAGATE

(Fitness, Chromosome)

INFORM_REF

(EP Parameters)

CONFIRM

(Agent Id)

Figure 1: Inter-agents communication protocol.

A method for estimating the total number of

messages TM requires to complete an evolution,

which has duration of T time units, is shown in (1).

101211110

6298

376

35143

12211

;

; ;

;

MsgnMsgTNApMsgMsg

MsgpMsgMsg

TNApMsgMsg

MsgnMsgtTnMsgMsg

MsgnMsgTNAppMsg

NaNAMsgTM

















(1)

Where:

: probability that an agent commits self-suicide.

: probability that an agent accepts to cross with another ag.

: probability to produce at least one descendant.

: time in which parameters are sought.

NA: the total number of agents.

: the total number of agents for node i.

n: the total number of nodes.

Msg

: the total number of messages of type i.

Next section provides some results from

experiments conducted with the proposal.

4 EVALUATION

In order to implement the inter-agents

communication protocol proposed in this paper as

well as the MAS-based evolutionary algorithm, a

JADE-based framework called EP-MAS.Lib (Paletta

et al, 2009) was developed. For evaluating the

proposal we have implemented a solution for two

different problems, varying the computational

capabilities demanded to calculate the fitness of an

individual or potential solution for the problem.

The first issue to be considered is related to the

Traveling Salesman Problem (TSP) which is a well-

known NP-hard COP (Lawler et al, 1985). In this

case, computational capabilities demanded are very

low. The experimentation was conducted using the

data relative to the 51-cities Christofides and Eilon

(Christofides et al, 1972).

The second problem has to do with finding the

proper setting of parameters required to configure an

Artificial Neural Network (ANN) for a particular

investigation that is currently being developed

(Paletta et al, 2008). Fitness in this problem consists

in training an ANN and obtains the corresponding

total average error aiming to reduce it. Unlike the

previous case, the calculation of this fitness is very

demanding on computational capabilities.

Both problems were implemented using a

conventional simple genetic program, as well as

using the distributed model presented in this paper,

aiming to compare the efficiency of each case to

deal with the same problem.

Based on the results obtained we observed:

1) A solution for TSP problem was obtained

more efficiently using the simple genetic program

than the MAS-based distributed proposal. The

difference is about 10 to 1 in execution time.

2) Related to the ANN configuration, the

simple genetic program needed 42.3 hours for

obtaining a satisfactory solution. However, by using

the MAS-based distributed proposal (with 3 nodes),

a solution was obtained in 6 hours approximately.

The results show that the proposed protocol

allows distributed computational capabilities among

more than one node in such a way to expedite the

process of convergence of the searching algorithm.

Table 1 shows the results obtained by using the

expression (1) for estimating the total number of

messages TM required for these experiments. As

expected the complexity of the problem is directly

proportional to the communication needs required

by the EP. Parameters are: p

=0.55; p

=0.8; p

=0.5;

=5 min; NA=300; Na

=100, i (1  i  3); n=3.

MANAGING COMBINATORIAL OPTIMIZATION PROBLEMS BY MEANS OF EVOLUTIONARY COMPUTATION

AND MULTI-AGENT SYSTEM

255

Table 1: Detail of the estimated total number of messages.

Messages

TSP

(T = 45 min)

ANN

(T = 360 min)

Msg

5,940

47,520

Msg

17,820

142,560

Msg

= Msg

216

Msg

648

Msg

= Msg

6,750

54,000

Msg

= Msg

5,400

43,200

Msg

= Msg

7,425

59,400

Msg

22,275

178,200

85,320

682,560

5 CONCLUSIONS AND FUTURE

WORK

In this paper we present a communication protocol

between agents to be used in a MAS scenario aiming

to resolve a specific COP. As we know, this

proposal differs from other similar works in the

following aspects:

 It focuses on the communication process

between the agents in the systems and therefore to

the cooperation needed for solving the evolutionary

algorithm, instead of the properly used elements of

the evolutionary algorithm (selection mechanism

and genetic operations).

 The evolutionary algorithm (selection and

variation) is not controlled by a central entity;

instead it’s controlled by all individuals (agents) of

the population actively involved in this process.

 The needed information (EP parameters and

problem specifications) is not located in a central

repository, but it is replicated for all who need it.

 The definition of a particular COP.

The obtained result point out that agent in a

MAS-based environment can interact with each

other to solve any COP by using the communication

protocol proposed.

We are working on reducing the flow of

messages and data that is required to avoid possible

bottleneck.

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