Distributed Frequency Assignment Using Hierarchical Cooperative Multi-agent System *

Recent demand for wireless communication continues to grow rapidly as a result of the increasing number of users, the emergence of new user requirements, and the trend to new access technologies. At the same time, the electromagnetic spectrum or frequencies allocated for this purpose are still limited. This makes solving the frequency assignment problem more and more critical. In this paper, a new approach is proposed using self-organizing multi-agent systems to solve distributed dynamic channel-assignment; it concerns distribution among agents which task is to assign personal station to frequencies with respect to well known constraints. Agents only know their variables and the constraints affecting them, and have to negotiate to find a collective solution. The approach is based on a macro-level management taking the form of a hierarchical group of distributed agents in the network and handling all RANs (Regional Radio Access Network) in a localized region regardless of the operating band. The approach defines cooperative self-organization as the process leading the collective to the solution: agents can change the organization by their own decision to improve the state of the system. Our approach has been tested on PHEADEPHIA benchmarks of frequency assignment Problem. The results obtained are equivalent to those of current existing methods with the benefits that our approach shows more efficiency in terms of flexibility and autonomy.


Introduction
With growth in the demand of mobile telephone services, the efficient use of available spectrum is becoming increasingly important.The studies of a frequency assignment problem (also called a channel assignment problem) in cellular mobile systems are so abundant [1][2][3][4][5].Various Artificial Intelligent (AI) techniques, including constraint satisfaction, simulated annealing, neural networks, taboo search, and genetic algorithms, have been applied to this problem [6][7][8][9][10][11][12].
An overview of the frequency assignment problem is as follows: For an existing set of, geographically divided, regions (called cells-typically hexagonal), frequencies (channels) must be assigned to each cell according to the number of call requests.Three types of electro-magnetic separation constraints exist. Co-channel constraint: the same frequency cannot be assigned to pairs of the cells that are geographically close to each other. Adjacent channel constraint: similar frequencies cannot be simultaneously assigned to adjacent cells. Co-site constraint: any pair of frequencies assigned to the same cell must have a certain separation.The goal is to find a frequency assignment that satisfies the above constraints using a minimum number of frequencies (more precisely, using the minimum span of the frequencies).It must be noted that there exist several variations of frequency assignment problems.The benchmark problems provided by the EUCLID-project Combinatorial Algorithms for Military Applications (CALMA) project are well-known in the constraint satisfaction/ optimization research community.This type of problem arises from a military application, and geographical information including cells is not described in the problem specification.Constraint satisfaction/optimization techniques can solve this type of problem quite efficiently.
The objectives of this paper are twofold.First, present and formulate the problem of frequency assignment.Second, establish a perspective of resolution based on the application of Hierarchical Multi-Agents System (HMAS) for an intelligent resources management that allows inserting dynamically the new links in the basin of the network.Unlike centralized conventional methods our approach provides a distributed management framework, which deals with intelligent behavior which is the product of cooperative activity of several agents to fill the limits of classical Artificial Intelligence (AI) for solving this complex problem.Through a passage of individual behavior to collective behavior characterized by a distributed control of distributed among entities (agents) governed by simple rules.Instead of representing each call as a variable, we represent a cell as a variable that has a very large domain.Furthermore, we determine the variable value step by step instead of determining a variable value at one time.To each cell is associated a cooperative agent that handles the assignment of a frequency.Within a Radio Area Network-RAN (Regional Radio Access Network) and at each step, an agent is elected by all its neighbors.The election is based on empirical rules for calculating the degree of separation of an agent, the degree of saturation and the improvement claimed by the neighbors for an assignment.The elected agent assigns the smallest frequency in the spectrum that meets all its constraints.In the case of a non permitted assignment, the agent may be served by a neighboring RAN, through a mechanism of cooperation between supervisor agents of both RANs.If no proposal has been received, the supervisor agent can make a Taboo Search for an improvement in the overall assignment in the associated RAN.
The rest of this paper is organized as follows.In Section II, we review the research contributions in the area frequency assignment.In Section III, we formulate the frequency assignment problem.In Section IV, we describe our resolution approach to this problem that utilizes hierarchical multi-agent system.Section V is reserved to show experimental evaluations using standard benchmark.Finally, Section VI concludes our work with a comparison to other current research and a projection for future issues.

Related Work
The current challenges in radio networks are: to ensure an efficient and full use of radio frequency resources and multimedia applications, Connect at best anywhere, anytime and with any network.Customize the more powerful features stimulated by the increasing consumers' demand.Find solutions for the mobile business.And tend toward several access technologies whose assignment is local and continuously and independently updated, ren-dering impossible any overall control.This lead to a very interesting and pertinent issue for radio spectrum is dynamic spectrum assignment problem.
The problem starts from some networks initial connections (namely robust) to develop progressively the subsequent connections according to the operational change of communication needs and taking into account the constraints of disturbances with all initial connections.
Constraint satisfaction techniques are a board family of greedy algorithm that guarantees an exhaustive search in the search space of a complete solution.But in some cases it can be impossible or impractical to solve these problems completely and the time and effort required to the search may be prohibitive, and the most straightforward way for solving such problems using constraint satisfaction techniques would be to represent each call as a variable (belonging to the domain of available frequencies), then to solve the problem as a generalized graphcoloring problem [7].However, solving real-life, largescale problems' using this simple formulation seems rather difficult without avoiding the symmetries between calls within one cell [2].
Unlike greedy methods, meta-heuristics seek to find an optimal solution with a good compromise in a reasonable time.These techniques are nowadays widely used; such as the following techniques that have become popular: Simulated Annealing (SA), Taboo search (TS), and Genetic Algorithms (GAs).
The taboo search technique is based on the intelligent search and embraces more efficient and systematic forms of direction of search.
The simulated annealing technique (SA) is a stochastic computational technique used for solving big optimization problem such as frequency assignment problem, by determining the global minimum value of an objective function with various degrees of freedom subject to the problem in a reasonable amount of time.This technique is more efficient than the Taboo search technique; its advantages are its generality and its capability to move to states of higher energy.On the other hand the Taboo Search (TS) presented her does not support this feature.This is why TS cannot run away from likely local minima and normally results inferior configurations [6].
Another way of the problem resolution consists of representing a cell as a variable that has a wide area of values, and tries to determine the value of this variable step by step instead of determining a value for this variable at one time.
Recently, neural networks have been considered one of these ways for the channel assignment problems.The  advantages of the algorithm are its inherent parallelism, its property to detect areas of different problem difficulty without heuristics, and the possibility of extending the algorithm to 'soft' interference criteria.One major disadvantage of a neural network is that it gives the local optimal value rather than the global optimal value.And the solution varies depending on the initial values [17].
Genetic Algorithms (GA) have an advantage over Neural Networks or Simulated Annealing in that genetic algorithms are generally good in finding very quickly an acceptably good global optimal solution to a problem [1]; even if, genetic algorithms do not guarantee to find the global optimum solution to the problem.In this algorithm, the cell frequency is not fixed before the assignment procedures as in the previously reported channel assignment algorithm using neural networks [17].But the Genetic algorithms are expensive in computing time, as they handle multiple solutions simultaneously.

Frequency Assignment Problem Formulation
A frequency assignment problem can be formalized as follows: Let be a set of n transceivers (TRXs), be the set of valid frequencies that can be assigned to a transceiver i t T  , (the cardinality of Fi could be different to each TRX).Furthermore, let be a set of given sectors (or cells) of cardinality m.Each transceiver i is installed in exactly one of the m sectors and is denoted as The set of constraints is represented by a m*m matrix called matrix of compatibility:  are numerical values greater than or equal to zero and they represent the mean and standard deviation respectively, of a Gaussian probability distribution used to quantify the interferences ratio (C/I) when sector i and j operate on a same frequency.Therefore, the higher the mean value is, the lower interferences are, and thus it will have a superior communication quality.A solution to the problem lies in assigning to all the TRXs (t i ) a valid frequency from its domain (F i ), in order to minimize the following cost function: where C sig will compute the co-channel interferences (C co ) and the adjacent-channel interferences (C adj ) for all sector t and u, in which the transceivers t and u are installed, that is, s(t) and s(u), respectively. are the interference matrix values at the entry M(s t , s u ) for the sectors s t and s u .In order to obtain the C sig cost from Equation (1), the following conditions are considered: where K, being a very large value, is defined in the configuration file of the network.The K value makes it undesirable to allocate the same or adjacent frequencies to TRXs that are installed in the same sector.In our approach to solve this problem, this restriction was incorporated in the creation of the new solution (frequency plan) produced by the algorithm.Therefore, we assure that the solution does not have this severe penalty, which causes the most undesirable interferences as shown in [1] and [3].

Resolution Approach and Development
The approach comes in the form of a group of distributed agents in the network where each regional network is overseen by a supervisor agent.That it combines an agent to each cell called a station agent.

Station Agent
An agent can be defined as a computer system located in an environment and which can act autonomously and flexibly to achieve the objectives for which it was designed [12].
To each link l i is associated an agent Ai responsible of assigning a value f i in its domain D i .
Two data are sufficient to characterize the agent outside its environment: First, the frequency value of the corresponding link: The agent chooses among the values in the frequency domain corresponding to this link: for each A i in A, the i i f D  , where is the frequency domain of l i .
i Second, the difficulty of an agent defined as a quantitative measure that reflects the current status of this agent.It is the decision criterion used to choose an agent.It is represented in the form of two essential and sufficient entities that are the degree of separation and the degree of saturation, and it is the criterion used to select the elected agent.

These two entities are intuitively and experimentally
Copyright © 2011 SciRes.IJCNS determined.
For any agent i A A  , we note the degree of separation of the corresponding link l i as the sum of the incident constraints values to stations.

 
The degree of saturation at step p is determined from the banned intervals for those links that are not yet assigned.It can be deduced by the number of unsatisfied constraints.
For i A A  , NIS(A i ) is the number of unsatisfied constraints with its value f i :   , for each such as 0 and 0

At step p and for each
The agent who has the greatest degree of saturation will be considered as the most on difficulty.
Each agent operates in a physical environment; it is its frequency domain.Even though these domains may be identical between several agents, these domains are not shared.
Similarly an agent has an unshared copy of constraints that allows it to be independent of other agents.
The social Environment consists of all neighbors of an agent from which it has only a partial view.It knows about its neighbors only their values and their difficulties.It has no idea about its neighbors' constraints, views, and domains.The communication is performed by sending messages and a mailbox is associated with each agent that stores the received messages from other agents [18].
The neighborhood of an agent Ai is defined by all agents connected by a constraint to this agent.

For each
straints is permanent.Any change of view leads to an e degree of sa ugh cooperation, the random does no d at th , the agent deactivates: he repo ill carry out the cycle (electio avior of an agent can be presented as follows: ne all of these neighbors .Any change of view leads to an immediate update of the state of constraints.The agent will be in a consistent state at any time. Behavior: The behavior of an agent takes place in three phases: One the one time and through the communication mechanism between the agent and its neighbors that is supposedly in place and robust, conducted by messages, where each message reaches in a finite time.And that each agent always handles the messages it receives, the agent manages to know the degree of saturation and values of agents in its neighborhood.Then decide if it moves or not.At the end of a movement, the corresponding environment is maintained.
The agent is autonomous, homogeneous in its behavior than its performance with those neighbors.Consistency between the view of the agent and its local con-immediate update of the state of constraints.
Thus an agent will be able to calculate th turation as soon as he knows the value of the agents in its neighborhood.These conditions are not blocking the measure in which agents communicate their information once they have them.
Note here that, thro t play a role as might be the case for other methods.This is not to randomly select an agent to explore more options.But rather to select an agent from among those agents considered equals which all lead to a good solution.So the agent with the greatest difficulty will try to improve its situation since he was elected.This phase marks one of the aspects of cooperation: agents let act the agent the greatest difficulty if it isn't the elected.
The next phase is only possible for an agent electe e previous phase.The elected agent will select and assign a value that considers the best for him and his neighbors from his private domain of values.And one that minimizes the sum of local cost constraints, based on its current information.
At the end of this phase rted to his neighborhood and his supervisor that he will not participate in the next election as one of its neighbors have not been elected.This egalitarian policy for the election allows any neighbor with the less difficulty to have the opportunity to be elected.While it is disabled, if one of its neighbors is elected, the agent is still invited to the assignment session: such deactivation is a result of the last phase.
Once booted, the agents w n, decision and assignment) but they can not finish themselves.It is the supervisor agent who will take over this task when the execution time limit is reached or a termination criterion is achieved: an overall objective corresponding to the results already known for this problem [19].

The beh
Step 1:

//the degree of saturation on
For all A j  V(A i ) such as

Supervisor Agent
The supervisor agent is first in charge of the cooperation ents associated to stations: called sta-RAN data associated to station agents: and collecting responses (until triggering a gent can communicate with other reso a blockage, a Taboo search is performed on in our forthcoming

Results
We have tested our approach of hierarchical multi agents ems/Philadelphia/ and in [20]), ulated based on an area in Ph nducted on an Intel Pentium In  between other neighbors RANs supervisor agents.Second, the supervisor agent oversees the management of assignments by:  Initializing ag tion agents. Sending all associated Frequency Domain, re-use matrix, stations rentals. Holding timeout).In case of a non permitted assignment within its RAN, the agent may resort to another supervisor agent.
The supervisor a urces outside of its frequency domain through a cooperation procedure similar to all supervisor agents of various RANs.
In the case of the overall allocation to achieve an optimal allocation of all stations of the associated RAN.This part will be considered in details publications.System (HMAS) simulated at a RAN level for the frequency assignment problem (FAP), such as it is modeled on the web page of the site of the Research Institute of Zuse Institute Berlin ZIB dedicated to an area on Philadelphia-Pennsylvania (http://fap.zib.de/probl which have been used widely in previous researches including [1, 14,15].
These problems are form iladelphia, Pennsylvania.The network consists of 21 cells as shown in Figure 1.
Our experiments were co side (with 4 GB of RAM).There are many variations for setting constraints and demands and several competing teams of researchers have worked on the same instances of problem.We present in Table 1 the parameter setting used in some approaches and adopted by ours evaluations.nce for co-channel constraints, assuming that the distance between adjacent cells is 1.For example, if N c = 12, while cell 1 and cell 5 can use the same frequency (the distance is 4), cell 1 and cell 4 cannot (the distance is 3)."acc" represents the separation required for adjacent channel constraints, and "C ii " represents co-site constraints.The demand vectors used in the table are as follows (case 3  Table 2 shows the results obtain e consider the theoretical lower-bounds as it represented in [1,5,20], and we use the best solution obtained so far.Ours results are compared with results of the best tree methods, from seven reported methods.The tree methods are: First, a constraint satisfaction method (CS) and second a Neural network (NN).thethird a Simulated Annealing (SA).The last row in the table shows our results.
To the extent of the authors' knowledge, the best pubhed results for these problems have been obtained by FASoft [1,9,15,20].FASoft is an integrated package of various methods for solving frequency assignment problems, such as heuristic sequential methods, methods using constraint satisfaction techniques, Simulated Annealing, GA, Tabu search, etc.We show the results obtained with Simulated Annealing (SA) and Tabu search (TS) reported in [9].These two methods are the most fficient among the various components of FASoft.Fur-2, our algorithm obtains optim orithm in e thermore, we show the best results obtained with a set of heuristic sequential methods (SE) reported in [5], and the results obtained with neural networks (NN) reported in [6], and the results obtained with a constraint satisfaction method (CS) reported in [1] ("..." in the table means that the result is not reported).
As shown in the To examine the efficiency of the proposed alg larger-scale problems, we show the evaluation results for the benchmark problems presented in [15,19].There are 7*7 symmetrically placed cells (49 cells in all) in these problems.Problem parameters are described in Table 3, where "C ij " is the minimal frequency separation between any pair of cells whose distance is less than c N , except for adjacent cells.19 14).This vector is randomly generated from a uniform distribution between 10 and 30.There are 976 calls in total.Table 4 shows the results obtained with our new method (hybrid Taboo search).For comparison, we show the results described in [15], i.e., the results obtained using neural networks (NN), and the best results obtained with a constraint satisfaction method (CS).
Since the optimality of the obtaine (19 1 d solution is guaranteed, and the execution time for these instances is very short, our approach obtains much better solutions than those of NN and CS for all instances and a very highquality solutions are obtained within a reasonably short running time.

Conclusions and Future Issues
In this algorithm, we represent a link as a variable with a rimental evaluations using real standard benchm ll-suited to this proble

Acknowledgements
The authors are grateful to all members of the Laboratory

References
[1] M. da S. Maximiano, M. A. Vega-Rodríguez, J. A. Gómezvery large domain, and determine the variable value dynamically and step by step.Which is handled by a computer system located in the environment and can act autonomously and flexibly to achieve the objectives for which it was designed.Furthermore, we have developed a powerful cell-ordering heuristic and introduced the limited discrepancy search to cope with large-scale problems.
Expe ark problems showed that for most of the problem instances, our approach can find better or equivalent solutions compared with existing current optimization methods.These results imply that paradigm of distributed agents is capable of solving realistic application problems, if we choose the appropriate problem representation, and provides a conceptual framework for modeling and simulating a complex system.Furthermore, it is particularly we m and offers distinct advantages compared to existing methods.It incorporates an extra macro-level management and handling all RANs in a localized region regardless of the operating band, where each regional network is overseen by a supervisor.It shows more efficiency in terms of flexibility and autonomy.It is continuously adaptable for a new insertion if a reallocation of radio frequency resources must be made.Since the system can be added to, modified and reconstructed, without the need for detailed rewriting of the application.This system also tends to be rapidly self-recovering and failure proof, usually due to the heavy redundancy of components and the self managed features.We can say that our approach is justified by: Adapting to reality, cooperation, the integration of expertise incomplete, modularity, effectiveness and reliability.Our future works also include evolutionary multi-agent algorithms that are stronger, introducing the hybrid genetic algorithms with iterative improvement of search.
of Electronics and Telecommunications in Mohammadia School of Engineers (EMI) for the contribution of their ideas, and for the contribution of such an approach and who, in one way or another, have helped to improve it.
affects the frequency f, D i the A i main A

Figure 1 .
Figure 1.Cellular geometry of philadelphia problems.

(A i ) ;
i

Table 2 . Comparaison of solution quality.
Table al solutions for all instances.Moreover, this method can obtain better or equivalent solutions compared with existing methods for all problem instances,