Evolving cellular automata for location management in ... - IEEE Xplore

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Evolving Cellular Automata for Location Management in Mobile Computing Networks Riky Subrata and Albert Y. Zomaya, Senior Member, IEEE Abstract—Location management is a very important and complex problem in mobile computing. There is a need to develop algorithms that could capture this complexity yet can be easily implemented and used to solve a wide range of location management scenarios. This paper investigates the use of cellular automata (CA) combined with genetic algorithms to create an evolving parallel reporting cells planning algorithm. In the reporting cell location management scheme, some cells in the network are designated as reporting cells; mobile terminals update their positions (location update) upon entering one of these reporting cells. To create such an evolving CA system, cells in the network are mapped to cellular units of the CA and neighborhoods for the CA is selected. GA is then used to discover efficient CA transition rules. The effectiveness of the GA and of the discovered CA rules is shown for a number of test problems. Index Terms—Cellular automata, genetic algorithms, mobile computing, mobility management.

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INTRODUCTION

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NE of the challenges facing mobile computing is the tracking of the current location of users—the area of location management. In order to route incoming calls to appropriate mobile terminals, the network must from time to time keep track of the location of each mobile terminal. Mobility tracking expends the limited resources of the wireless network. Besides the bandwidth used for registration and paging between the mobile terminal and base stations, power is also consumed from the portable devices. Furthermore, frequent signaling may result in degradation of Quality of Service (QoS), due to interferences. On the other hand, a miss on the location of a mobile terminal will necessitate a search operation on the network when a call comes in. Such an operation, again, requires the expenditure of limited wireless resources. The goal of mobility tracking, or location management is to balance the registration (location update) and search (paging) operation, so as to minimize the cost of mobile terminal location tracking. Two simple location management strategies are the Always-Update strategy and the Never-Update strategy. In the Always-Update strategy, each mobile terminal performs a location update whenever it enters a new cell. As such, the resources used (overhead) for the location update would be high. However, no search operation would be required for incoming calls. In the Never-Update strategy, no location update is ever performed. Instead, when a call comes in, a search operation is conducted to find the intended user. Clearly, the overhead for the search operation would be high, but no resources would be used for the location

. R. Subrata is with Parallel Computing Research Laboratory, Department of Electrical and Electronic Engineering, The University of Western Australia, Perth, Western Australia 6907. . A.Y. Zomaya is with the School of Information Technologies, The University of Sydney, Sydney, NSW 2006 Australia. E-mail: [email protected]. Manuscript received 5 Oct. 2001; accepted 4 June 2002. For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number 115143. 1045-9219/03/$17.00 ß 2003 IEEE

update. These two simple strategies represent the two extremes of location management strategies, whereby one cost is minimized and the other maximized. Most existing cellular systems use a combination of the above two strategies. One of the common location management strategy used in existing systems today is the location area scheme [18], [19], [26]. In this scheme, the network is partitioned into regions or location areas (LA), with each region consisting of one or more cells (Fig. 1). The never-update strategy can then be used within each region, with location update performed only when a user moves out to another region/location area. When a call arrives, only cells within the LA for which the user is in needs to be searched. For example, in Fig. 1, if a call arrives for user X, then the search is confined to the 16 cells of that LA. It is recognized that in general the optimal LA partitioning (one that gives the minimum location management cost) is an NP-complete problem [8]. Another location management scheme similar to the LA scheme is suggested in [1]. In this strategy, a subset of cells in the network is designated as the reporting cells (Fig. 2). Each mobile terminal performs a location update only when it enters one of these reporting cells. When a call arrives, search is confined to the reporting cell the user last reported and the neighboring bounded nonreporting cells. For example, in Fig. 2, if a call arrives for user X, then search is confined to the reporting cell the user last reported in and the nonreporting cells marked P . Obviously, certain reporting cells configuration leads to unbounded nonreporting cells, as shown in Fig. 3. It was shown in [1] that finding an optimal set of reporting cells, such that the location management cost is minimized, is an NP-complete problem. In [9], a heuristic method to find near optimal solutions is described. In this paper, we propose to develop a parallel and distributed reporting cells planning algorithm based on a recently emerging and promising technique of combining Published by the IEEE Computer Society

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Fig. 1. Regions representing location areas (LA) and individual cells (in this figure, there are four LA, each consisting of 16 cells).

evolutionary computation and cellular automata (CA) to create an “evolving” cellular automata system. Recent results suggest that highly parallel and distributed algorithms can “evolve” using such a hybrid system, solving complex problems ranging from classification to multiprocessor scheduling [2], [5], [12], [13], [14], [21], [23]. Cellular Automata (CA) represents a system of distributed, locally interacting cells that evolves according to a set of rules. Based on this micro, local interactions with no global coordination, a macro or global behavior is produced. Such a pattern is readily observed in nature and the universe in general. The universe is full of patterns and structure—from individual cells in the body, to animals in an ecosystem, their collective forms complex autonomous existences of their own, with no central control orchestrating their actions. Through seemingly selfish and simple interaction of individuals, a global behavior emerges. Each individual, simply by interacting with its nearest neighbors, unwittingly contributes to the “collective.” Cellular Automata can be thought of as a model of naturally existing systems. Natural systems, through evolution, have produced highly complex systems showing globally coordinated information processing, with no global coordination. In contrast to natural systems, many of today’s system utilizes “global criterion” that requires global coordination. We will show that, through evolution

Fig. 2. A network with reporting cells (shaded areas represent reporting cells).

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Fig. 3. A network with reporting cells and unbounded nonreporting cells.

of a cellular automaton, the global criteria of reporting cells problems are translated to local transition rules of cellular units. The cellular automaton is evolved through the use of Genetic Algorithms (GAs). Specifically, the CA transition rules are found, or evolved, using a genetic algorithm. The next section is an overview of the location management problem and viewing it as an optimization problem with a description of the cost functions that can be used to lead to the best results. This is followed by the development of a strategy that incorporates cellular automata and genetic algorithms to solve management location problems. The results section provides a number of detailed simulations that shows the applicability of the proposed approach.

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LOCATION MANAGEMENT COST

As noted above, location management involves two elementary operations of location update and location inquiry, as well as network interrogation operations. Clearly, a good location update strategy would reduce the overhead for location inquiry. At the same time, location updates should not be performed excessively, as it expends on the limited wireless resources. To determine the average cost of a location management strategy, one can associate a cost component to each location update performed, as well as to each polling/ paging of a cell. The most common cost component used is the wireless bandwidth used (wireless traffic load imposed on the network). That is, the wireless traffic from mobile terminals to base stations (and vice-versa) during location updates and location inquiry. While there are also “fixed wire” network traffic between controllers within the network during location updates and location inquiry—“network interrogation,” they are considered much cheaper and we will therefore not consider it.

Fig. 4. A network with reporting cells (shaded areas represent reporting cells).

SUBRATA AND ZOMAYA: EVOLVING CELLULAR AUTOMATA FOR LOCATION MANAGEMENT IN MOBILE COMPUTING NETWORKS

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Fig. 5. One-dimensional cellular automaton. Shown is a cellular automaton with 12 cells and the edges wrap around. The cells have two (binary) possible states of on (white) and off (shaded).

The total cost of the above two cost components (location update and cell paging) over a period of time T , as determined by simulations (or analytically) can then be averaged to give the average cost of a location management strategy. For example, the following simple equation can be used to calculate the total (wireless) cost of a location management strategy: T otal Cost ¼ C NLU þ NP :

ð1Þ

Where NLU denotes the number of location updates performed during time T , NP denotes the number of paging performed during time T and C is a constant representing the cost ratio of location update and paging. It is recognized that the cost of location update is usually much higher than the cost of paging—several times higher [11], mainly due to the need to setup a “signaling channel.” In light of this fact, we use C ¼ 10 [8], [25].

2.1 Network Structure Most, if not all, of today’s wireless network consists of cells. Each cell contains a base station, which is wired to a fixed wire network. These cells are usually represented as hexagonal cells (Fig. 2), resulting in six possible neighbors for each cell. For more information on wireless networks and communications, refer to [28], [29], [30]. In the reporting cells location management scheme, some cells in the network are designated as reporting cells. Mobile terminals do location update (update their positions) upon entering one of these reporting cells. When calls arrive for a user, the user has to be located. Some cells in the network, however, may not need to be searched at all, if there is no path from the last location of the user to that cell, without entering a reporting cell. That is, the reporting cells form a “solid line” barrier, which means a user will have to enter one of these reporting cells to get to the other side. For example, in Fig. 4, a user moving from cell 4 to cell 6 would have to enter a reporting cell. As such, for location management cost evaluation purposes, the cells that are in bounded areas are first identified and the maximum area to be searched for each cell (if a call arrives for that cell) is calculated. Suppose we call the collection of all the cells that are reachable from a reporting cell i without entering another reporting cell as the vicinity of reporting cell i. By definition, we also include the reporting cell i. Then, the vicinity value (number of cells in the vicinity) of a reporting cell i is the

maximum number of cells to be searched, when a call arrives for a user whose last location is known to be cell i. As an example, in Fig. 4, the vicinity of reporting cell 9 includes the cells 0, 1, 4, 8, 13, 14, and cell 9 itself. The vicinity value is then 7, as there are seven cells in the vicinity. Each nonreporting cell can also be assigned a vicinity value. However, it is clear that a nonreporting cell may belong to the vicinity of several reporting cells, which may have different vicinity values. For example, in Fig. 4, cell 4 belongs to the vicinity of reporting cells 2, 5, 9, and 12, with vicinity values 8, 8, 7, and 7, respectively. For Location Management cost evaluation purposes, the maximum vicinity value will be used. As such, in this case, the vicinity value of eight is assigned to cell 4. We further associate with each cell i a movement weight and call arrival weight, denoted wmi and wci , respectively. The movement weight represents the frequency or total number of movement into a cell, while the call arrival weight represents the frequency or total number of call arrivals within a cell. Clearly, if a cell i is a reporting cell, then the number of location updates occurring in that cell would be dependent on the movement weight of that cell. Further, because call arrivals result in a search/paging operation, the total number of paging performed would be directly related to the call arrival weight of the cells in the network. As such, we have the following formula for the total number of location updates and paging (performed during a certain time period T ). X wmi NLU ¼ i2S

NP ¼

N ÿ1 X

ð2Þ wcj vðjÞ:

j¼0

Where NLU denotes the number of location updates performed during time T , NP denotes the number of paging performed during time T , wmi denotes the movement weight associated with cell i, wcj denotes the call arrival weight associated with cell j, vðjÞ denotes the vicinity value

TABLE 1 Possible Neighborhood States and A Transition Function

Fig. 6. Class 4 cellular automaton (Transition Function f = 01110110).

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Fig. 7. Nearest neighbors of cell 5 (the neighbors of cell 5 at radius r ¼ 1 are shaded).

TABLE 2 Selected Neighborhood States and A Transition Function

Fig. 9. Sequential search results for a 4 4 network. A “1” represents reporting cell and a “0” represents nonreporting cell.

arrivals, giving the cost per call arrival. Such “normalization” does not affect the relative location management costs of different reporting cells configuration and is what we have done in the experiments. In the above, si denotes the state of cell i and sik denotes the state of the kth neighbor of cell i. In this case, we have six neighboring cells.

of cell j, N denotes the total number of cells in the network and S denotes the set of reporting cells in the network. By using (1) and (2), we get the following formula to calculate the location management cost of a particular reporting cells configuration: T otal Cost ¼ C

X i2S

wmi þ

Nÿ1 X

wcj vðjÞ:

ð3Þ

j¼0

Where C is a constant representing the cost ratio of location update and paging, as described earlier. In the above equation, the vicinity value vðjÞ calculation will undoubtedly take most of the computing time. We can also divide the total cost shown above by the total number of call

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CELLULAR AUTOMATA

Cellular Automata (CA) [3], [4], [7], [20], [24] are decentralized, discrete space-time systems that can be used to model physical systems. Simple, one-dimensional CA consists of a grid of cells (Fig. 5) with states that evolve according to a set of rules, based on the states of its surrounding cells. The grid may be finite or infinite in length. For simulation purposes, the grid is usually fixed in length and assumed to wrap around at the edges, as shown in Fig. 5. Further, the state of a cell i at time t þ 1 is governed by the states of its surrounding cells. Assuming a uniform CA rule—where each cell is governed by the same transition function, then we have: ÿ ¼ f stiÿr ; ; stiÿ1 ; sti ; stiþ1 ; ; stiþr : ð4Þ stþ1 i Where sti denotes the state of cell i at time t, fðÞ denotes the transition function that defines the rule governing state

Fig. 8. A network of size 4 4.

TABLE 3 Data Set for A 4 4 Network

Fig. 10. GA results for a 4 4 network. The figure shows the minimum, average, and maximum fitness of the chromosomes (representing the CA rule) at each generation.


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Fig. 11. CA run for the best rule found at the 20th generation.

change of a cell, AND r is the radius of the cells’ neighborhood. For a cellular automaton with neighborhood radius r ¼ 1, then (4) reduces to (5) below. For cellular automaton with binary states, then there are eight possible neighborhood states of {000, 001, 010, 011, 100, 101, 110, 111}. Table 1 shows all the possible neighborhood states and an example transition function of f ¼ 10; 011; 000.


ÿ sitþ1 ¼ f stiÿ1 ; sti ; stiþ1 :

ð5Þ

From such simple rules and initial starting configurations, a variety of “behavior” has been observed. The different classes of behavior include [3]: .

Class 1. This class of cellular automata evolves for a finite period of time to a homogeneous state (all cells

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. .

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have the same state/value). Starting with an initial random state, the cellular automaton quickly converges to a homogeneous state. Class 2. Structure of simple or periodic patterns evolves in this class of cellular automata. Class 3. These cellular automata evolve to chaotic and a periodic patterns. A small change in the initial states usually results in major changes at later stages. Class 4. Complex structures evolve in this class of cellular automata (e.g., see Fig. 6). The behavior of these cellular automata is generally not predictable.


3.1 Cellular Automata Based Planner We use cellular automata (CA) for the reporting cells problem in the following way. Each cellular unit in the CA is associated with each cell in the network. Since the cells in the network are hexagonal, each cell can have a maximum of six neighbors. Further, each cell can be either a reporting cell (represented as a “1”) or a nonreporting cell (represented as a “0”). This leads to two (binary) possible states for each cellular unit in the CA.


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3.1.1 Selected Neighborhood The local neighborhood for the cells also needs to be defined. In this experiment, a neighborhood of radius r ¼ 1 is chosen. This leads to each cell having a selected neighborhood of six cells (Fig. 7). Further, it is clear that some cells in the network will not have exactly six neighbors. As an example, cell 7 in Fig. 7 only has three neighboring cells. For such cells, dummy cells are added, so that those cells will have exactly six neighbors. For example, cell 7 in Fig. 7 will have three dummy cells added. These dummy cells are then assigned a value (state) of “2”—representing its nonexistence. The dummy cells always have a state of “2” and does not participate in the evolution of the CA. Table 2 shows the

possible states of the selected neighborhood and a possible transition function. Using a selected neighborhood of six cells, this means each cell has six neighbors and each of the six neighbors has three possible states (of “0”, “1” and “2”). The cell itself has two possible states (of “0” and “1”). As such, the total number of neighborhood states is 37 2 ¼ 1; 458 (Table 1). This leads to CA rule of length 1,458 bits, leading to a total of 21458 possible CA transition functions. Suitable CA rules are then discovered using by a GA.

3.2

A Framework of Cellular Automata and Genetic Algorithms A genetic algorithm (GA) [6],[16], [17], [22] is a biologically inspired optimization and search technique developed by Holland [10]. Its behavior mimics the evolution of simple, single celled organisms. It is particularly useful in situations where the solution space to be searched is huge, making sequential search computationally expensive and time consuming. TABLE 4 Data Set for A 4 4 Network

Fig. 16. A run for the 200 CA rules at the 200th generation. Shown above is the average value from the 200 random test data.

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Fig. 17. Sequential search result for a 4 4 network.

GA is a type of guided random search technique, able to find “efficient” solutions in a variety of cases. Efficient here is defined as solutions that, though they may not be the absolute optimal, is within the constraints of the problem and is found in a reasonable amount of time and resources. To put another way, the effectiveness or quality of a GA (for a particular problem) can be judged by its performance against other known techniques—in terms of solutions found and time and resources used to find the solutions. That is, much like everything else in life, we judge by relative performance or benchmark—have we done better than our competitors? It should also be pointed out that in many cases (much like everything else in life) the absolute optimal is not known. In this respect, GA has shown itself to be extremely effective in problems ranging from optimizations to machine learning [15], [16], [17], [27]. The GA used for discovering efficient CA rules is shown below.


Fig. 18. GA results for a 4 4 network.

(ALGORITHM 1 GA FOR CA RULES DISCOVERY): INPUT: PARAMETERS FOR THE GA. Output: Population of CA rules, P . Each of these rules can be used for the CA run. Begin Initialize the population, P and a mating pool P next . Evaluate P . While stopping conditions not true do Sort P in descending order of fitness. Apply Selection from the worst nð1 n population sizeÞ rules in P to P next . The best rules in P ðof size population size ÿ nÞ are left untouched and survive to the next generation intact. Crossover P next .


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Fig. 21. Sequential search results for a 4\times4 network. Fig. 20. CA run for the 200 CA rules at the 200th generation.

Mutate P next . Copy the n rules of P next to P , replacing the worst n rules in P . Evaluate P . End. First, a population of rules is created. In our case, a population of 1,000 chromosomes (each representing a CA rule) is used. At initialization, the value for each CA rule is randomly generated. This initial population is then evaluated. The evaluation of a rule is as follows: .

.

.

At each generation of the GA, a new set of CA test data is generated. In our case, the set consists of four randomly generated reporting cells configuration, which forms the initial state configuration for the CA. The set consists of four randomly generated configurations, because a rule may give good result for a particular configuration, but not for others. As such, using the sum of the four results give a better indication of the “fitness” of a rule. The rule is then tested using this set of test data. Given a rule and a test data, the CA is allowed to evolve for 50 runs. The states of the cellular automaton at the end of the 50 runs, which represent the reporting cells configuration, is then input into the location management cost function—see (3). The sum of the four results is then used as the “fitness value” of the rule. Here, the direction of optimization is minimizing, so rules that give lower

values (meaning lower location management cost) are better than ones that give high values. After the initial evaluation, the GA goes into the “evolution loop.” The GA continues to evolve until the stopping conditions are met. Such conditions include maximum computation time, rule similarity, and number of iterations/generations. At each generation, the chromosomes/rules in the population is sorted in descending order, according to their fitness. In this experiment, the best 80 rules are kept and survive to the next generation intact. Since a new set of test data is generated at each generation, the same rule tested this generation may not give the same fitness value the next generation. It can be said that the evaluation function is noisy and may give a rather randomized output; keeping the best rules allow the rules to be tested again—possibly several more times if it survives the generational tests. This in turn, leads to a more reliable fitness estimates of the rules. In other words, such strategy means that chromosomes/ rules that are likely to survive from generation to generation would be ones that give consistent good results, independent of the initial configuration (test data). Such end effect is certainly what we desire. To the rest of the 920 chromosomes/rules, a selection, crossover, and mutation operator is applied. Tournament



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selection is applied to the 920 chromosomes, with probability 0.8 to create a mating pool of 920. To the chromosomes in the mating pool, two-point crossover with probability 0.8 and gene mutation operator of probability 0.001 is applied. These 920 chromosomes are then copied to the current population P , which, together with the best 80 chromosomes, forms the next generation of chromosomes.

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RESULTS

In this section, we present numerical results of the evolving, cellular automata-based algorithm described above. Several test networks of 16, 36, and 64 cells are used to demonstrate the performance of the algorithm.

Fig. 24. A run for the 200 CA rules at the 200th generation.

4.1 Network (1) In this first experiment, a network of size 4 4 is used, as shown in Fig. 8. For location management cost evaluation purposes, the data set shown in Table 3 is used. For a network of size 4 4, there are 16 cells, which is small enough for a sequential search of the optimum reporting cells configuration. The result of the sequential search is shown in Fig. 9. For this experiment, the GA is run for 200 generations, using the parameters described earlier. The result of the GA run is shown in Fig. 10. As shown by the graph, the GA finds the optimum rules around the 70th generation. An optimum rule is one that leads to the optimum reporting-cell configuration of value 12.25 (see Fig. 9). Since there are four CA test set created randomly at each generation of the GA, the minimum value shown on the graph is 12:25 4 ¼ 49. Evolutions of the rules throughout the generations are shown in Fig. 11 which shows a CA run of the best rule found after the 20th generation of the GA. In the figure, the States column represents the states of the 16 cells in the

Fig. 25. Network of size 6 6.


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network, with “1” representing reporting cell and “0” representing nonreporting cell. The Value column represents the location management cost per call arrival, associated with a particular reporting cells configuration. The “evolution” of each cell, governed by a fixed CA rule, can clearly be seen on the figure. As can be seen, the states of the cellular automaton start to oscillate at step 27. After 50 generations of the GA, the best rule found is run on the CA, as shown in Fig. 12. As shown in the figure, the states of the CA stabilize at step 33. However, it does not lead to the optimum configuration value of 12.25. At the 100th generation, the best rule is again run on the CA and the result shown in Fig. 13. In this case, the cellular automaton stabilizes (converge to a solution) at step 28 and gives the optimum configuration value of 12.25.



The results of the CA run for the best rule found at the 150th and 200th generation is also shown in Figs. 14 and 15, respectively. As can be seen, the best rule found after the 200th generation (the end of the GA run) converges to the optimum solution more quickly than the best rule found after the 100th generation. As the rules are subjected to a different CA test set at each GA generation, the rules that are likely to survive generation to generation intact are ones that give consistent good results, independent of the CA test set. Intuitively, one would expect such rules to have “quick convergence.”

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Fig. 29. GA results for an 8 8 network. Fig. 28. CA run for the 200 CA rules at the 400th generation.

At the end of the GA run, we have a population of rules (1,000 of them to be exact). The first 200 of these (unique) rules are then tested for “quality.” To test them, some numbers of test data are generated and the rules are then tested using these test data. In this case, the 200 rules are tested using 200 random initial reporting-cells configuration. The 200 test data are created randomly for each rule so each rule would most likely not have the same set of test data. As can be seen from Fig. 16, 29 of the rules are able to always find the optimum configuration (of 12.25), for the 200 random CA initial states.

4.2 Network (2) Another network of size 4 4 is used in this experiment with a different data set (Table 4). The optimum reporting cells configuration is first searched using sequential search (see Fig. 17): TABLE 7 Data Set for an 8 8 Network

The result of the GA, evolved for 200 generations, is shown in Fig. 18. The figure shows the GA that discovers the optimum rules at the 60th generation. The found rules, however, are not the best, as they do not give the optimum value using the randomly generated set of test data at generation 66, 67, and 72. The GA rapidly corrects this situation and finds rules that “pass” subsequent generational tests. At the end of the 200th generation, the best rule found is run on the CA. Fig. 19 shows the result of the run. At step 4 of the run, the cellular automaton converges to a steady state, giving the optimal reporting cells configuration. From a population of 1,000 rules at the end of the 200th generation, the first 200 unique rules are each tested using 200 random test data. Each rule would most likely not have the same set of 200 random test data, as new test data are created for each rule. As can be seen from Fig. 20, 55 of the rules are always able to find the optimum configuration of reporting cells, for the 200 random CA initial states.

4.3 Network (3) A third network of size 4 4 is used, using the data set of Table 5. An optimal solution for the network is shown in Fig. 21. The result of the GA run, for 200 generations, is shown in Fig. 22. In this one, the GA discovers the optimum rule at generation 59, but the found rule keeps “failing” subsequent generational tests. It is not until around the 140th generation that the GA finds a CA rule that performs well for each set of tests generated at each generation. Fig. 23 shows the result of a CA run, using the best rule found at the end of the 200th generation. The first 200 unique rules at the end of the 200th generation are once again tested using 200 random test data, as shown in Fig. 24. In this one, there is one rule that always gives the optimum configuration for the random 200 CA initial states. 4.4 Network (4) In this experiment, a network of size 6 6 is employed (Fig. 25). The data set used for the experiment is given in Table 6. The cell numbering used in the data set is of the same format to that shown in Fig. 8. For this one, the search space is of size 236 ¼ 68; 719; 476; 736 and is too large for sequential search.


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In this experiment, the GA is run for 400 generations. The result is shown in Fig. 26. As can be seen, the GA converges to a solution around the 270th generation and remains relatively flat after that. Fig. 27 shows the “evolution” of the cells, using the best rule found at the 400th generation of the GA. Performance of the 200 rules (from a population of 1000), tested using 200 randomly generated test data is shown in Fig. 28. As can be seen, there are scores of rules that gives an average location management cost below 12.5 (per call arrival).

4.5 Network (5) Finally, another network, similar in structure to the previous two but of size 8 8: The data set used for this experiment is shown in Table 7. As before, the cell numbering used in the data set is of the same format to that shown in Fig. 8. The evolution of the population of CA rules is again plotted, as shown in Fig. 29. One CA run of the best rule found

at the end of the GA run (generation 400) is shown in Fig. 30 below. At the end of the GA run, the first 200 chromosomes/ rules of the population is tested. Fig. 31 shows the result of the test for the 200 rules, using 200 randomly generated test data for each rule. As can be seen, the majority of the rules give cost per call arrival of less than 16.

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CONCLUSION

This paper proposed the use of cellular automata (CA) combined with a genetic algorithm (GA) to create a parallel, evolving reporting cells planning algorithm. Mapping cells in the network to cellular units of the CA and using selected CA neighborhood, GA was used to discover efficient CA transition rules. Results of the experiment show that GA can be effectively used to discover CA rules suitable for the reporting cells problem. Furthermore, the results demonstrate that discovered CA rules are able to find optimal, or near optimal solutions, to the reporting cells problem—as the system evolves, better and more robust CA rules are discovered. This necessitates more concerted efforts and research in this direction.

ACKNOWLEDGMENTS Riky Subrata acknowledges the assistance of the Jean Rogerson scholarship.

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VOL. 14,

NO. 1,

JANUARY 2003

Riky Subrata received the BE (Hons.) and BCom degrees from the University of Western Australia in 2000. He is currently working toward the PhD degree at the Department of Electrical and Electronic Engineering, University of Western Australia. His current research interests include mobility management, mobile computing, wireless networks, biologically inspired techniques, and distributed algorithms. Albert Y. Zomaya is the CISCO Systems Chair Professor of Internetworking in the School of Information Technologies, The University of Sydney. Prior to that he was a full professor in the Electrical and Electronic Engineering Department at the University of Western Australia, where he also led the Parallel Computing Research Laboratory during the period 19902002. He served as deputy- and acting-head in the same department, and held visiting positions at Waterloo University and the University of Missouri-Rolla. He is the author/coauthor of five books, 150 publications in technical journals and conferences, and the editor of three books and seven conference volumes. He is currently an associate editor for the Journal of Interconnection Networks, the International Journal on Parallel and Distributed Systems and Networks, Journal of Future Generation of Computer Systems, and the International Journal of Foundations of Computer Science. He is also the founding editor of the Wiley Book Series on parallel and distributed computing. He is the editor-in-chief of the Parallel and Distributed Computing Handbook (McGraw-Hill, 1996). Dr. Zomaya is the chair of the IEEE Technical Committee on Parallel Processing (1999-Present). He is also a board member of the International Federation of Automatic Control (IFAC) committee on Algorithms and Architectures for Real-Time Control, and serves on the executive board of the IEEE Task Force on Cluster Computing. He has been actively involved in the organization of national and international conferences. Dr. Zomaya is a chartered engineer, a Fellow of the Institution of Electrical Engineers (United Kingdom), a senior member of the IEEE, and the IEEE Computer Society, and member of the ACM. He received the 1997 Edgeworth David Medal from the Royal Society of New South Wales for outstanding contributions to Australian Science. In September 2000, he was awarded the IEEE Computer Society’s Meritorious Service Award. His research interests are in the areas of high-performance computing, parallel and distributed algorithms, mobile computing, and networking.

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