Using the grouping genetic algorithm (GGA) for channel assignment in

Using the grouping genetic algorithm (GGA) for channel assignment in a cluster-based mobile ad hoc network Mahboobeh Parsapoor, [email protected], Halmstad University, and Urban Bilstrup, [email protected], Halmstad University

 Abstract— Next generation tactical military network will be based on mobile ad hoc networks (MANET). These networks require efficient spatial channel reuse in order to provide high spectral efficiency and this is only achieved by efficient channel assignment optimization. For a clustered network topology the basic goal is to assign different channels to adjacent clusters, i.e. a graph coloring problem. Unfortunately, is the optimal solution for graph coloring problems intractable, the problem is NP-hard. As a consequence heuristic methods must be applied, which provide solutions with as close to optimal result as possible. In this article the grouping genetic algorithm is applied for solving the channel assignment problem in a cluster based mobile ad hoc network. The used multi objective function minimizes interference and maximizes the spectral efficiency.

I.

N

INTRODUCTION

ext generation military radio networks, that will replace legacy combat radio network (CNR), at the tactical edge are to a large extent so called mobile ad hoc networks (MANET). Such a tactical MANET will typically contain 50 to 100 nodes and a clustered network topology seems to fit the structure of the military organization very well supporting a company. For large military operations many of these MANETS must coexist in the same geographical area as a consequence it is very important to minimize the spectrum utilization of each network. These networks are anticipated to provide IP based services all the way out to the individual vehicle or individual soldier at the tactical edge, providing situational awareness by services like [1]: intelligence, surveillance, target acquisition, and reconnaissance (ISTAR) and blue force tracking etc. Providing these kinds of services all the way out to the tactical edge will require a large need for bandwidth [2] and since the spectrum is a very limited resource it will require very high spectral utilization efficiency. High spectral utilization efficiency can only be achieved by efficient spatial channel reuse. The spatial channel assignment problem can be classified as a graph coloring problem, which in general is identified as a NP-hard class of problem [3]. An optimal solution for assigning orthogonal channels to adjacent clusters using a minimum number of channels (chromatic index) would not be found in polynomial time. However, heuristic methods such as genetic algorithms (GA), and swarm intelligence (SI), ant colony

optimization (ACO), have the ability to find near optimal solution in polynomial time [4]-[6] for this kind of problems. This paper presents initial experimental results of applying a centralized grouping genetic algorithm [7]-[8], for the channel assignment problem in a cluster based mobile ad hoc network. The considered optimization criteria are: maximizing spectral efficiency and minimizing the co-channel interference between clusters. This paper is organized as follows: in Section II, a brief review of the channel assignment problem for cluster-based MANET is given. In Section II, we describe briefly the genetic algorithm (GA) and the grouping genetic algorithm (GGA); furthermore the problem is defined and objective functions are described. In Section IV, the results of applying the GGA for the channel assignment problem in a cluster based MANET are presented. In Section V, we conclude with some final notes. II.

CHANNEL ASSIGNMENT FOR CLUSTER BASED MANET

Resource assignment for flat networks was early considered as broadcast scheduling [9] and link scheduling [10] in the timespace domain i.e., node and link graph coloring problems [11]. Later the channel assignment problem was generalized for frequency and code based channels [12]. One of the problems with a flat network topology, only considering nearest neighbor coloring, is that it suffers from the hidden terminal problem. To avoid this problem a well-defined entity for channel assignment and spatial channel reuse can be formed by aggregating nodes into a clustered network topology, as shown in figure 1.

Cluster head

Gateway

Figure 1. A clustered mobile ad hoc network.

Leaf node

Assigning channels to the clusters is achieved by first contracting the entire network graph (figure 1) to a sub-graph where only the cluster heads, nodes with minimum ID based on the lowest ID clustering algorithm [13], are represented as nodes and links are representing gateway connections between cluster heads. Then node coloring is applied on the contracted graph to assign different channels to adjacent clusters. III.

GROUPING GENETIC ALGORITHM FOR CHANNEL ASSIGNMENT

A. Genetic algorithm (GA) In general, genetic algorithm, a well-known evolutionary algorithm, is a stochastic method to search an optimal or near optimal solution among the potential solutions which refer to as individuals. Each individual, chromosome, consists of genes, one for each dimension, to cover the search space. Genetic algorithm stars by generating an initial population, a set of individuals with random value for each gene. Fitness function is applied to evaluate the individual to select them for genetic operation, crossover and mutation. These operations result to generate new individuals which are referred to as offspring. Also, the selecting operation is applied to select a set of individuals as a next generation. The genetic algorithm can be summarized as following steps [4]: 1. Encoding solutions of problem into chromosomes. 2. Creating an initial population, set of chromosomes. 3. Evaluating chromosomes, individuals, ‘in term of their fitness’ in order to select parents to produce new individuals. 4. Using genetic operations, crossover and mutation in order to reproduce new chromosomes, offspring. 5. Evaluating the new population, combination of parents and offspring, to select next generation. Iterating the above procedure, genetic algorithm converges to the best solution. B. Details of grouping genetic algorithm (GGA) The Grouping genetic algorithm (GGA) which was proposed for grouping optimization problems [3], [6]-[7] e.g., bin packing and graph coloring, is based on a group-based representation scheme. Each chromosome is divided into two parts: the first part, object part, identifies to which group labels, genes belong, the second part, group part, instantiate the groups that are used. Objects are encoded on a one gene for one group basis (see figure 2).

f f 3 f1 f 4 f1 f 6 f 5 f1 : f 5 f 3 f1 f 2 f 4 f 6 2      Object ( Clusterhead )

Group ( FrequecyCh annel )

Figure 2. Grouping representation of chromosome for channel assignment problem.

The GGA has three genetic operators: crossover, mutation and inversion. The function of GGA is according to[7]: 1) Initialize population using grouping representation; 2) Evaluate population, sort the population; 3) Select the best population using roulette wheel selection; 4) Apply crossover operation; 5) Apply mutation operation; 6) Apply inversion operation; 7) Evaluate population; 8) Stop, if the termination condition is satisfied. The operators change the group part and the object part is adjusted to the changes. The crossover operation of GGA is according to [4], [7]-[8]: 1) Select at random two crossing sites, delimiting the crossing section site, in each of two parents. 2) Inject the contents of the crossing section of the first parent at the first crossing site of the second parent. 3) Overwrite the object part of parent two such that the membership of the newly inserted groups is enforced. 4) If necessary, adapt the resulting groups, according to the constraints and the cost function to be optimized. 5) Repeating the same procedure (step 2-4) for the two parents with their roles permuted to generate the offspring. The mutation operation [4], [7]-[8] has similar procedure as crossover operation. Following steps explain the mutation operation: 1) A chromosome is selected for mutation and a number of labels in the group part are deleted (see figure 3). 2) The genes of object part that have taken the deleted group labels, would be unlabeled, which means they would lose the taken group labels. 3) According to the constraints and the cost function, the unlabeled genes are assigned to remained group labels. 4) If the constraints are not satisfied, a new label is added to assign the object part.

f f 3 f 4 f 5 f1 f 4 : 2    Object ( Clusterhea d )

f f 3 Xf 5 f 1 X : 2  Object ( Clusterhea d )

f f1 f 3 f 4 f 2 5   Group ( FrequecyCh annel )

f 5 f1 f 3 f 2    Group ( FrequecyCh annel )

Figure 3. Mutation operator for channel assignment problem.

Inversion [7]-[8] is the additional operator which is introduced for the grouping representation scheme. This operator is only applied on the group part of the chromosome. Two points of chromosome in the group part are randomly marked and then the order of the genes between these two points is reversed (see figure 4).

f2 f3 f 4 f5 f1 : f5 f1 f3 f4 f2  f 2 f3 f4 f5 f1 : f5 f1 f 2 f4 f3      Object(Clusterhea d ) Group(FrequecyCh annel)

fl

F1 (x)  w 1  ( m  f l )   i  g ( x , f ) ) i

Object(Clusterhea d ) Group( FrequecyCh annel)

Figure 4. Inversion operator for channel assignment problem.

C. GGA for channel assignment problem There is more than one possible criterion for the channel assignment problem in a cluster-based MANETs to satisfy. The most common constraint is that adjacent cluster should be assigned different channels. However as in most interference limited systems it’s a tradeoff between spectral efficiency and power limitation (interference). As consequence the channel assignment problem can be seen as a ‘multiple-objective optimization problem’ and the found solution might not fulfill the optimal values of both objectives. Due to the conflict between the multiple objectives, we have to choose a ‘bestcompromised solution’ among the set of ‘pareto optimal solutions’ [4]. The GGA is applied for seeking a solution for channel assignment problem with respect to optimize a single objective function and multiple-objective function. The steps of the GGA channel assignment algorithm are as follows:

(1)

i 1

Where w1 is the normalized weight, which is defined according to (2) and Nc is the number of clusters and m is the number of used channels.

w1 

1 N c  f u  (m  f l )

(2)

In the first trial the previous cost function is used, in the second trial a multi objective cost function is applied where second and a third objectives are added. The second objective is described by (3), F2 represents the number of cluster-head that utilize the same channel. Nc

F2   I i

(3)

i 1

Where is the cardinality of the set of clusters that utilize the same channel as the i th cluster. The weight of this function, w2 , is defined as 1 / N c2 . The third objective is described by (4),

F3 represents the

1) An integer representation is used for each chromosome that is divided into two parts. The first part, the object part, represents the specific channels assigned to each cluster while the second part contains the available channels. The second part, the group part, has the permutation representation. While the first part can be represented in arbitrary manner using the available channels of the second part.

overall co-channel interference power for all clusters utilizing the same channel inside the network.

2) The population size, which means that number of individuals in each generation, is chosen between 50 and 250, and the maximum size of a generation is 1000. For initialization of population, a random value between the upper limit and lower limit is considered for each individual. The chromosome is instantiated to try to assign the channel in such a way that co-channel interference between clusters is avoided.

The numerator of (4) is calculated for all clusters that utilizes the same channel. While, denominator of (4) is calculate for all cluster of network. Here D j is the distance

3) The genetic operations, crossover, mutation and inversion are applied as described previously. 4)

Equation (1) is the evaluation function for maximizing the spectral efficiency, i.e. minimizing the total number of used channels. Assuming that a chromosome, x , has l channels in its group part. Where, g ( x, f i ) means the numbers of clusters that are allocated by i th channel in the chromosome which, where

fi is the channel that is

assigned to this specific chromosome.

Ii

F3

Pi  Nc



D

n j

j 1

c Nc

D

n j

j 1, j  i

(4)

between j th cluster-head and this cluster-head and n is the pass loss exponent. Here, we assume that n it is equal to 2. The weight of this function W3 is 1/Nc . The algorithm seeks for a solution that maximizes a utility function [14]. The utility function is simply defined as the weighted summation (5) of three functions, (2) - (4). These functions are maximizing the spectral efficiency, minimizing the interference power and the total number of clusters which interfere. 3

U   w i Fi

(5)

i 1

IV.

N UMERICAL RESULTS

For simulation part, the used network model is generated

using MATLAB. Assuming that N nodes are placed in a 1000 x 1000 meter square area and the individual node coordinates, x and y, is drawn from uniform distributions. The communication range and interference range are assumed to be 250 meter and 500 meter respectively. The clustering of the network is conducted by using the lowest ID clustering algorithm [13]. The initial simulations in this paper consider 25 – 125 nodes. The minimum number of channels is set to 4 and the maximum available number of channels is set to 15. The features of GGA for the multi objective optimization and single objective optimization are summarized in Table 1. Also the results are obtained from running GGA 5 times for each scenario. TABLE I. Optimization Method Multiple objective function Single objective function

Selection method Roulette wheel selection 1 Roulette wheel selection 1

The numbers of allocated channels that are found using the two cost functions are depicted in the bar charts of figure 6. Considering the multi objective function as the cost function causes an increase in the number of allocated channels; thus, it decreases the spectral efficiency. In contrast, in all solution that found by using only F1 as cost function, the number of allocated channels is the same as the minimum available channels. The minimum number of used channels with a random channel assignment and a found solution by optimizing multiple objective functions are the same and is equal to 6. However, the maximum of assigned channel using multi objective function is less than 8, while the maximum number of used channels is 10 with a random solution.

THE FEATURES OF GGA Features Crossover Mutation rate rate

Inversion rate

0.4

0.35

0.2

0.3

0.25

0.2

The minimum and average values of the two tried cost functions versus the different number of nodes are depicted in figure 5. Also, for comparison the value of F1 is calculated when random channel assignment is applied. In the case when using multi-objective function the average value of cost function is equal to the minimum value of the cost function. However, the average and minimum values for when only, F1, is used as cost function differs to some extent. From the perspective of algorithm convergence, using multi objective function as the cost function is better than only using F1 as objective function.

Figure 5. Cost function values versus the different number of nodes.

Figure 6. Number of clusters and number of utilized channels versus number of nodes.

Figure 7 shows the average interference power in network, it clearly indicates the increase in average interference power when the number of nodes increases. However, it is noticeable that the difference between interference powers using the different cost functions is about 10 dB; using the multiobjective cost function decreases the interference power of network. Thus, in the case which is interference constrained, using the multi-objective function, is more desirable than using only F1 as objective function. It indicates that the two suggested criteria have strong conflict with each other’s and a best solution for second constraint (see figure 6, blue line,), is worst solution for the first on (see figure 8, blue line). A compromise solution using multiple objective functions satisfies both constraints better than a random solution.

Figure 7. Over all interference power in the network versus number of nodes

The number of required generations (iterations) versus the number of nodes by using the two cost functions is shown by the bar-chart in figure 8. It shows that in order to converge to the best solution, a larger number of generations are required when using the multi-objective cost function. Moreover, using multi-objective cost function increase the number of clusters. It seems that the number of nodes or number of clusters has not large impact on the number of required generations and the computational complexity of the algorithm.

Figure 8. The number of required generations versus number of nodes.

V.

CONCLUSION

In this paper we present the initial results of applying GGA, an evolutionary algorithm, for optimizing the channel assignment for a cluster based mobile ad hoc network (MANET). At this initial phase we concentrated on identifying good objective function for a centralized implementation. The present results indicate that the proposed multi objective function can find a solution that satisfies proposed objective functions. The results indicate that when the number of nodes increases, there is no noticeable change in the number of assigned channels in the network, which means that this method can be

considered for large scale network. Furthermore, it seems that the number of nodes (or number of clusters) does not have a large impact on the number of required generations for convergence. The initial results obtained from applying GGA and our proposed multi-objective function show that the solutions not only minimize interference power but also minimize the number of allocated channels. The multiobjective function as the cost function causes an increase in the number of allocated channels compared to the case when only the number of channels is used as objective function; which indicate the present tradeoff between the spectral efficiency and interference power. In future work we believe that it is more important to take the interference power into account so other weighting functions will be tried out more carefully. Furthermore other evolutionary algorithms as ant colony optimization (ACO) and imperialist competitive algorithm (ICA) will be applied for the channel assignment problem of a clustered based MANET. Distributed versions of the algorithms must be derived and intra cluster scheduling could be included. The present lowest ID clustering algorithm will be replaced with a genetic algorithm based clustering method and the network model will include mobility and traffic scenarios. Power control should be included in order to limit the increase in interference power when the number of nodes increases. REFERENCES [1] M. J. Ryan and M. R. Frater, Tactical Communications for the Digitized Battlefield, Qrtech House, 2002. [1] P. Rehmus et. al. The Army’s Bandwidth Bottleneck, The Congress of the United States, Congressional Budget Office (CBO), August 2003. [2] M. R. Garrey and D. S. Johnson, COMPUTERS AND INTRACTABILITY, A Guide to the Theory of NP-Completeness, W. H. Freeman and company, 1997. [3] M. Gen, and R. Cheng, Genetic Algorithms and Engineering Optimization, John Wiley & Sons, 2000. [4] A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence, John Wiley & Sons, UK, 2005. [5] T. S. C. Felix and M. K. Tiwari, Swarm Intelligence: Focus on Ant and Particle Swarm Optimization, InTech, 2007. [6] E. Falkenauer, “A new representation and operators for genetic algorithms applied to grouping problems,” Evolutionary Computing, Vol. 2, No.2, pp. 123-144, 1994. [7] A. E. Eiben, J. K. V. D. Hauw, and J. I. V. Hemert , "Graph Coloring with Adaptive Evolutionary Algorithms," Journal of Heuristics, Vol. 4, No. 1, pp. 25-46, 1998. [8] A. Ephremedis and S. Kutten, “Scheduling Broadcasts in Multihop Radio Networks,” IEEE Transactions on Communications, Vol. COM-38, pp. 456460, April, 1990. [9] B. Hajek and G. Sasaki, “Link Scheduling in Polynomial Time,” IEEE Transaction on Information Theory, Vol. 34, No. 5, pp. 910-917, September 1988. [10] R. Diestel, Graph Theory, 2nd ed., Springer, 2000. [11] R. Ramanathan, “A unified framework and algorithm for (T/F/C)DMA channel assignment in wireless networks,” in Proc. IEEE Conf. Computer Communications, Vol. 2, Kobe, Japan, pp. 900-907, April 1997. [12] R. Agarwal and M. MOTWANI, "Survey of clustering algorithms for MANET ," IJCSE, Vol. 2 Issue 2, pp. 98-104, 2009. [13] T. W. Rondeau and C. W. Bostia, Artificial Intelligence in Wireless Communications, Artech House, Boston, 2009.