Using Ant Colony Algorithm for Solving Minimum MPR Set and OPNET Simulation

Xianming ZHAO, Huazhu SONG, Hongxia XIA, Luo ZHONG

Department of Computer Science and Technology Wuhan University of Technology

Wuhan, China E-mail: freshzhaoxm@163.com, mingjs@vip.163.com

Abstract--Finding the minimum MPR set is a NP-complete

problem in OLSR protocol, and intelligent computing methods

can be used to solve it. Based on analyzing the defects of the

strategy of the greedy heuristic algorithm, ant colony algorithm

is imported to solve the minimum set of MPR problem. Firstly,

defining the out-degree and the in-degree of a node, and in

accordance with the out-degree and in-degree constraints, ant

colony algorithm based on the graphic is given to find the

minimum sets of MPR in this paper. Then, three kinds of ant

colony algorithm model such as Ant-Cycle, Ant-Quantity and

Ant-Density are improved, and the analysis of the convergence

curves about the three kinds of model is described by Matlab. As

the result shows that Ant-Cycle model has a faster rate of

convergence, the ant colony algorithm of solving a minimum

MPR sets based Ant-Cycle Model is determined. After using the

OPNET to simulate the algorithm, the statistics show that the

connectivity and data consistency of nodes, which also prove the

rationality of the algorithm.

Keywords-Minimum MPR sets; Ant Colony Algorithm;

Optimized Link State Routing protocol(OLSR); OPNET simulation

I. INTRODUCTION

Mobile Ad-hoc network, known as MANET, has a self-creation, self-organizing and self-management features [1-3]. MANET Working Group proposed the optimal link state routing protocol (OLSR), it is a table-driven proactive routing protocol, with control information to percept and the establish the wireless ad hoc network, and disseminate topology information through optimized approach. That is using HELLO and TC messages to find the link state information,

and then broadcast link state information through the MANET. At last, that makes network information up-to-date [4,5]; Among them, the Multipoint Relays (MPR) is the key concept in the agreement, since MPR node is responsible for transmitting link state information across the network, so finding the node’s minimum MPR sets is a key problem. Amir Qayyum, who proved that the minimum MPR set problem is a NP-complete problem, he gave a strategy based on the greedy heuristic algorithm [6].

Ant colony algorithm (ACA) is an algorithm that used to find and optimize the probability-based path in a diagram by simulating ant activity, the choice of the path, the update on the amount of information on the path and coordination between the ants and other mechanisms. It continually optimize the exchange of information between the individual and mutual collaboration to find the optimal solution eventually, so it is widely used in solving complex problems, such as applied in QoS network routing successfully, power failure and some other solution of NP-complete problem [7]. Through researches and comparative analysis, this paper gives an ant colony algorithm to solve the minimum MPR sets and discusses the three kinds of models of ant colony algorithm. At last, this model is simulated by OPNET software, the results shows this algorithm reasonable.

II. FINDING THE MINIMUM MPR SETS

A. The minimum MPR sets of nodes

Each node calculates its own MPR sets independently in Network. If the nodes’ MPR sets meet the following conditions:

The 1st International Conference on Information Science and Engineering (ICISE2009)

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(1) There is a bidirectional asymmetric link between nodes and its MPR node;

(2)Nodes sent packets through the MPR relay; the packets could reach the entire node’s all two-hop neighbors.

Next minimize the number of MPR nodes, that set is the minimum set of MPR. Well, MPR will be able to effectively transmitted TC packets.

Amir Qayyum gave an algorithm to find a node’s MPR set basing on the greedy heuristic algorithm. The algorithm can find a MPR set in a relatively short time, however, the got set may not be the optimal solution. Jian Zhao and others: remove redundant nodes through judging and re-sorting the node’s original MPR set, and then get the minimum MPR set [8]. Xinming Zhang, who used genetic algorithms to find the optimal MPR [9], he proposes a new algorithm based on the genetic algorithm, but if the group size is too small, optimal performance of this algorithm will not be very good, and it is easy to fall into local optimal solution.

B. The description of solving the minimum MPR set based on Ant colony algorithm

Use graphic G = (V, E, W) to describe the algorithm, in which V = (0, 1, 2, ..., n) is a collection of all nodes; E = ((i, j), i≠j, i, j ∈ V) is used to describe the use of a collection of

adjacency list; Wij describes the out-degree of node j; ( )ij tτ

describes the amount of information between the node i and the node j in time t. Experimental observation showed that the ants in the campaign will leave some pheromone, and the posterior ants would choose their paths to go according to the amount of pheromone left by previous ants. There are more pheromone on a path, the more probably the posterior ants would choose. When Wij = 0, the ant stops moving, that is, this cycle stops. Array In_d[n] is used to record the in-degree of each node. If node l is not a two-hop node (0≤l≤n), then In_d[l] = 0.

The ant-colony algorithm to solve the minimum MPR set of nodes is described as follows: Step 1: Initialization: Nc= 0 (Nc is the number of iteration or searching), at the same time initialize Wij matrix, place m ants on the first vertex. Step 2: For each ant k (k = 1, 2... m), goes to the next eligible

node j according to the probability of ( )kijp t , then record the

number of ants on each path; if In_d[j] = 1, then add node j in

MPR set. Then ( )kijp t is:

[ ( )] [ ( )][ ( )] [ ( )]

0

( )

ij ikk

is iss allowedk

t W tj allowed

t W tkij

otherwise

p t

βα

βατ

τ⊂

⋅∈

⋅⎧⎪⎪⎨⎪⎪⎩

∑=

，

，

(1)

in which, allowedk is a collection of the nodes that the ant k is allowed to pass; α is the information stimulating factor, β is the expectations stimulating factor. Step 3: Update the strength of information on the path. In order to avoid residual information to cover up enlightening information caused by excessive residual pheromone, for each ant, at the end its cycle, update the amount of information on the path:

( ) (1 ) ( ) ( )ij ijt n t tτ ρ τ τ+ = − ⋅ + Δ （2）

1

( ) ( )m

kij ij

k

t tτ τ=

Δ = Δ∑ （3）

ρ (0<ρ<1) is the pheromone evaporation parameter. ( )kij tτΔ is

the amount of information which ant k left in the path of (i ,j) in this cycle. Step 4: Nc Nc+1; Step 5: If Nc is less than a predetermined number of iterations, then switch to Step 2. Step 6: Verify whether all one-hop nodes in the MPR set cover the two-hop nodes. Step 7: If not cover all the two-hop nodes, select a one-hop node who has the largest number ant and add it into the MPR set, then turn to Step 6; otherwise, output the MPR set.

C. Three models of improved ant colony algorithm

Here the three models in above-mentioned ant colony algorithm are modified accordingly.

In Ant-Cycle Model:

{ * , ( , )0,( ) kQ S if ant k passed path i j in this cyclek

ij otherwisetτΔ = (4）

in which, Q says pheromone intensity, to some extent, which

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affects the speed of this algorithm’s convergence; Sk shows the total nodes’ out-degree of ant k in the cycle.

In Ant-Quantity Model:

{ * , ( , ) 10,( ) ijQ W if ant k passed path i j between time t and tk

ij otherwisetτ +Δ = （5）

In Ant-Density Model:

{ , ( , ) 10,( ) Q if ant k passed path i j between time t and tk

ij otherwisetτ +Δ = （6）

These three models have their own advantages and disadvantages, and we should select the appropriate model based on specific issues. Here, m is the number of ants, n is the number of nodes, Nc is the number cycle, and when n is large enough, then the time complexity [10] of this ant colony algorithm still is T(n)=O(Nc.n2.m). Compared with the strategy based on the greedy heuristic algorithm, the speed of this algorithm’s convergence is slower, however, it ensure that the collection of MPR is the smallest.

In the MATLAB experiment, this paper takes the same topology graphic with Amir Qayyum: 50 nodes, and finding the minimum MPR sets of node S. Set m = 20, ρ = 0.1, Q = 1.2, after several experiments to determine the parameters α = 1.5, β = 2.5 (better results), and test the three models of the improved ant colony algorithm, then we get the convergence curve as shown in Figure 1.

Abscissa shows the time and ordinate shows the amount of information in Figure 1. It shows that Ant-Cycle model has a faster convergence speed, so Ant-Cycle model should be chosen to solve this problem. However, the algorithm is based on the cost of convergence rate to improve accuracy, as its time complexity is higher than the greedy heuristic algorithm.

1a. Ant-Cycle Model 1b. Ant-Quantity Model 1c. Ant-Density Model

Figure 1. The convergence curve of Ant-Cycle, Ant-Quantity and Ant-Density Model Figure 2. Schematic diagram of the node model

III. OPNET SIMULATIONS

A. Model Design

This chapter verifies the feasibility of the proposed algorithm by studying the node connectivity and data consistency with using OPNET tool. Basing on the needs of this article, we design the simulation node model as shown in Figure 2, which includes the four basic functions: generate package, handling package, receive/transmit packets and time control (separated with frames in Figure 2). The node model designs five modules: token_src, pk_src, timer, pk_deal, snd_pk, which realize the nodes’ packets generation and processing and some other functions. There are

multi-functional links in the receive/transmit packets module, so it is free to choose the course of links in the receiving/sending data packets, and of course each link has a different rate.

Since there are many process modules in the node model, here we take the design of pk_deal process modules as examples to describe. In the pk_deal processing module, mandatory statuses are as following: init, from_src, from_radio and MPR; idle is the non-mandatory state. MPR, which covers the ant colony algorithm above, mainly is used to calculate the node’s minimum set for packets sending. The line with the direction arrow presents state transition, and the string in

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brackets refers to the conditions about the state transition (as shown in Figure 3).

Figure 3. Design of pk_deal module Figure 4. Waveforms of receiving and sending data Figure 5. Statistics of sending and receiving packets

B. Simulation results

Simulation network topology graphic is as Amir Qayyum’s. Nodes are needed to adjust the transmitting power, as well as the distance between nodes in order to distinguish one-hop nodes and two-hop nodes. Node A is able to calculate its MPR set, and then transmits information according to the node in MPR set.

Set the entire simulation time for 60s, node A calculates its minimum MPR set before 10s, and a packet is sent every 10s from the 10s. Figure 4 is the waveform diagram of node A’s sending packets, node b’s forwarding packets and node3’s receiving packets (abscissa is simulation time and longitudinal coordinates is the number of packets sending per second). It’s obvious that three waves are similar in Figure 4, so it proves that nodes’ connectivity. Figure 5 shows node A’s sending waveform and node3’s receiving packets. There are five peaks in the sending waveform of node A, in other words, node A sent five packets. The number of node3’s receiving packets is exactly 5, which proves the consistency of sending data and receiving data.

The simulation results show that the algorithm of solving the minimum MPR set based on ant colony algorithm is feasible. Since there is a little data in the whole simulation process and the whole network is in an ideal state, so only a small delay; to the actual MANET, its network topology is often changed. Therefore it is necessary not only to select routing protocols to improve the network performance, but also to improve the algorithm and consider the routing layer QoS when network has a variable topology, high-speed data and high liquidity.

IV. CONCLUSIONS

In this paper, an ant colony algorithm is improved for solving it. Through the analysis of different models of ant colony algorithm in and comparative experiments, the selected Ant-Cycle model of ant colony algorithm has a good convergence and could find the smallest MPR set in required time, which indicate that the algorithm is reasonable and correct. Further, this article simulates algorithm using the OPNET and simulation results show the feasibility of the algorithm. In further study, the algorithm will be further optimized and the time complexity will be lowed in ensuring the correct solution of finding the minimum MPR set.

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