Ant based probabilistic routing with pheromone and antipheromone mechanisms

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Ant based probabilistic routing with pheromone and antipheromone mechanisms

(Manuscript to be submitted to the IEEE Transactions on Evolutionary Computation

Special Issue on Ant Algorithms and Swarm Intelligence)

Harilaos G. Sandalidis, Kostas Mavromoustakis and Peter Stavroulakis

Telecommunication Systems Institute of Crete (T.S.I.),

Iroon Polytehniou 37 str.,

73133 Chania, Crete, Greece.

Tel.: +30-821-28457, Fax: +30-821-28459

E-mail: [email protected], [email protected]

Contacting author:

Prof. Peter Stavroulakis

Telecommunication Systems Institute of Crete (T.S.I.),

Iroon Polytehniou 37 str.,

73133 Chania, Crete, Greece.

Tel.: +30-821-28457, Fax: +30-821-28459

E-mail: [email protected]

Keywords: Adaptive routing, Ant system, Probabilistic routing, Pheromone andantipheromone principles

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Ant based probabilistic routing with pheromone andantipheromone mechanisms

Harilaos G. Sandalidis, Kostas Mavromoustakis and Peter Stavroulakis

Abstract−− Using the idea of probabilistic routing, calls in an ant based decentralized

scheme are not routed according to the largest probabilities in the pheromone tables but

randomly according to these probabilities. This principle can be particularly helpful in

order to further minimize possible node congestion problems. An additional

incorporation of the antipheromone mechanism in the operation of artificial ants helps

in better biasing the network. This paper examines the behavior of such a routing

scheme using a proper set of suitable metrics.

Index Terms−− Adaptive routing, Ant system, probabilistic routing, Pheromone and

antipheromone principles

I. INTRODUCTION

The objective of routing is to establish a successful connection between any two nodes in a

communication network maximizing network performance. The way that routing is

implemented influences several important network characteristics such as grade of service, cost

reliability etc. Roughly speaking, a good routing scheme has to be computationally efficient

and inexpensive to apply, capable to select the best route depending on various constraints, and

perform correctly in the face of unusual or unforeseen circumstances. Having all the above in

mind it becomes evident that the problem of finding a proper route is not an easy task. Real

networks consist of a large number of nodes and show to have a dynamically unpredictable

behavior mainly because traffic load is not uniformly distributed. It is therefore clear that the

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algorithm used for this task has to avoid overloaded nodes and activate alternative routes

whenever load conditions are drastically changing.

A lot of different routing schemes appeared in the literature and the most basic are

discussed in [1] and [2]. The majority of these mentioned schemes are suitable in finding short

routes according to defined optimization criteria but decisions are usually made off-line (non-

adaptive). Adaptive schemes are in principle more attractive because they can keep abreast of

any possible changes in network load and failures. Routing algorithms can be also classified

into centralized and decentralized. Centralized schemes allow a central controller to act as the

supervisor of the entire network. Although these routing methods seem to be quite attractive,

their application to real networks is time inefficient and algorithmically complex and therefore

they are used only in particular cases. Decentralized schemes involve a number of controllers

each of which supervises a part of a network, and consist of a modern alternative approach to

routing problems.

Heuristic techniques and especially computational intelligence (neural networks, fuzzy logic

etc.) have been extensively used in the past in the area of wireline communications mainly

because they can give fast and quite reliable solutions to difficult problems (routing, call

admission switching etc) [3]. However, the majority of them require the use of an explicitly

well defined cost function whose minimization leads to a sub-optimal route.

Swarm intelligence is a new challenging branch of artificial life which takes advantage of the

collective behavior of animals with limited intellectual faculties (insects, flocking birds, schools

of fish) to solve algorithmically complex problems. The way social insects behave can be

applied to implement effective decentralized routers without the use of such a function. In a

seminal work by Dorigo et al. [4], [5], [6], intelligent agents in the means of artificial ants

were applied for shortest path searching on constrained graphs. Artificial ants are laying small

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pieces of information (analogous to chemical pheromone trails laid by natural ants) to network

nodes. Using this kind of information, ants communicate with each other and they can find

short routes from their nest to a food source and vice versa. Based on similar principles,

Schoonderwoerd et al. [7], [8] proposed an ant-based routing model for wireline

communication networks whereas Di Caro et al. presented AntNet, a much more realistic

application to Internet routing [9], [10].

In the Schoonderwoerd et al. model, artificial ants lay artificial pheromones on network

nodes in order to find optimum routes with non-heavy traffic load for network calls and

achieve load balancing. Simulation results applied to a synchronous digital hierarchy network

used by the British Telecom, showed that the ant based routing is a quite effective

decentralized scheme compared to the software agents' approach proposed in [11].

In the Schoonderwoerd et al. model, calls are routed according to the largest probabilities in

the pheromone tables that exist in every node of the network. That is they only follow a

particular route which in some cases may be not the optimal one due to possible congestion

problems which often appear in overloaded networks. An additional extension to the above-

mentioned routing scheme is the consideration of probabilistic routing where calls are not

routed according to the largest probabilities in the pheromone tables but randomly according to

these probabilities. Therefore calls can now select more than one path to reach their final

destination. In order to overcome possible drawbacks of this routing scheme and make it

competitive against the previous ant based approaches, an additional mechanism in the way

artificial ants operate, called antipheromone, is used.

In this paper we examine the application of the ant based probabilistic routing to a proper

network topology. Section II gives a brief outline of the Schoonderwoerd et al. model. Section

III describes the basic principles of the proposed routing scheme. The performance of this

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approach is examined through a number of various metrics which are good indicators of the

network performance on the one hand (throughput, call failures) and the ants' behavior

characteristics on the other (mean pheromone quantity etc.). Detailed simulation results are

presented in section III.

II. THE SCHOONDERWOERD ET AL. MODEL

Ant colony optimization algorithms have been inspired by the foraging behavior of real ant

colonies and specialized for the solution of minimum cost or shortest path problems on graphs.

The way they are operate has been extensively studied in [6] and [12]. Real ants deposit

pheromone on the ground while walking which influence the rest of them to follow, in

probability, the same route. Using this mechanism they can find the shortest path between two

nodes (nest, food). Dorigo et al, were first to apply the above simple principle to solve the

famous NP-complete problem of travelling salesman (TSP) using artificial pheromone trails.

These correspond to specific distributed numeric information which are affected by the ants to

reflect their experience gained while solving a particular problem. [4], [6].

Schoonderwoerd et al. [7] and [8] have developed a quite similar model to cope with the

dynamic aspects of routing problems in communication networks. Their main intention was to

propose an efficient decentralized routing scheme in order to route calls via parts of the

network that have spare capacity. It has to be noted that in real communication networks

which are characterized by nonuniform traffic distribution between their nodes, the shortest

routes between two nodes is not necessarily the ideal solution.

In the Schoonderwoerd et al. model every node has a routing table which indicates the

direction of a call in order to reach the final destination. Artificial ants modify the table entries

and thus continually affect the current network state. For this reason, routing tables are called

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pheromone tables. As an example, figure 1 shows a typical pheromone table for node 1 for a

simple network configuration with 5 nodes. Ants behave as particular calls that properly

polarize the network and achieve load balancing. By this way the changing load over the whole

network is efficiently distributed and hence the number of lost calls is minimized. This

decentralized routing scheme appears to be quite attractive since it allows the parallel

operation of ants and calls that are activated in the network.

Roughly speaking this decentralized scheme works as follows:

At every simulation time step every node generates an ant with a random destination. Ants

are walking according to probabilities given in pheromone tables. Their speed, unless they are

delayed on a particular node, is one node per simulation time steps. When an ant arrives to a

node, the entry corresponding to the node from which the ant came is increased by the

quantity:

P

PPold

∆+∆+=Ρ

1 (1)

where ûp is the pheromone increase. The other entries in the table of this node are decreased

accordingly following the formula:

P

PP old

∆+=

1 (2)

Ants are dying when they reach their destination. In order to force ants to choose short

lengths, pheromone increase reduces progressively with the age of the ant using the equation:

bt

a

age

+=∆Ρ (3)

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where tage is the number of time steps passed since the birth of the ant. a and b are proper

constants chosen by the designer. Possible congestion problems are faced by delaying ants at

congested nodes according to the formula:

[ ]sdeCdelay ⋅−⋅= (4)

where C and d are constants and s is the spare capacity of the node. The following constant

values were found to consist a suitable set: a= 0.08, b=0.005, C=80, d=0.0755 (See [7]). The

incorporation of delay reduces the ant flow rate from the congested node to its neighboring

ones permitting pheromones for other alternative choices to increase rapidly and makes

delayed ants older. Therefore they have less influence on pheromone tables.

Calls are operating independently and in parallel with ants. When a call is set up every node

has a certain probability to be the destination node. These probabilities are generated at the

start of every run and lie between 0.01 and 0.07. At every time step a call is generated by

following Poisson distribution and the duration is exponentially distributed with an average of

170 steps. In order to determine the path for a call from a specific node to a destination, the

route, where intermediate nodes have large pheromone, is selected. This route is valid if the

destination can be reached unless one of the nodes on the route is congested. If that happens,

the call is blocked.

Hence there is an indirect interaction between calls and ants in the means that ants affect the

routing tables and calls influence the load on nodes which effect the ants with the delay

mechanism. A more detailed description of the method is given in [7].

III. ANT BASED PROBABILISTIC ROUTING

An additional extension to the above-mentioned system is the consideration of probabilistic

routing where calls are not routed according to the largest probabilities in the pheromone

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tables but randomly according to these probabilities. Therefore calls can now select more than

one path to reach their final destination. This principle can be particularly helpful in avoiding

possible congestion problems in overloaded networks. In order to overcome possible

drawbacks of this routing scheme and make it competitive against the previous ant based

approaches, some additional mechanisms have to be taken into account. Such mechanisms can

be incorporated into the characteristics of artificial ants so that the enhanced ant entities are

able to properly polarize the network in order the probabilistic routing have at least

comparative performance with the routing scheme proposed by Schoonderwoerd et al.

A way of achieving this is by using antipheromone mechanisms which, differently from

pheromones, are used for reducing the values of probabilities maintained in the pheromone

tables. In this approach every ant has a random destination and moves from one node to

another on the basis of the probabilities included in the pheromone table. When an ant reaches

its destination node, the probabilities included in the pheromone table, which correspond to the

node from which they come from, are renewed. With this renewal the pheromone either

increases according to how short is the distance or decreases when the distance that the ant has

covered is longer than the one that has already been recorded (at the pheromone table of the

starting point for the particular destination). The increase and decrease of pheromone can be

illustrated in figure 2.

Noise can be considered in order to handle the so called shortcut and blocking problems.

The shortcut problem occurs when a new shorter route becomes suddenly available and the

blocking one when an older route is no longer valid. In both cases, it is difficult for the artificial

ants that realize only the quantity of laid pheromone, to have an adequate dynamic reaction and

find the new proper routes.

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Noise avoids freezing the routes that remain static for a long time and suddenly change and

also encourages the easier discovery of a proper route that appears suddenly due to the release

from congestion of a node. Using that consideration we can handle more easily shortcut and

blocking problems. For this reason a noise factor f is considered. An ant has a probability f to

select a pure random path and (1-f) to choose a path according to the pheromone tables on the

nodes. This property can be clearly shown in figure 3. Let's suppose that an ant is launched on

node 6. Then it has f probability to select a random node between 3, 7, 11, 12 and 13 and (1-f)

probability to select an intermediate node among the previous ones according to the

pheromone tables following the principles of the probabilistic ant routing explained before. An

indicative value 5% noise factor was used by Schoonderwoerd et al. in their model and was

also chosen in our simulation. It must be noted that values of noise factor greater than 6% are

shown to have a dramatic increase of call failures and hence decrease the performance of the

routing scheme.

The ant based probabilistic routing method has been applied to a network topology of 25

nodes shown in figure 4. Each node is represented as a class structure containing various

parameters (identification of the node, adjacent nodes, capacity etc). Nodes are interconnected

to each other following the structure of figure 4 and a possible such interconnection is shown

in figure 5. Every node has a maximum number of capacities, which in our case is 40 storage

units. (See figure 6).

The initialization guidelines follow the ones proposed by Schoonderwoerd et al. in their

model [7]. The network is initialized with equal probabilities for neighbor nodes in every

pheromone table and this takes place for a fixed period of time steps before the calls are

applied. During initialization the artificial ants bias the pheromone tables so that proper short

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routes can be easily found. With this manner, the behavior of generated calls is examined with

a greater amount of fidelity.

IV. SIMULATION RESULTS

A simulation program has been implemented using the programming languages of Java and

C. We have chosen these specific languages in order to combine the benefits of Java as a visual

programming language permitting inheritance with the fast execution of C based algorithms.

The program follows the general guidelines proposed in [7] and [8] briefly discussed in

sections II and III.

The results regarding the various metrics in both the absence and presence of noise

presented in the next section, are the mean value of 100 repeated trials between 0 and 15.000

approximately simulation time steps. This procedure was followed in order to avoid possible

variability problems between runs due to the initial random selection of call probabilities,

random generations and lengths of calls.

In order to examine the performance of the ant-based probabilistic routing various metrics

have been taken into account. In general the metrics used can be classified into two categories:

The first one has to do with the network performance whereas the second contains parameters

about the ant heuristic algorithm.

At first we examine the case where no noise is included. Figure 7 shows the efficiency of

this routing scheme for various simulation time steps regarding the number of call failures. The

number of call failures is a basic metric used also in Schoonderwoerd et al. formulation [7]. As

it can be shown, the maximum number of call failures occurs at about 1000 time steps. After

2500 steps failures are getting steady (smaller variations of failures). The rate in which calls

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arrive in the system and the variations in throughput are shown in figures 8 and 9 respectively.

The mean delay per node appears in figure 10.

For comparison reasons we have also simulated and examined the performance of the

Schoonderwoerd et al. routing scheme using the same model assumptions. Figures 11, 12 and

13 show the number of call failures, the arrival rate and the throughput. More analytical results

are presented in [13]. The two routing schemes show to have comparable performance (The

performance of the ant based probabilistic routing enhanced with the antipheromone

mechanisms is slightly better). However the fact that the new scheme allows the possibility of

calls to follow different paths leads to a better link utilization which may be advantageous in

the case of overloaded networks.

Figures 14, 15 and 16 show the performance of the new scheme under the effect of noise. A

noise factor 5% was used. The incorporation of noise decreases slightly the performance of the

routing scheme asthis can be easily noticed.

As regards to the second category various interesting metrics have been taken into account.

Figure 17 shows the mean number of ants per each node of the network. The mean number of

ants used for the whole network is shown in figure 18. It can be easily seen that after 8000

time steps this number is about 500. The mean value of pheromone quantity for all routing

tables in every node is shown in figure 19.

V. CONCLUSIONS

This paper examined the behavior of an ant based decentralized router using an adequate set

of commonly acceptable and some newly introduced metrics. The routing scheme presented is

an extension of the one presented in [7]. A further mechanism of antipheromone has been

considered in the operation of the artificial ant and calls are now following more than one path

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according to the values of pheromone tables. In the case of wireline communication networks

this adaptation helps in congestion avoidance and achieves an adequate grade of resources

utilization.

The heuristic algorithm presented can be easily compared with other routing methods used

in networks operating with some commonly used protocols such as ALOHA, Ethernet, FDDI

and DQDB. A possible application of the scheme to the areas shown in figure 20 is also an

interesting topic of further research.

REFERENCES

[1] A. S. Tanenbaum, Computer Networks, Prentice-Hall 3nd edition, 1996.

[2] J. Walrand, Communication Networks: A First Course, McGraw Hill 2nd edition,

1998.

[3] A. Vasilakos A and W. Pedrycz, Computational Intelligence in Telecommunications

Networks, CRC Press, 2000.

[4] M. Dorigo, V. Maniezzo and A. Colorni, "Positive feedback as a search strategy",

Tech. Rep. No.91-016, Dip Elettronica, Politecnico di Milano, Italy 1991.

[5] M. Dorigo, Ottimizzazione, Apprendimento Automatico, ed Algoritmi Basati su

Metafora Naturale (Optimization, Learning and Natural Algorithms Ph.D.Thesis,

Politecnico di Milano, Italy (in Italian), 1992.

[6] Dorigo M., V. Maniezzo and A. Colorni, "The Ant System: Optimization by a Colony

of Cooperating Agents". IEEE Transactions on Systems, Man, and Cybernetics–Part

B, vol. 26, No. 1, 1996, pp. 29–41.

[7] R. Schoonderwoerd, O. Holland, J. Bruten and L. Rothkrantz, "Ant-based Load

Balancing in Telecommunications Networks", Adaptive Behavior, vol. 5, 1997,

pp. 169-207.

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[8] R. Schoonderwoerd, O. Holland and J. Bruten, "Ant-like Agents for Load Balancing in

Telecommunications Networks", Proceedings of Agents'97, Marina del Rey, CA,

1997, pp. 209-216.

[9] Di Caro G. and M. Dorigo, "AntNet: A Mobile Agents Approach to Adaptive

Routing", Tech. Rep. IRIDIA/97-12, Uni-ver-sité Libre de Bruxelles, Belgium, 1997.

[10] Di Caro G. and M. Dorigo, "AntNet: a mobile agents approach to adaptive routing",

Ninth Dutch/Belgian Artificial Intelligence Conference, Antwerp, Belgium, 1997,

pp. 12–13.

[11] S. Appleby and S. Stewart, Mobile software agents for control in telecommunications

networks, BT Technology Journal, vol. 12, 1994, pp. 104-113.

[12] E. Bonabeau and G. Théraulaz, "Swarm smarts", Scientific American March 2000.

[13] H.G. Sandalidis, K. Mavromoustakis and P. Stavroulakis, "Performance Measures of

an Ant based Decentralised Routing Scheme for Circuit Switching Communication

Networks", Special Issue On Computational Intelligence In Telecommunications

Networks, Softcomputing Journal, Springer Verlag (To be published)

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Fig. 1: Pheromone (routing) table for node 1

Fig. 2: Consideration of antipheromone mechanism

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Figure 12: Rate of call arrival (Schoonderwoerd et al. model)

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Ant based probabilistic routing with pheromone and antipheromone mechanisms

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