evolving cellular automata for location management in ......evolving cellular automata for location...

Evolving Cellular Automata for LocationManagement 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.

æ

1 INTRODUCTION

ONE of the challenges facing mobile computing is thetracking of the current location of users—the area of

location management. In order to route incoming calls toappropriate mobile terminals, the network must from timeto time keep track of the location of each mobile terminal.

Mobility tracking expends the limited resources of thewireless network. Besides the bandwidth used for registra-tion and paging between the mobile terminal and basestations, power is also consumed from the portable devices.Furthermore, frequent signaling may result in degradationof Quality of Service (QoS), due to interferences. On theother hand, a miss on the location of a mobile terminal willnecessitate a search operation on the network when a callcomes in. Such an operation, again, requires the expendi-ture of limited wireless resources. The goal of mobilitytracking, or location management is to balance the registra-tion (location update) and search (paging) operation, so asto minimize the cost of mobile terminal location tracking.

Two simple location management strategies are theAlways-Update strategy and the Never-Update strategy. Inthe Always-Update strategy, each mobile terminal performs alocation update whenever it enters a new cell. As such, theresources used (overhead) for the location update would behigh. However, no search operation would be required forincoming calls. In the Never-Update strategy, no locationupdate is ever performed. Instead, when a call comes in, asearch operation is conducted to find the intended user.Clearly, the overhead for the search operation would behigh, but no resources would be used for the location

update. These two simple strategies represent the twoextremes of location management strategies, whereby onecost is minimized and the other maximized. Most existingcellular systems use a combination of the above twostrategies.

One of the common location management strategy usedin existing systems today is the location area scheme [18],[19], [26]. In this scheme, the network is partitioned intoregions or location areas (LA), with each region consisting ofone or more cells (Fig. 1).

The never-update strategy can then be used within eachregion, with location update performed only when a usermoves out to another region/location area. When a callarrives, only cells within the LA for which the user is inneeds to be searched. For example, in Fig. 1, if a call arrivesfor user X, then the search is confined to the 16 cells of thatLA. It is recognized that in general the optimal LApartitioning (one that gives the minimum location manage-ment cost) is an NP-complete problem [8].

Another location management scheme similar to theLA scheme is suggested in [1]. In this strategy, a subset ofcells in the network is designated as the reporting cells(Fig. 2). Each mobile terminal performs a location updateonly when it enters one of these reporting cells. When a callarrives, search is confined to the reporting cell the user lastreported and the neighboring bounded nonreporting cells.For example, in Fig. 2, if a call arrives for user X, thensearch is confined to the reporting cell the user last reportedin and the nonreporting cells marked PP . Obviously, certainreporting cells configuration leads to unbounded nonre-porting cells, as shown in Fig. 3. It was shown in [1] thatfinding an optimal set of reporting cells, such that thelocation management cost is minimized, is an NP-completeproblem. In [9], a heuristic method to find near optimalsolutions is described.

In this paper, we propose to develop a parallel anddistributed reporting cells planning algorithm based on arecently emerging and promising technique of combining

IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 14, NO. 1, JANUARY 2003 13

. R. Subrata is with Parallel Computing Research Laboratory, Department ofElectrical and Electronic Engineering, The University of WesternAustralia, Perth, Western Australia 6907.

. A.Y. Zomaya is with the School of Information Technologies, TheUniversity 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 Published by the IEEE Computer Society

evolutionary computation and cellular automata (CA) tocreate an “evolving” cellular automata system. Recentresults suggest that highly parallel and distributed algo-rithms can “evolve” using such a hybrid system, solvingcomplex problems ranging from classification to multi-processor scheduling [2], [5], [12], [13], [14], [21], [23].

Cellular Automata (CA) represents a system of distrib-uted, locally interacting cells that evolves according to a setof rules. Based on this micro, local interactions with noglobal coordination, a macro or global behavior is pro-duced. Such a pattern is readily observed in nature and theuniverse in general. The universe is full of patterns andstructure—from individual cells in the body, to animals inan ecosystem, their collective forms complex autonomousexistences of their own, with no central control orchestrat-ing their actions. Through seemingly selfish and simpleinteraction of individuals, a global behavior emerges. Eachindividual, simply by interacting with its nearest neighbors,unwittingly contributes to the “collective.”

Cellular Automata can be thought of as a model ofnaturally existing systems. Natural systems, through evolu-tion, have produced highly complex systems showingglobally coordinated information processing, with no globalcoordination. In contrast to natural systems, many oftoday’s system utilizes “global criterion” that requiresglobal coordination. We will show that, through evolution

of a cellular automaton, the global criteria of reporting cellsproblems are translated to local transition rules of cellularunits. The cellular automaton is evolved through the use ofGenetic Algorithms (GAs). Specifically, the CA transitionrules are found, or evolved, using a genetic algorithm.

The next section is an overview of the location manage-ment problem and viewing it as an optimization problemwith a description of the cost functions that can be used tolead to the best results. This is followed by the developmentof a strategy that incorporates cellular automata and geneticalgorithms to solve management location problems. Theresults section provides a number of detailed simulationsthat shows the applicability of the proposed approach.

2 LOCATION MANAGEMENT COST

As noted above, location management involves twoelementary operations of location update and location inquiry,as well as network interrogation operations. Clearly, a goodlocation update strategy would reduce the overhead forlocation inquiry. At the same time, location updates shouldnot be performed excessively, as it expends on the limitedwireless resources.

To determine the average cost of a location managementstrategy, one can associate a cost component to eachlocation update performed, as well as to each polling/paging of a cell. The most common cost component used isthe wireless bandwidth used (wireless traffic load imposedon the network). That is, the wireless traffic from mobileterminals to base stations (and vice-versa) during locationupdates and location inquiry. While there are also “fixedwire” network traffic between controllers within the net-work during location updates and location inquiry—“net-work interrogation,” they are considered much cheaper andwe will therefore not consider it.

14 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 14, NO. 1, JANUARY 2003

Fig. 1. Regions representing location areas (LA) and individual cells (in

this figure, there are four LA, each consisting of 16 cells).

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

cells).

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

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

cells).

The total cost of the above two cost components (locationupdate and cell paging) over a period of time TT , asdetermined by simulations (or analytically) can then beaveraged to give the average cost of a location managementstrategy. For example, the following simple equation can beused to calculate the total (wireless) cost of a locationmanagement strategy:

Total Cost ¼ C �NLU þNP : ð1Þ

Where NLU denotes the number of location updatesperformed during time TT , NP denotes the number of pagingperformed during time TT and C is a constant representingthe cost ratio of location update and paging. It is recognizedthat the cost of location update is usually much higher thanthe cost of paging—several times higher [11], mainly due tothe 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 fixedwire network. These cells are usually represented ashexagonal cells (Fig. 2), resulting in six possible neighborsfor each cell. For more information on wireless networksand communications, refer to [28], [29], [30].

In the reporting cells location management scheme, somecells in the network are designated as reporting cells.Mobile terminals do location update (update their posi-tions) 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 besearched at all, if there is no path from the last location ofthe user to that cell, without entering a reporting cell. Thatis, the reporting cells form a “solid line” barrier, whichmeans a user will have to enter one of these reporting cellsto get to the other side. For example, in Fig. 4, a user movingfrom cell 4 to cell 6 would have to enter a reporting cell. Assuch, for location management cost evaluation purposes,the cells that are in bounded areas are first identified andthe maximum area to be searched for each cell (if a callarrives for that cell) is calculated.

Suppose we call the collection of all the cells that arereachable from a reporting cell i without entering anotherreporting 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 callarrives for a user whose last location is known to be cell i.As an example, in Fig. 4, the vicinity of reporting cell 9includes the cells 0, 1, 4, 8, 13, 14, and cell 9 itself. Thevicinity value is then 7, as there are seven cells in the vicinity.

Each nonreporting cell can also be assigned a vicinityvalue. However, it is clear that a nonreporting cell maybelong to the vicinity of several reporting cells, which mayhave different vicinity values. For example, in Fig. 4, cell 4belongs to the vicinity of reporting cells 2, 5, 9, and 12, withvicinity values 8, 8, 7, and 7, respectively. For LocationManagement cost evaluation purposes, the maximumvicinity value will be used. As such, in this case, thevicinity value of eight is assigned to cell 4.

We further associate with each cell i a movement weightand call arrival weight, denoted wmi and wci, respectively.The movement weight represents the frequency or totalnumber of movement into a cell, while the call arrivalweight represents the frequency or total number of callarrivals within a cell. Clearly, if a cell i is a reporting cell,then the number of location updates occurring in that cellwould be dependent on the movement weight of that cell.Further, because call arrivals result in a search/pagingoperation, the total number of paging performed would bedirectly related to the call arrival weight of the cells in thenetwork. As such, we have the following formula for thetotal number of location updates and paging (performedduring a certain time period TT ).

NLU ¼Xi2S

wmi

NP ¼XNÿ1

j¼0

wcj � vðjÞ:ð2Þ

Where NLU denotes the number of location updatesperformed during time TT , NP denotes the number of pagingperformed during time TT , wmi denotes the movementweight associated with cell i, wcj denotes the call arrivalweight associated with cell j, vðjÞ denotes the vicinity value

SUBRATA AND ZOMAYA: EVOLVING CELLULAR AUTOMATA FOR LOCATION MANAGEMENT IN MOBILE COMPUTING NETWORKS 15

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).

TABLE 1Possible Neighborhood States and A Transition Function

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

of cell j, N denotes the total number of cells in the networkand S denotes the set of reporting cells in the network.

By using (1) and (2), we get the following formula tocalculate the location management cost of a particularreporting cells configuration:

Total Cost ¼ C �Xi2S

wmi þXNÿ1

j¼0

wcj � vðjÞ: ð3Þ

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

arrivals, giving the cost per call arrival. Such “normalization”does not affect the relative location management costs ofdifferent reporting cells configuration and is what we havedone in the experiments.

3 CELLULAR AUTOMATA

Cellular Automata (CA) [3], [4], [7], [20], [24] are decen-tralized, discrete space-time systems that can be used tomodel physical systems. Simple, one-dimensional CAconsists of a grid of cells (Fig. 5) with states that evolveaccording to a set of rules, based on the states of itssurrounding cells. The grid may be finite or infinite inlength. For simulation purposes, the grid is usually fixed inlength and assumed to wrap around at the edges, as shownin Fig. 5.

Further, the state of a cell i at time tþ 1 is governed bythe states of its surrounding cells. Assuming a uniform CArule—where each cell is governed by the same transitionfunction, then we have:

stþ1i ¼ f stiÿr; � � � ; stiÿ1; s

ti; s

tiþ1; � � � ; stiþr

ÿ �: ð4Þ

Where sti denotes the state of cell i at time t, fðÞ denotesthe transition function that defines the rule governing state


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

are shaded).

TABLE 2Selected Neighborhood States and A Transition Function

In the above, si denotes the state of cell i and sik denotes the state of thekth neighbor of cell i. In this case, we have six neighboring cells.

Fig. 8. A network of size 4� 4.

TABLE 3Data Set for A 4� 4 Network

Fig. 9. Sequential search results for a 4� 4 network. A “1” represents

reporting cell and a “0” represents nonreporting cell.

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.

change of a cell, AND r is the radius of the cells’neighborhood.

For a cellular automaton with neighborhood radiusr ¼ 1, then (4) reduces to (5) below. For cellular automatonwith binary states, then there are eight possible neighbor-hood states of {000, 001, 010, 011, 100, 101, 110, 111}. Table 1shows all the possible neighborhood states and an exampletransition function of f ¼ 10; 011; 000.

stþ1i ¼ f stiÿ1; s

ti; s

tiþ1

ÿ �: ð5Þ

From such simple rules and initial starting configura-

tions, a variety of “behavior” has been observed. The

different classes of behavior include [3]:

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


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


have the same state/value). Starting with an initialrandom state, the cellular automaton quickly con-verges 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 ofcellular automata (e.g., see Fig. 6). The behavior ofthese 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 (repre-

sented as a “0”). This leads to two (binary) possible states

for each cellular unit in the CA.




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 andGenetic 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.



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.


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

(ALGORITHM 1 GA FOR CA RULES DISCOVERY):

INPUT: PARAMETERS FOR THE GA.

Output: Population of CA rules, PP . Each of these rules

can be used for the CA run.

Begin

Initialize the population, PP and a mating pool PPnext.

Evaluate PP .

While stopping conditions not true do

Sort PP in descending order of fitness.

Apply Selection from the worst

nð1 � n � population sizeÞ rules in PP to PPnext.

The best rules in PP ðof size population sizeÿ nÞare left untouched and survive to the next

generation intact.

Crossover PPnext.


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

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


Mutate PPnext.

Copy the n rules of PPnext to PP , replacing the worst

n rules in PP .

Evaluate PP .

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 testdata is generated. In our case, the set consists of fourrandomly generated reporting cells configuration,which forms the initial state configuration for theCA. The set consists of four randomly generatedconfigurations, because a rule may give good resultfor a particular configuration, but not for others. Assuch, using the sum of the four results give a betterindication 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 toevolve for 50 runs. The states of the cellularautomaton at the end of the 50 runs, which representthe reporting cells configuration, is then input intothe 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 ofoptimization 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, indepen-

dent 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


Fig. 20. CA run for the 200 CA rules at the 200th generation.


Fig. 21. Sequential search results for a 4\times4 network.


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

PP , which, together with the best 80 chromosomes, forms the

next generation of chromosomes.

4 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.

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 optimumreporting cells configuration. The result of the sequentialsearch is shown in Fig. 9.

For this experiment, the GA is run for 200 generations,using the parameters described earlier. The result of the GArun is shown in Fig. 10. As shown by the graph, the GA findsthe optimum rules around the 70th generation. An optimumrule is one that leads to the optimum reporting-cell config-uration of value 12.25 (see Fig. 9). Since there are four CA testset created randomly at each generation of the GA, theminimum value shown on the graph is 12:25� 4 ¼ 49.

Evolutions of the rules throughout the generations areshown in Fig. 11 which shows a CA run of the best rulefound after the 20th generation of the GA. In the figure, theStates column represents the states of the 16 cells in the



Fig. 24. A run for the 200 CA rules at the 200th generation. Fig. 25. Network of size 6� 6.

network, with “1” representing reporting cell and “0”representing nonreporting cell. The Value column repre-sents the location management cost per call arrival, asso-ciated with a particular reporting cells configuration. The“evolution” of each cell, governed by a fixed CA rule, canclearly be seen on the figure. As can be seen, the states of thecellular automaton start to oscillate at step 27.

After 50 generations of the GA, the best rule found is runon the CA, as shown in Fig. 12. As shown in the figure, thestates of the CA stabilize at step 33. However, it does notlead to the optimum configuration value of 12.25.

At the 100th generation, the best rule is again run on theCA and the result shown in Fig. 13. In this case, the cellularautomaton stabilizes (converge to a solution) at step 28 andgives 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.”





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, somenumbers of test data are generated and the rules are thentested using these test data. In this case, the 200 rules aretested using 200 random initial reporting-cells configura-tion. The 200 test data are created randomly for each rule soeach rule would most likely not have the same set of testdata. As can be seen from Fig. 16, 29 of the rules are able toalways find the optimum configuration (of 12.25), for the200 random CA initial states.

4.2 Network (2)

Another network of size 4� 4 is used in this experimentwith a different data set (Table 4).

The optimum reporting cells configuration is first

searched using sequential search (see Fig. 17):

The result of the GA, evolved for 200 generations, isshown in Fig. 18. The figure shows the GA that discoversthe optimum rules at the 60th generation. The found rules,however, are not the best, as they do not give the optimumvalue using the randomly generated set of test data atgeneration 66, 67, and 72. The GA rapidly corrects thissituation and finds rules that “pass” subsequent genera-tional tests.

At the end of the 200th generation, the best rule found isrun on the CA. Fig. 19 shows the result of the run. At step 4of the run, the cellular automaton converges to a steadystate, 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 using200 random test data. Each rule would most likely not havethe same set of 200 random test data, as new test data arecreated for each rule. As can be seen from Fig. 20, 55 of therules are always able to find the optimum configuration ofreporting 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 ofTable 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 atgeneration 59, but the found rule keeps “failing” subse-quent generational tests. It is not until around the 140thgeneration that the GA finds a CA rule that performs wellfor each set of tests generated at each generation. Fig. 23shows the result of a CA run, using the best rule found atthe end of the 200th generation.

The first 200 unique rules at the end of the 200th generationare once again tested using 200 random test data, as shown inFig. 24. In this one, there is one rule that always gives theoptimum 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 inTable 6. The cell numbering used in the data set is of thesame format to that shown in Fig. 8. For this one, the searchspace is of size 236 ¼ 68; 719; 476; 736 and is too large forsequential search.


Fig. 28. CA run for the 200 CA rules at the 400th generation.

TABLE 7Data Set for an 8� 8 Network

Fig. 29. GA results for an 8� 8 network.

In this experiment, the GA is run for 400 generations. Theresult is shown in Fig. 26. As can be seen, the GA convergesto a solution around the 270th generation and remainsrelatively flat after that.

Fig. 27 shows the “evolution” of the cells, using the bestrule found at the 400th generation of the GA. Performanceof the 200 rules (from a population of 1000), tested using 200randomly generated test data is shown in Fig. 28. As can beseen, there are scores of rules that gives an average locationmanagement 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.

5 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 inthe network to cellular units of the CA and using selected CAneighborhood, GA was used to discover efficient CAtransition rules. Results of the experiment show that GAcan be effectively used to discover CA rules suitable for thereporting cells problem. Furthermore, the results demon-strate that discovered CA rules are able to find optimal, ornear optimal solutions, to the reporting cells problem—as thesystem evolves, better and more robust CA rules arediscovered. This necessitates more concerted efforts andresearch in this direction.

ACKNOWLEDGMENTS

Riky Subrata acknowledges the assistance of the Jean

Rogerson scholarship.

REFERENCES

[1] N.A. Bar and I. Kessler, “Tracking Mobile Users in WirelessCommunications Networks,” IEEE Trans. Information Theory,vol. 39, pp. 1877-86, 1993.

[2] T. Bossomaier, T. Cranny, and D. Schneider, “A New Paradigmfor Evolving Cellular Automata Rules,” Proc. 1999 Congress onEvolutionary Computation (CEC ’99), 1999.

[3] B. Chopard and M. Droz, Cellular Automata Modeling of PhysicalSystems. New York: Cambridge Univ. Press, 1998.

[4] E.F. Codd, Cellular Automata. New York: Academic Press, 1968.



Fig. 31. A run for the 200 CA rules at the 400th generation.

[5] F. Corno, R.M. Sonza, and G. Squillero, “Exploiting the SelfishGene Algorithm for Evolving Cellular Automata,” Proc. IEEEINNS ENNS Int’l Joint Conf. Neural Networks IJCNN 2000 NeuralComputing: New Challenges and Perspectives for the New Millennium,2000.

[6] D.E. Goldberg, Genetic Algorithms in Search, Optimization, andMachine Learning. Reading, Mass.: Addison-Wesley, 1989.

[7] E. Goles and S. Martinez, Cellular Automata and Complex Systems.Boston: Kluwer Academic, 1999.

[8] P.R.L. Gondim, “Genetic Algorithms and the Location AreaPartitioning Problem in Cellular Networks,” Proc. IEEE 46thVehicular Technology Conf. Mobile Technology for the Human Race,1996.

[9] A. Hac and X. Zhou, “Locating Strategies for Personal Commu-nication Networks, a Novel Tracking Strategy,” IEEE J. SelectedAreas in Comm., vol. 15, pp. 1425-36, 1997.

[10] J.H. Holland, Adaptation in Natural and Artificial Systems. AnnArbor, Mich.: Univ. of Michigan Press, 1975.

[11] T. Imielinski and B.R. Badrinath, “Querying Locations in WirelessEnvironments,” Wireless Comm. Future Directions, 1992.

[12] M.F. Jimenez, “Evolving Three-Dimensional Cellular Automata toPerform a Quasiperiod-3 Collective Behavior Task,” Physical Rev.E (Statistical Physics, Plasmas, Fluids, and Related InterdisciplinaryTopics), vol. 60, pp. 4934-40, 1999.

[13] M.F. Jimenez, J.P. Crutchfield, and M. Mitchell, “Evolving Two-Dimensional Cellular Automata to Perform Density Classification:A Report on Work in Progress,” Parallel Computing, vol. 27,pp. 571-85, 2001.

[14] C. Kameshima, S. Endo, and K. Yamada, “Research Work forArchitectonics of Evolutional Computation in Acquiring CA-Rules,” Bull. of the Faculty of Eng., Univ. of the Ryukyus. no., vol. 60,pp. 99-103, 2000.

[15] C.L. Karr and L.M. Freeman, Industrial Applications of GeneticAlgorithms. Boca Raton, Fla.: CRC Press, 1999.

[16] Z. Michalewicz, Genetic Algorithms + Data Structures = EvolutionPrograms. Berlin: Springer-Verlag, 1994.

[17] M. Mitchell, An Introduction to Genetic Algorithms. Cambridge,Mass.: MIT Press, 1996.

[18] S. Okasaka, S. Onoe, S. Yasuda, and A. Maebara, “A New LocationUpdating Method for Digital Cellular Systems,” Proc. 41st IEEEVehicular Technology Conf. Gateway to the Future Technology inMotion, 1991.

[19] D. Plassmann, “Location Management Strategies for MobileCellular Networks of Third Generation,” Proc. IEEE 44th VehicularTechnology Conf., 1994.

[20] E. Rietman, Creating Artificial Life: Self-Organization. Blue RidgeSummit, Penn.: Windcrest/McGraw-Hill, 1993.

[21] F. Seredynski, “Evolving Cellular Automata-Based Algorithms forMultiprocessor Scheduling,” Solutions to Parallel and DistributedComputing Problems, pp. 179-207, A.Y. Zomaya, F. Ercal, andS. Olariu, eds. New York: John Wiley and Sons, 2001.

[22] M.D. Vose, The Simple Genetic Algorithm: Foundations and Theory.Cambridge, Mass.: MIT Press, 1999.

[23] J. Werfel, M. Mitchell, and J.P. Crutchfield, “Resource Sharing andCoevolution in Evolving Cellular Automata,” IEEE Trans. Evolu-tionary Computation, vol. 4, pp. 388-93, 2000.

[24] S. Wolfram, Cellular Automata and Complexity: Collected Papers.Reading, Mass.: Addison-Wesley, 1994.

[25] H. Xie, S. Tabbane, and D.J. Goodman, “Dynamic Location AreaManagement and Performance Analysis,” Proc. 43rd IEEE Vehi-cular Technology Conf. Personal Comm. Freedom Through WirelessTechnology, 1993.

[26] K.L. Yeung and T.S.P. Yum, “A Comparative Study on LocationTracking Strategies in Cellular Mobile Radio Systems,” Proc.-Comm. for Global Harmony IEEE Global Telecomm. Conf. TechnicalProgram Conf. Record, (GLOBECOM ’95), 1995.

[27] K.K. Yu, “A Quasi-Static Cluster-Computing Approach forDynamic Channel Assignment in Cellular Mobile CommunicationSystems,” Proc. Gateway to 21st Century Comm. Village VTC 1999Fall IEEE VTS 50th Vehicular Technology Conf., 1999.

[28] M.F. Catedra and J.P. Arriaga, Cell Planning for Wireless Commu-nications. Boston, Mass: Artech House, 1999.

[29] T.S. Rappaport, Cellular Raido and Person Communications: SelectedReadings. Piscataway, N.J.: IEEE, 1995.

[30] G.L. Stuber, Principles of Mobile Communication. Boston: KluwerAcademic, 1996.

Riky Subrata received the BE (Hons.) and BCom degrees from theUniversity of Western Australia in 2000. He is currently working towardthe PhD degree at the Department of Electrical and ElectronicEngineering, University of Western Australia. His current researchinterests include mobility management, mobile computing, wirelessnetworks, biologically inspired techniques, and distributed algorithms.

Albert Y. Zomaya is the CISCO Systems ChairProfessor of Internetworking in the School ofInformation Technologies, The University ofSydney. Prior to that he was a full professor inthe Electrical and Electronic Engineering De-partment at the University of Western Australia,where he also led the Parallel ComputingResearch Laboratory during the period 1990-2002. He served as deputy- and acting-head inthe same department, and held visiting positions

at Waterloo University and the University of Missouri-Rolla. He is theauthor/coauthor of five books, 150 publications in technical journals andconferences, and the editor of three books and seven conferencevolumes. He is currently an associate editor for the Journal ofInterconnection Networks, the International Journal on Parallel andDistributed Systems and Networks, Journal of Future Generation ofComputer Systems, and the International Journal of Foundations ofComputer Science. He is also the founding editor of the Wiley BookSeries on parallel and distributed computing. He is the editor-in-chief ofthe Parallel and Distributed Computing Handbook (McGraw-Hill, 1996).Dr. Zomaya is the chair of the IEEE Technical Committee on ParallelProcessing (1999-Present). He is also a board member of theInternational Federation of Automatic Control (IFAC) committee onAlgorithms and Architectures for Real-Time Control, and serves on theexecutive board of the IEEE Task Force on Cluster Computing. He hasbeen actively involved in the organization of national and internationalconferences. Dr. Zomaya is a chartered engineer, a Fellow of theInstitution of Electrical Engineers (United Kingdom), a senior member ofthe IEEE, and the IEEE Computer Society, and member of the ACM. Hereceived the 1997 Edgeworth David Medal from the Royal Society ofNew South Wales for outstanding contributions to Australian Science. InSeptember 2000, he was awarded the IEEE Computer Society’sMeritorious Service Award. His research interests are in the areas ofhigh-performance computing, parallel and distributed algorithms, mobilecomputing, and networking.

. For more information on this or any computing topic, please visitour Digital Library at http://computer.org/publications/dlib.


evolving cellular automata for location management in ......evolving cellular automata for location...

Documents