Assignment of cells to switches using firefly algorithm

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Assignment of cells to switches using firefly algorithm

  1. 1. InternationalINTERNATIONAL Communication Engineering & Technology (IJECET), ISSN 0976 – Journal of Electronics and JOURNAL OF ELECTRONICS AND COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEISSN 0976 – 6464(Print)ISSN 0976 – 6472(Online)Volume 3, Issue 3, October- December (2012), pp. 211-218 IJECET© IAEME: www.iaeme.com/ijecet.aspJournal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEMEwww.jifactor.com ASSIGNMENT OF CELLS TO SWITCHES USING FIREFLY ALGORITHM Deepak Sharma1, Rajesh Kumar2 and Shrikant3, 1 (Department of Electronics and communication, Panipat Institute of Engg. and Technology, Samalkha, Panipat, India, tcmdeepak@gmail.com) 2 (Department of Electronics and communication, Panipat Institute of Engg. and Technology, Samalkha, Panipat, India,kr_rajesh88@rediffmail.com) 3 (Department of Electronics and communication, Panipat Institute of Engg. and Technology, Samalkha, Panipat, India, writetoshrikantjoshi@gmail.com) ABSTRACT In this paper we consider the problem of assignment of cells to switches in an optimum manner. It is a combinatorial optimization problem that is known to be NP-hard. We consider three types of costs. One is the cost of handoff between cells. The other is the cost of cabling or trunking between a cell and its associated switch. The third cost is switching cost which includes the cost for transferring a call to other switch. The problem is constrained by the capacity of switch and assignment of a cell to a unique switch. Firefly algorithm is implemented in this paper to solve the problem of assignment of cells to switches and results are compared with that of Particle swarm optimization. Keywords: Firefly algorithm, Optimization, Particle swarm optimization.I. INTRODUCTION During the last 30 years, there has been a tremendous growth in the deployment of mobile communication systems. Now a days the mobile networks are migrating towards broadband services based on high speed wireless access technologies [1]. Even though significant improvement to communication infrastructure has been aimed in the mobile industry, the issues concerning the assignment of cells to switches in order to minimize the cabling cost, handoff cost and switching cost in a reasonable time still remain challenging. The same problem is addressed in this paper. Our motive is to minimize three costs namely: cabling cost, handoff cost and switching cost. Cabling cost involves the consumption of resources while maintaining communication link 211
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME between two users [2]. A handoff occurs when the mobile network transfer the call from one base station to another. Merchant [3] gave a comprehensive description about handoffs. Intuitively, the cells among which the handoff frequency is high should be assigned to the same switch as far as possible to reduce the cost of handoffs. The consumption of resources when a call is switched from one Mobile Switching Center (MSC) to another comes under switching cost. Switching cost occurs when two user which are communicating belong to different MSCs. However, since the call handling capacity of each switch is limited, this should be taken as a constraint. Incorporating the cabling cost, handoff cost and switching cost that occurs when a call is connected between a cell and a switch, we have an optimization problem, called the cell to switch assignment problem. In the field of deployment of mobile communication system Arif Marchant and Bhaskar Sengupta [5] added there precious idea of assignment of cells to the switches in 1995. After then a number of ideas comes in the same series. In 1999 Partha Sarathi Bhattacharjee, Debashis Saha, Amitava Mukherjee [9] presented a paper for comparative study of various heuristics proposed to solve the problem of optimally assigning cells to switches in a Personal Communication Services (PCS) Network. In 2000 some work has been done by Partha Sarathi Bhattacharjee, Debashis Saha, Amitava Mukherjee [12] with the problem of balancing traffic (load) amongst MSCs. SwarupMandal, DebashisSaha, AmbujMahanti [13] in 2002 presented a paper in which the assignment of cells to switches was done using the novel Block Depth First Search (BDFS) [13] algorithm using an admissible heuristic so as to minimize the paging, updating and physical infrastructure costs. Samuel Pierre and Fabien Houeto [14] solved the same problem using Taboo Search. In 2002 Alejandro Quintero and Samuel Pierre solved the same problem of using Memetic Algorithm [15]. In 2004 SwarupMandal, DebashisSaha, AmbujMahanti proposed a technique to assign the cells to the switches to minimize a total cost of operation (TCO) [16]. Syam Menon and Rakesh Gupta [17] in 2004 presented the idea of price mechanism using Simulated Annealing. In 2008 a paper is published by Siba K. Udgata, U. Anuradha, G. Pawan Kumar, Gauri K. Udgata [22] in which the problem of assignment of cells to switches is solved using an algorithm of Swarm Intelligence. This paper presented idea to solve the problem of assignment of cells to switches using Firefly Algorithm. In next section the mathematical formulation has been done for this problem. In the next section it is shown how firefly algorithm can be implemented for this problem. Then in section VI experiments and results are displayed and the last section contains conclusion and future scope.II. PROBLEM FORMULATION The problem of assignment of cells to switches was first introduced by Arif Merchant and BhaskarSengupta [3] in 1995. The assignment of cell to the switches is an NP-Hard problem, having an exponential complexity (n cells and m switches). He introduced two types of costs namely handoff cost and cabling cost. He also proposed a heuristic method to solve this problem. Now in this paper another cost called Switching cost [6] is introduced which is the cost for 212
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEMEtransferring a call form one switch to another. Thus in this paper we have an optimizationproblem for minimizing the above costs which is stated as follows: Assign all the cells in a geographical area to the available number of switches in order tominimize the total cost which is the sum of cabling cost, handoff cost and switching costmaintaining the following two constraints. 1) Each cell must be assigned to exactly one switch and 2) Each switch has some limited capacity and assignment of cells must be done in such a way so that the total load on the switch should not exceed the capacity of the switch.Various symbols used are: • Let no. of cells be ‘n’ and no. of switches be ‘m’ • hij – handoff cost between cell i and cell j • cik – cabling cost between cell i and switch k • dij – distance between cell i and switch (MSC) j • Mk – call handling capacity of switch k • λi - No of communication in cell i • Yij – 1 if cell I and j are assigned to same switch and 0 otherwise. • Xik – 1 if cell I is assigned to switch k and 0 otherwise.For all cases, the range of i, j and k are defined as: 1 ≤ ݅ ≤ ݊, 1 ≤ ݆ ≤ ݊, 1 ≤ ݇ ≤ ݉2.1 Formulation of Constraints 1) Each cell must be assigned to exactly one switch ௠ ෍ ‫ݔ‬௜௞ = 1, 1 ≤ ݅ ≤ ݉ (1) ௞ୀଵ 2) Each switch has some capacity ௡ ෍ ߣ௜ ‫ݔ‬௜௞ ≤ ‫ܯ‬௞ , 1 ≤ ݇ ≤ ݉ (2) ௜ୀଵ2.2 Formulation of cost Function2.2.1 Total Cabling CostThis is formulated as a function of distance between base station and switch and number of callsthat a cell can handle per unit time [7]. ܿ௜௝ (ߣ௝ ) is the cost of cabling per kilometre which is alsomodelled as a function of the number of calls that a cell can i handles as: ܿ௜௝ = ‫ܣ‬௜௝ + ‫ܤ‬௜௝ ߣ௝ (3) ௠ ෍ ܿ௜௝ (ߣ௝ )݀௜௝ ‫ݔ‬௜௝ , ݅ = 1,2, … ݊ (4) ௝ୀଵ2.2.2 Total handoff costWe consider two types of handoffs, one which involves only one switch and another whichinvolves two switches. The handoff that occurs between cells that belong to the same switchconsume much less network resources than what occurs between cells that belongs to twodifferent switches. 213
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME ௡ ௡ ෍ ෍ ℎ௜௝ (1 − ‫ݕ‬௜௝ ) (5) ௜ୀଵ ௝ୀଵ 2.2.3 Total Switching Cost Let βi is the total no of calls MSC i can handle per unit time and Fi(βi) is the cost function of switching a call in MSC i. Thus the load at MSC i is given by: ௡ ߚ௜ = ෍ ߣ௝ ‫ݔ‬௝௜ , ݅ = 1 … ݉ (6) ௝ୀଵ Fi(βi) involves both the cost of switching and the cost of maintaining a call at MSC. Thus Fi(βi) can be represented as: ‫ܨ‬௜ (ߚ௜ ) = ߙ⁄(ߤ௜ − ߚ௜ ) , ߚ௜ < ߤ௜ (7) Where ߤ௜ denote the call switching capacity of MSC i and α is a constant. The total switching cost involved is defined by: ௠ ෍ ߚ௜ ‫ܨ‬௜ (ߚ௜ ) (8) ௜ୀଵ So our objective is to minimize the total cost which can be formed by the summation of all three costs. The objective function is given by: ௠ ௡ ௡ ௠ ݂ = ෍ ܿ௜௝ (ߣ௝ )݀௜௝ ‫ݔ‬௜௝ + ෍ ෍ ℎ௜௝ (1 − ‫ݕ‬௜௝ ) + ෍ ߚ௜ ‫ܨ‬௜ (ߚ௜ ) (9) ௝ୀଵ ௜ୀଵ ௝ୀଵ ௜ୀଵIII. EXISTING METHODOLOGIES Assigning cells to switches in cellular mobile network being an NP-hard problem and enumerative search methods are not appropriate to solve large sized instances of this problem [8]. Thus, heuristic approaches, like Genetic Algorithm [9] [10], Tabu Search [8], Simulated Annealing [2], Memetic Algorithm [11], Ant Colony Optimization [12] and Particle Swarm Optimization [13] have been developed for this kind of problem. These are the heuristics and meta-heuristics proposed by various authors to solve assignment of cells to switch problem. An experimental result from various authors shows that those techniques are to their best depending upon the problem size. The experiment conducted by the author Shxyong Jian Shyu [14] shows that ACO gives better results for cell assignment problem compared to other existing methods. Siba K. Ugata [6] uses PSO for solution of same problem and found better results then ACO. All these algorithms considered only cabling cost and handoff cost except [6]. In our approach we also added switching cost to the total cost.IV. IMPLEMENTATION OF FIREFLY ALGORITHM Firefly algorithm is developed by Xin-She Yang [7] in 2008 which is inspired by the mutual attraction of fireflies based on the absorption of light and distance between two fireflies. Algorithm considers that each firefly has fixed position in the space and it always move towards a greater light source, then is his own. 214
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME Firefly algorithm idealizes some of the characteristics of the firefly behavior. They follow three rules: 1) All the fireflies are unisex, 2) Each firefly is attracted only to the fireflies, that are brighter than itself; strength of the attractiveness is proportional to the firefly’s brightness, which attenuates over the distance; the brightest firefly moves randomly and, 3) Brightness of every firefly determines its quality of solution; in most of the cases, it can be proportional to the objective function. Using these three rules Firefly Algorithm may look as follows: Step 1 • Initialize the number of cells (n), switches (m) and number of fireflies (p) in the solution space. • Initialize position of cells and switches randomly in the search space. • Calculate distance between each cell and switch. Here this distance is simple Euclidean distance. Step 2 • Generate the assigned matrix (xij) for each firefly where each particle is between 0 and 1. • The row of the matrix represents switches and column represents cells. Step 3: Obtain solution matrix from the assigned matrix by making the largest value of each column to 1 and all other are set to 0. Step 4: Calculate the total cost based on this solution matrix using (9). Step 5 • On the basis of cost calculated in step 4 the brightest firefly is found which has the minimum cost for the assignment. • Now update the position of all fireflies based on the attractiveness and distance of other firefly. • Now update the position of best firefly randomly. Step 6: Repeat step 3 to 5 until stopping criterion is met.V. EXPERIMENTS AND RESULTS To test the effectiveness of Firefly Algorithm for the cell assignment problem, we design and conduct a series of experiments. All the experiments are done using a MATLAB code for various cases of cells and switches for firefly algorithm. Regarding the test problems, we assume that the cells lie on a hexagonal grid of roughly equal dimensions in 2 dimensions. The parameters used for firefly algorithm are number of cells (n), number of switches (m) and number of fireflies (p). Values of constants used are as follows: • Randomness, α=1 • absorption coefficient, γ=1 • brightness at source, β=1 The parameters used in the initialization of problem are: 215
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME • handoff cost between two cells= 0 to 14 per hour • constant A used in cabling cost=1 • constant B used in cabling cost=0.001 • call handling capacity of a switch=98000 • constant α used in switching cost=40 • number of communication in a cell=0 to 200 per hour Table - 1 Experimental Result Switches, Total cost Total Cost Execution Execution cells (Firefly) (PSO) Time (Firefly) Time (PSO) 2, 25 1915 1936 0.152 0.201 2, 50 7894 7954 0.174 0.228 2, 100 33414 33528 0.205 0.259 2, 150 78213 78279 0.342 0.383 2, 200 134200 134280 0.489 0.514 2, 250 216370 216410 0.542 0.668 3, 25 2417 2478 0.163 0.203 3, 50 10973 11022 0.187 0.229 3, 100 45208 45290 0.213 0.261 3, 150 102230 102310 0.254 0.315 3, 200 181870 181920 0.305 0.357 3, 250 288090 288160 0.364 0.388 5, 25 2979 3011 0.201 0.282 5, 50 13642 13735 0.225 0.311 5, 100 54395 54481 0.251 0.345 5, 150 124880 124940 0.292 0.369 5, 200 220030 220160 0.355 0.377 5, 250 344020 344180 0.403 0.409 10, 25 3711 3800 0.278 0.304 10, 50 15273 15411 0.296 0.318 10, 100 61999 62158 0.321 0.339 10, 150 138280 139020 0.367 0.371 10, 200 248710 249360 0.409 0.411 10, 250 390140 391420 0.461 0469 216
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME 5.1 Analysis of Result Motion of fireflies is best for the above values of α, β and γ. For lesser values of these parameters the change in the assignment is very low. As the number of cells and switches is increased the final cost value also increased and with these large problem instances it is taking more number of iterations and more time. We have conducted experiments to find the minimum total cost by repeating the experiments for 5, 10, 15 times for each set of parameters. These experiments reveals that the optimum cost obtained in each execution is always nearer to the average cost. The CPU time taken in each execution is also noted for comparison purpose. Table 1 shows the minimized cost for different cases of cells and switches. It also compare the minimized cost by the two algorithms: Firefly and PSO and from this list we can see that comparatively lesser cost is found using Firefly and so it is better in terms of finding minimum cost. Form experiments it is noted that the total minimized cost can be reduced with larger number of iterations and also with larger number of fireflies. From experiments it is noted that in most cases the convergence is achieved in lesser number of iterations when we have large number of fireflies but this doesn’t happen in every case. In table 1 a comparison of two algorithms in terms of CPU execution time is also shown and Firefly algorithm is better then PSO in terms of execution time also. This time difference is not so much. The CPU time will be high as the number of iterations is increased. But for same number of iterations we can see that this execution time is less in FA as compared to PSO.V. CONCLUSION AND FUTURE SCOPE From the experiments performed we can conclude that firefly algorithm can be implemented successfully for the assignment of cells to the switches. As the number of fireflies is increased the probability of finding the minimum cost and in less number of iterations is increased. The CPU time requirement is less in case of firefly algorithm as compared to PSO. We can also improve the performance of this algorithm by selecting the initial position of firefly not randomly but with any of the heuristics. It will converge to the minimum cost in comparatively lesser number of iterations. REFRENCES [1] P. Bhattacharjee, D. Saha, A. Mukherjee, Heuristics for assignment of cells to switches in a pcsn: a comparative study:, Intl. Conf. on Personal Wireless Communications, Jaipur, India, 1999, pp. 331-334. [2] Syam Menon, Rakesh Gupta, Assigning cells to switches in cellular network by incorporating a pricing mechanism into simulated annealing, IEEE Transetions on system, men and cybernetics, Part B, Vol. 34, No. 1, pp. 558-565, Feb 2004. [3] Arif Merchant and BhaskarSengupta, Assignment of cells to switches in PCS network, IEEE Transections on Networking, Vol 3 No 5, pp 521-526, Oct 1995. 217
  8. 8. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 –6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME[4] Ron Wehrens and Lutgarde M.C. Buydens, Classical and non-classical optimization methods,Encyclopedia of Analytical Chemistry, R.A. Meyers (Ed.), Ó John Wiley & Sons Ltd,Chichester, pp. 9678–9689, 2000.[5] T. Schlick, optimization methods in computational chemistry, in eds. K.B. Lipkowitz, D.B.Boyd, Reviews in Computational Chemistry, VCH, New York, Chapter 1, Vol. 3, 1992.[6] Siba K. Udgata, U. Anuradha, G. Pawan Kumar, Gauri K. Udgata, Assignment of Cells toSwitches in a Cellular Mobile Environment using Swarm Intelligence, IEEE InternationalConference on Information Technology, 2008, pp 189-194.[7] Xin-She Yang, Firefly Algorithm For Multimodal Optimization, Luniver Press, 2008.[8] P. Bhattacharjee, D. Saha, A. Mukherjee, A simple heuristic for assignment of cells toswitches in a pcs network, Wireless Personal Communication, Vol 12, pp. 209-224, 2000.[9] D.E. Goldberg, Genetic Algorithm in Search, Optimization and Machine Learning, Addison-Wesley, Reading, 1989.[10] T. Shigeyoshi, G. Ashish, Genetic Algorithm with a Robust Solution Searching Scheme,IEEE Transections on Evolutionary Computation, pp. 201-208, 1997.[11] P. Moscato, M.G. Norman, M. Balero, E. Onate, M. Jane, J.L. Larriba, B. Suarez, MemeticApproach for the Travelling Salesman Problem Implementation of a Computational Ecology forCombinatorial Optimization on message-Passing Systems, Parallel Computing and TransputerApplications, IOS Press, Amsterdam, pp. 177-186, 1992.[12] Dorigo M, Maniezzo V, Colorni A, The Ant System: Optimization by a Colony ofCooperating Agents, IEEE Transactions on Systems, Man and Cybernetics-Part B, Vol 26(1), pp.29-41, 1996.[13] James Kennedy, Russell Eberhart Particle swarm optimization, Proc. IEEE Intl. Conf. onNeural Networks (Perth, Australia), IEEE Service Center, Piscataway, NJ, 1995, pp.1942-1948.[14] Shxyong Jian Shyua, B.M.T. Linb, Tsung Shen Hsiaoa, Ant Colony Optimization for theCell Assignment Problem in PCS Network, March, 2005. 218

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