Imperialist Competitive Algorithm for DSA in Cognitive Radio Networks Mahboobeh Parsapoor
Urban Bilstrup
School of Information Science, Computer and Electrical Engineering Halmstad University Halmstad, Sweden
[email protected]
School of Information Science, Computer and Electrical Engineering Halmstad University Halmstad, Sweden
[email protected]
Abstract—In this paper a novel optimization method called imperialist competitive algorithm (ICA) is applied to solve the channel assignment problem in a mobile ad hoc network. First the imperialist competitive algorithm (ICA) is described, which has been proposed as an evolutionary optimization method, and after that it is explained how it can seek a near optimal solution for the channel allocation problem in a cognitive mobile ad hoc radio network. The simulation results are compared with the results that were obtained by applying island genetic algorithm. Keywords- cognitive radio networks; dynamic spectrum access; imperialist competitive algorithm; interference power
I.
INTRODUCTION
Dynamic spectrum access has been proposed as one of the most important task of a cognitive radio. Various types of AI algorithms have been proposed for autonomic management of spectrum access. Based on the analysis of spectrum, a cognitive manager make decisions about transmission parameters (e.g. transmit power, frequency, time duration, etc.) to optimize the desired objective functions. The objective function can for example be defined as throughput, interference and the required quality of service (QoS) [1]-[2]. Finding an optimal channel allocation to minimize some objective function for example interference is unfortunately a NP-hard problem. Thus, heuristic methods must be applied to find near-optimal channel [3]-[4]. In cognitive radio networks, different types of AI algorithms have been applied for the channel allocation problems [5]. In fact, depending on the architecture of the cognitive radio network, different methods can be applied. For example, in a mobile ad hoc network where the availability of channel is dynamic, genetic algorithms (GAs) have been proposed to solve the channel allocation problem [5] with the objective function of minimizing interference. The next section gives a short review of heuristic methods applied for the channel. Sec. III, describes channel allocation problem in cognitive radio networks. ICA, is applied for channel allocation in cognitive radio networks in sec. IV. Finally, we conclude the paper and give some final remarks about ICA in Sec. V.
II.
A SHORT REVIEW OF DYNAMIC SPECTRUM ACCESS
Dynamic spectrum access (DSA) has been defined as a method to adapt the usage of spectrum resource to the present situation and the user requirements [2]. Different heuristic methods differ from each other in terms of DSA models and the specific architecture of the radio network, e.g. it is classified as centralized and distributed. For centralized DSA, optimization and auction theory methods have been applied for finding a near optimal solution. For optimization-based methods the objective function is often to minimize interference-temperature or maximize the transmission rate. While auction-based methods often have an objective function that is related to economic aspects. So far, several AI methods, such as genetic algorithms (GAs), Markov chain model and game theory have been suggested to solve the channel allocation problem in cognitive radio networks. III.
THE CHANNEL ALLOCATION PROBLEM
In this paper we are considering the same model and taking the same assumption as done in [5], accordingly the channel allocation problem can be formulated as follows: 1. The cognitive radio network has N cr cognitive nodes (1). NODE = n1 ,..., nN cr (1)
{
2.
}
There are L full duplex links.
3. The network is defined by a communication graph given by (2). Gc = ( NODE , Lc ) (2)
Where Lc is a set of direct links between ni , transmitting node i, and n j receiving node j. 4. Another graph (3) is defined as the interference graph, the set of transmissions that interfere at the
978-1-61284-683-5/12/$31.00 ©2012 IEEE
and the initial population size, N pop , is
receiving nodes’ of L .
c
GI = ( NODE , LI )
(3)
5. The cognitive nodes sense the spectrum to find available channels. Thus, for each node a set of available channels, Ci , are determined. There are N cr sets of available channels for the cognitive radio network. 6. The available channels for each link are the intersection between these two sets. For each link between two nodes i and
j , H i , j = Ci ∩ C j defines the available
channels. 7. Each possible combination of selecting the channels are given by h which is a vector of length L . The element of h determine the channel that is allocated to the link that is between
ni and n j .
8. An near optimal channel allocation is a vector, h , that maximizes the equation of (4).
f(h) = (
∑
wi , j h
li , j ∈LC 1+ Li , j
)
(4)
h
Here, wi , j , is the capacity of each link and Li , j is the number of links that suffers from interference under channel allocation h . The possible combination of channels allocations grows exponentially with increasing number of nodes. Thus, the channel allocation problem is a NP-hard problem [3]-[5]. Evolutionary algorithms are well-known optimization methods for NP-hard optimization problem. Next section suggests a new type of evolutionary optimization method to solve the channel allocation problem. IV.
countries. The population, the countries, is classified into two groups: the colonies and the imperialists. As a first step of ICA, an initial population is defined, i.e., countries. Then, the empires are formed; each empire consists of one imperialist and some colonies. The countries that have the highest costs are considered as the imperialists. They start to take possession of colonies, countries with lowest costs. In this way, each imperialist creates an empire. After forming the empires, the movement of colonies toward the imperialists is started. An assimilated colony moves toward the relevant imperialist by x units. Where x is a random value from the uniform distribution as (6).
x =U(0,β ×d)
{
country = f1 ,..., f N p
}
(5)
Where N p is the number of parameters for each solution,
(6)
Where d is the distance between a colony and its corresponding imperialist. Due to the movement of colony to its imperialists, it may reach to a higher cost than it’s imperialist. Thus, the position of colony and imperialist must be exchanged. The last evolutionary step of ICA is a competition between imperialists to take possession of the weakest colonies of weakest empires. This competition leads to increase the cost of the powerful imperialist and decrease the cost of the weakest imperialist. During the competition, the weakest colony from the weakest empire is picked and joined to the most powerful imperialist. The weakest empires, whose colonies are joined to other empires, will be eliminated. The algorithm is converged to a global optimum when there is one empire [7]. The following evolutionary operators are used by ICA : 1.
Assimilation operator: this operator updates the cost function of colonies by moving them to their corresponding imperialist.
2.
Revolution operator: this operator updates the cost function of colonies through random change of some features of colonies, optimization parameter.
3.
Exchange operator: this operator updates the position state of colonies and imperialists.
4.
Competition operator: this operator updates the position of the colonies from one imperialist to another, in fact imperialists start competing to take possession of colonies of each other.
IMPREALIST COMPETITIVE ALGORITHM FOR CHANNEL ALLOCATION
A. Imperialist Competitive Algorithm The Imperialist Competitive Algorithm (ICA) is an optimization method based on human social evolution [7]. It is an evolutionary algorithm that has been inspired by the competition between the imperialists to take possession of other countries. An individual in ICA is defined as a country and the optimization parameters are referred as the cultural features. Thus, a solution can be defined using Equation (5) [7].
the number of
B. ICA applied to the Channel Allocation problem To solve the channel allocation problem using ICA, each country, a set of optimization parameters, is defined as a vector of allocated channels (7).
Country = {...,hi , j ,...}
(7)
The initial population is generated by selecting features
{
}
from the intersection links, H = ..., H i , j ,... , in a random manner. The cost of each country is calculated according to (4). The imperialists are determined based on the values of cost functions and the empires are formed. Thus, the initial population is divided into the colonies and the imperialists, which take procession of the colonies based on their powers,
2.
The distance, D colony ,imprialist , between the colony, which is chosen to move toward its imperialist, and the imperialist is calculated. The round ( x ) is calculated to determine the number of the colony’s features that should be assimilated to the corresponding features of its imperialists. The round ( x ) represent the number of links whose allocated channels should be changed. Where x is chosen from a random uniform distribution using (13).
x = U(0,β × N diffi )
(13)
Where N diff is the number of colony’s features that
pi ,using Equations (8), (9) and (10).
differs with corresponding features of imperialist.
COST = {...,cos ti ,...}
(8)
N _ cos ti = cos ti − min(COST)
(9)
3. For each feature, which was chosen in the previous step, a random channel from the set of available channels for that link is chosen. As mentioned before, for a link, li , j , H i , j is the set of available channels for that link.
pi =
N _ cos ti
(10)
pop
∑ N _ cos ti i =1
First the normalized cost, N
_ cos ti , for each imperialist is
calculated using (9). Using (10), the normalized power,
pi , of
each imperialist is calculated. The normalized power shows the ability of imperialist to take possession of colonies. The number of colonies that are joined to each imperialist is determined by using (11).
N colony ,i = round ( p i
× N
colony
)
(11)
The revolution operator is performed in two steps: First step: round ( x ) determines the number of colonies that should be generated, x is chosen from a uniform distribution using (14). Where
1
Rrev is first revelation rate.
1
x = U(0,R rev )
(14)
Second step: this step is done if there is no change in cost functions during a number of iterations. Thus, round ( x ) determines the number of features that should be changed, where x is chosen from a uniform distribution (15). It can be considered as regeneration. Where
Where N colony ,i shows the number of colonies of the i th imperialist.
1.
revelation rate. 2
Following steps explain the assimilation operator for channel allocation problem: For each empire, round ( x ) is calculated to determine the number of the colonies to move towards their corresponding imperialist. Where x is a random variable with a uniform distribution using (12). Where N colony ,i is the number of colonies of this empire.
x = U(0,β × N colony ,i )
(12)
2
R rev is second
x = U(0,R rev ) V.
(15)
SIMULATION RESULTS
For the evaluation, we consider three scenarios, networks containing 5, 20 and 25 nodes uniformly distributed in a square. Similar to [5], the area of the square is based on the number of nodes. Thus, 100 nodes are placed in a 1700×1700 meter square area. The transmission range and interference range of each node is 250 meters and 500 meters. Each node senses 20 channels with the same capacity and selects Ci channels as a set of the available channels. The upper limit and the lower limit for the number of selected channels are 2 and 8 respectively.
VI. Table I and Table II present the average of maximum values of f (h ) and the number of iterations for different number of nodes. The simulation is repeated 10 times for each scenario. As can be seen In table II, for a network with more than 20 nodes, the ICA is converged to near-optimal solution using the less number of iterations than the Island genetic algorithm. TABLE I. DIFFERENCE BETWEEN THE OBJECTIVE FUINCTION OF ICA AND GA FOR CHANNEL ALLOCATION PROBLEM IN AD HOC NETWORKS WITH DIFFERENT NODES Cognitive Radio Networks 5 Nodes
20 Nodes
25 Nodes
ICA
8.6
25.84
26.24
Island_GA[5]
9.0
18.09
21.62
TABLE II.
DIFFERENT NUMBER OF ITERATION FOR ICA AND GA FOR CHANNEL ALLOCATION PROBLEM IN AD HOC NETWORKS WITH DIFFERENT NODES Average of number of iteration
Cognitive Radio Networks 5 Nodes
20 Nodes
25 Nodes
ICA
5
19.5
21.5
Island_GA[5]
1
29.6
29.2
It is obvious that increase in the number of nodes, increases the number of iteration that is necessary to converge. Table I presents the performance of ICA to find a near-optimal solution for the channel allocation problem in small-scale networks. Fig.1 depicts the values of f (h ) during the iterations for networks with different nodes. Ii indicates the robustness of ICA and shows how ICA converges to the maximum value already after 27th iteration. The number of possible solutions is near to 1.5E+08 [5] that is a large space to search. However, ICA shows a flexible characteristic in searching for nearoptimal solution.
In this paper, we propose a novel optimization method called ICA for the channel allocation problem in cognitive radio networks. We applied ICA as a centralized method with the objective function of minimizing interference between nodes. In previous work ICA has been applied as a continuous optimization method which is not applicable for the channel allocation problem, a discrete optimization problem. We propose a discrete optimization method based on ICA and define procedures for the two evolutionary operators, assimilation and revolution. The performance of ICA is evaluated by applying it to networks with different number of nodes. The convergence is compared with Island Genetic algorithm. The obtained results indicate that ICA has the ability to converge fast. In comparison with island genetic algorithm, ICA requires less number of iteration to achieve the same results. As future work, a multi-objective function to maximizing the spectral efficiency and minimizing interference power will be defined. Also we will suggest a distributed optimization method based on ICA for the cognitive manager. We will apply it for optimizing other objective functions such as throughput and the required quality of service in cognitive radio networks. REFERENCES [1] [2]
[3] [4]
[5]
[6]
[7]
Figure 1. The value of cost function versus number of iterations, for networks with 20 nodes (dashed line) and 25 nodes (dotted line).
CONCLUSION
T. W. Rondeau and C. W. Bostia, Artificial Intelligence in Wireless Communications, Artech House, Boston, 2009. E. Hossain, D. Niyato, Z. Han, Dynamic Spectrum Access and Management in Cognitive Radio Networks, Cambridge University Press, UK, 2009. S. Matsui, I. Watanabe, and K. Tokoro, "Application of the parameter free genetic algorithm to the fixed channel assignment problem", presented at Systems and Computers in Japan, pp. 71-81, 2005. X. N. Fu, A. G. Bourgeois, P. Z. Fan, and Y. Pan, "Using a genetic algorithm approach to solve the dynamic channel-assignment problem," International Journal of Mobile Communications (IJMC, USA), Vol.4, No.3, pp.333-353, 2006. D. H. Friend, M. Y. El Nainay, Y. Shi, and A. B. MacKenzie, “Architecture and Performance of an Island Genetic Algorithm-based Cognitive Network”, in Proc. IEEE CCNC’08, (LasVegas, NV), pp. 993–997, 10–12 Jan. 2008. N. Baldo, A. Asterjadhi, M. Zorzi, "Dynamic Spectrum Access Using a Network Coded Cognitive Control Channel," IEEE Transactions on Wireless Communications, Vol.9, pp.2575-2587, 2010. E. Atashpaz-Gargari, C. Lucas, "Imperialist Competitive Algorithm: An algorithm for optimization inspired by imperialistic competition". IEEE Congress on Evolutionary Computation 2007, pp. 4661–4666, 2007.
