Mathematical and Computer Modelling 52 (2010) 1976–1981

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Mathematical and Computer Modelling

journal homepage: www.elsevier.com/locate/mcm

An improved ant colony optimization for the communication networkrouting problemDongming Zhao a,∗, Liang Luo b, Kai Zhang aa School of Electronics Engineering and Computer Science, Peking University, Beijing, Chinab Department of Control Science and Engineering, Huazhong University of Science and Technology, China

a r t i c l e i n f o

Article history:Received 23 September 2009Received in revised form 25 December 2009Accepted 31 January 2010

Keywords:ACOCommunication network routing problemIACOAnt-weight strategy

a b s t r a c t

Ant colony optimization (ACO) is a population-based meta-heuristic for combinatorialoptimization problems such as the communication network routing problem (CNRP). Thispaper proposes an improved ant colony optimization (IACO) technique, which adapts anew strategy to update the increased pheromone, called the ant-weight strategy, and amutation operation, to solve the CNRP. The simulation results for a benchmark problemare reported and they are compared to the simple ant colony optimization (ACO) results.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Communication networks can be classified as either circuit switched or packet switched. Circuit-switched networks relyon a dedicated connection from source to destination which is made once at start-up and remains constant until the tear-down of the connection. An instance of a circuit-switched network would be China Telecom’s telephone network. Packet-switched networks work quite differently however, and all data to be transmitted is partitioned into segments and sentas a data packet. Data packets can arrive out of order in a packet-switched network, with a variety of paths taken throughdifferent nodes in order to get to their destination. The internet and office LAN are both good examples of packet-switchednetworks. Some techniques can be employed to optimize the flow of traffic around a network, such as flow and congestioncontrol, where nodes action packet acknowledgements from destination nodes to either increase or decrease the packettransmission speed. The area of interest in this paper concentrates on the idea of communication network routing androuting tables. These tables hold information used by a routing algorithm tomake a local forwarding decision for the packeton the next node it will visit in order to reach its final destination.One of the issues with communication network routing (especially in very large networks such as the internet) is

adaptability. Not only can traffic be unpredictably high, but the structure of a network can change as old nodes are removedand new nodes added. This perhaps makes it almost impossible to find a combination of constant parameters to route anetwork optimally. Packet-switched networks dynamically guide packets to their destination via routing tables stored in alink state and are selected via a link state algorithm.The link state algorithm works by giving every node in the network a connectivity graph of the network. This graph

depicts which nodes are directly connected. Values are stored for connected nodes in the graphwhich represent the shortestpath to other nodes. One such link state algorithmused in network routing is Dijkstra’s algorithm.When a path between twonodes is found, its weight is updated in the table. Should a shorter path be found, the new optimal weight will be updatedto the table, replacing the old value. The algorithm allows traffic to be routed around the network whilst connecting to theleast number of nodes as possible. The systemworks but does not take into account the influx of traffic and load balancing.

∗ Corresponding author.E-mail addresses: dmzhao@pku.edu.cn (D. Zhao), luoliang@mail.hust.edu.cn (L. Luo), zhangkai@pku.edu.cn (K. Zhang).

0895-7177/$ – see front matter© 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.mcm.2010.04.021

D. Zhao et al. / Mathematical and Computer Modelling 52 (2010) 1976–1981 1977

By replacing Dijkstra’s algorithm with a generic algorithm, paths taken by calls could be scored by how short a paththey took; that way, if they were queued on a busy network, they would perform badly. Consequently, other paths wouldscore better relatively, and be chosen. This would work in real time and would allow the routing system to adapt as packetsare transmitted. The use of ACO algorithms has been proposed to solve this problem [1–3]; these algorithms use virtualpheromone tables much like when an ant follows a path dropping pheromones to reinforce it. The quicker the ants movedown a path, the greater the throughput of ants, and thus the greater concentration of pheromone. In the same way,pheromone tables in ACO algorithms allow fast routes to score a higher chance of being selected whilst the less optimalroute scores a low chance of being selected.In most ACO routing algorithms, the quality of a path is evaluated from its number of hops and communication delay.

Therefore, a path with a smaller number of hops and shorter communication delay gets more pheromone and is used fortransfer of data packets with a higher probability. However, the difficulty of ACO routing algorithms in communicationnetworks lies in the facts that the amount of pheromone is updated some time before it is utilized in sending packets andthat link disconnections frequently occur because of node movements. Therefore, even though a path with a small numberof hops and short communication delay has much pheromone, the path may become unavailable quickly due to the linkdisconnections.To solve this problem, we propose an improved ant colony optimization (IACO) technique with a new pheromone

updating rule that can integrate the global feature and the local feature, a mutation operation and the 2-opt exchange forthe CNRP. The remainder of the paper is organized as follows. Section 2 presents the mathematical model for the CNRP. InSection 3, we present the IACO technique with the ant-weight strategy and the mutation operation. Some computationalresults are discussed in Section 4, and lastly, the conclusions are provided in Section 5.

2. The communication network routing problem

The CNRP is described as a weighted graph G(t) = (V (t), E(t)), where V (t) and E(t) are the node set and the edge setat time t , respectively. Nodes are located on a two-dimensional field and move in the field. A node v1 ∈ V (t) has a distinctidentifier IDv1 . Each node has the same communication range R > 0. When a node v2 is within radius R of a node v1 at timet , then an edge (v1, v2) is included in the edge set, and v2 is called a neighbor of v1. If a node v1 sends out a packet to itsneighbor v2 at time t , the packet is received correctly by v2 at time t+δ1 only when v2 keeps staying within communicationrange of v1 during the period from t to t + δ1, where δ1 > 0 represents the communication delay between v1 and v2. Ifv2 goes out of the communication range once during the period, v2 cannot receive the packet [4]. We assume that, withthe availability of a global positioning system (GPS), it is possible for a node to know its global position, the velocity anddirection of its movement, and the global time.An ant is an autonomous agent that can migrate from one node to another on the network. An ant can migrate between

two nodes just like the transfer of a packet. That is, an agent that starts its movement from a node v1 to v2 at time t arrivesat v2 at time t + δ2 only when v2 continues to be a neighbor of u during the period from t to t + δ2, where δ2 represents themigration delay between the nodes. Each node v1 is provided with a whiteboard, i.e., a local storage where the node u andants on u can write, read and erase information. Access to a whiteboard is done exclusively: when multiple ants on a nodeexecute their operations, the operations are sequentially executed in an arbitrary order.In this paper, we consider a routing problem in a communication network. We assume that a source node knows the

identifier of a destination node to send a packet. The goal of the problem is to construct one or more robust paths from asource to a destination node and to deliver data packets to the destination along the paths.

3. Improved ACO for the CNRP

3.1. Generation of solutions

UsingACOwhose colony scale is P , an individual ant simulates a source node, and its route is constructed by incrementallyselecting a destination node until all nodes have been visited. The nodes which have already been visited by an ant or whichhave violated the capacity constraints are stored in the infeasible node list (tabu).The decision making about combining customers is based on a probabilistic rule taking into account both the visibility

and the pheromone information. Thus, to select the next customer j for the kth ant at the ith node, the ant uses the followingprobabilistic formula [4].

pij(k) =

τ αij × η

β

ij∑h6∈tabuk

τ αih × ηβ

ih

j 6∈ tabuk

0 otherwise

(1)

where pij(k) is the probability of choosing to combine nodes iand j on the route, τij the pheromone density of edge (i, j), ηijthe visibility of edge (i, j), α and β the relative influence of the pheromone trails and the visibility values, respectively, andtabuk is the set of the infeasible nodes for the kth ant.

1978 D. Zhao et al. / Mathematical and Computer Modelling 52 (2010) 1976–1981

3.2. Mutation operation

The idea of the mutation operation is to randomly mutate the traversed links and hence produce a new solution thatis not very far from the source node. In this paper, the mutation operator is designed to conduct a packet according to thequality of the path such as its number of hops and the communication delay. The steps for the mutation operation are asfollows.Step 1 Select twopaths from the selected parent solution at randomand select themutating points fromeachmutating path.Step 2 Exchange the destination node in the different paths and generate the child solution.Step 3 Ensure the local optimality of the child solution. The 2-opt exchange is applied to improve the mutated paths in the

child solution. Finally, the representation and the paths of the mutated child solution are achieved.

Each route of the solution is mutated with a certain probability Fm. Usually, the diversity of the solution is large at thebeginning of a run and decreases with time. We adapt the mutation rate during a run to promote a fast convergence to goodsolutions during the first generations and to introduce more diversity for escaping from local optima during later stages.The mutation probability at time t is

Fm(t) = Fminm + (Fmaxm − Fminm)1−t/T . (2)

3.3. Local search

In the 2-opt exchange, all possible pairwise exchanges of node locations visited by packets are tested to see if an overallimprovement in the objective function can be achieved.

3.4. Update of pheromone information

The updating of the pheromone trails is a key element to the adaptive learning technique of ACO and the improvementof future solutions [5]. First, pheromone updating is conducted by reducing the amount of pheromone on all edges in orderto simulate the natural evaporation of the pheromone and to ensure that no one path becomes too dominant. This is donewith the following pheromone updating equation:

τ newij = ρ × τoldij +

K∑k

∆τ kij ρ ∈ (0, 1), (3)

where τ newij is the pheromone on the edge (i, j) after updating, τ oldij the one before updating, ρ the constant that controlsthe speed of evaporation, k the number of the route, K the number of the routes in the solution, with K > 0, and δτ kij is theincreased pheromone on edge (i, j) of route k found by the ant.The pheromone increment updating rule uses the ant-weight strategy as follows [6]:

∆τ kij =

QK × L

×Dk − dijmk × Dk

if edge (i, j) in the kth route

0 otherwise(4)

where Q is a constant, L the total length of all routes in the solution, i.e. L =∑k Dk, Dk the length of the kth route in the

solution, dij the length of edge (i, j), andmk the number of nodes in the kth route;mk > 0.

3.5. Overall procedure

The flowchart of our IACO procedure for the CNRP is shown in Fig. 1.

4. Simulation results

In this section, the simulation results are presented to demonstrate that our algorithm can achieve high performancewith low communication cost. A number of test comparisons will be done to show how IACO can improve the routing ofa communication network when paths are no longer valid and new routes have to be chosen. For this, a bi-directional,unweighted topological network consisting of 30 nodes has been created, and it closely resembles the network of ChinaMobile Communications Corporation (CMCC). After a basic number of parameters have been set, the simulation is run:• Simulation Speed — 1000 tick/s• Total calls to make — 5000• Maximum concurrent calls — 60• Node capacity — 35• Call duration — 170 (the length (in ticks) of a call)• Reduce I/O — bypasses the network visualization to increase simulation speed• Return on connection — returns the node immediately to source after connection.

D. Zhao et al. / Mathematical and Computer Modelling 52 (2010) 1976–1981 1979

Fig. 1. The flowchart of the IACO procedure.

4.1. IACO versus simple ACO

The first test contains two simulations, as Fig. 2 shows.

• Simulation 1 — simple ACO algorithm.• Simulation 2 — IACO.

From this simulation it is clear that, even by the time the first 500 calls have been completed, IACO has reduced theaverage number of hops by approximately 1.5 nodes. This is made more apparent by the end of the simulation, where thebest paths aremademore biased as a choice and are reinforced as the optimal route, resulting in IACO improving the networkperformance by almost 3.5 hops. To view the algorithm from a different perspective the following graph depicts the systemrunning with the simple ACO algorithm and then activated on the 2000th call. This can be identified by a label, and it resultsin a decline of average hops by almost 2.

1980 D. Zhao et al. / Mathematical and Computer Modelling 52 (2010) 1976–1981

10

9

8

7

6

5

4

3

2

1

0 1000 2000 3000 4000 5000 6000

Average number of hops

Ave

rage

num

ber

of h

ops

Number of complete calls

simple ACO

IACO

Fig. 2. Simulation results of simple ACO and IACO.

9

8

7

6

5

4

3

2

1

0 1000 2000 3000 4000 5000 6000

Ave

rage

num

ber

of h

ops

Number of complete calls

loop elimation OFF

loop elimation ON

Fig. 3. Loop removal versus non-loop removal.

4.2. Loop elimination

Before an ant returns back to its source node, an optimization technique of loop elimination can be invoked. As shownin Fig. 3, the problem with loops is that they can receive several times the amount of pheromone that they should, leadingto the problem of self reinforcing loops.

5. Conclusion

In this paper, we have proposed a new IACO routing algorithm for communication networks. In our algorithm, each antevaluates the quality of a route for its pheromone. The pheromone increment updating rule uses the ant-weight strategy. Thesimulation results have shown that higher packet delivery ratio with lower communication cost results with our algorithmthan with simple ACO.

Acknowledgements

This research is supported by theNatural Science Foundation of China (60533010, 30670540, 60503002), and theNationalHigh Technology Research and Development Program (863 Program) of China (2006AA01Z104).

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