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International Journal o Distributed Sensor Networks

simple structure. BSAs strategies or generating trial popula-tions and controlling the amplitude o the search-directionmatrix and search-space boundaries give it very powerulexploration and exploitation capabilities. BSA seems to be

very promising [].

() Mimic Biological Swarm Behaviors: Swarm Intelligence.Swarm intelligence [, ], inspired by the behaviorso somesocial living beings such as bird ocks and sh schools andcolonies o ants, termites, bees, and wasps, is a disciplinethat deals with natural and articial systems composedo many individuals that coordinate their activities usingdecentralized control and sel-organization []. Te mostwell-known swarm intelligence techniques include particleswarm optimization (PSO) [, ], ant colony optimization(ACO) [, ], and articial bee colony algorithm (ABC)[].

() Mimic Biological Immune System:Articial Immune Sys-

tem. Articial immune system (AIS), inspired by the biolog-ical immune system, is an emerging kind o computationalparadigms that belong to the computational intelligenceamily. Te work in the eld o AIS was initiated by Farmer[]. In their research, a dynamic model o the immunesystem that was simple enough to be simulated on a computerwhere the antibody-antibody and antibody-antigen reactionsare simulated via complementary matching strings was intro-duced [].

As introduced above, the primary approaches o bioin-spired computation are inspired rom some the character-istics o the biological systems in nature such as differentbiological behaviors or structures, but they have a common

drawback in that they usually neglect the biological livingcondition. Troughout the lie phenomena in nature, liecycle and survival o the ttest as timeless, constant, anduniversal natural laws are two basic survival rules or liesindividual and colony. Following these rules, lives living onthe earth reproduce offspring rom generation to generationand are born again and again or hundreds o millions oyears. However, by careul analysis, we know that lives cannotlive without a certain biological living condition. Tereore,biological living condition is an essential actor or lies livingand evolution. Here, biological living condition is reerredto as living space inormation. In this paper, computer andprogram are employed to simulate the principles o lie cycle

and survival o the ttest, combined with the considerationo living space inormation, so as to establish a new crowdbased computational intelligence approach, namely, livingspace evolution (LSE). LSE has reected two new ideas.One is living space evolution: under the guidance o livingspace inormation, the offspring o lie concentrate andevolve continuously towards richer living spaces. Te other ismultiple offspring reproduction: a lie can reproducemultipleoffspring within one generation, which stimulates real lives innature.

Te rest o the paper is organized as ollows. LSE dynamicmodel is set up in Section . Section gives the descriptiono LSE algorithm in detail. Digital demonstration in Section

illustrates the procedure o LSE. Examples or LSEs applica-tion are presented in Section . Finally, conclusions are drawnin Section .

2. LSE Dynamic Model

Lie is cyclic, which is a natural law. Lie cycle has twomeanings. Te rst is that the lietime o a lie is limited. Tesecond is that the lie has the ability to reproduce offspringunder certain conditions. On the other hand, lie must obeythe rule o survival o the ttest which is another natural lawin order to continue to be alive on the earth. Subject to thesetwo laws, the lies signicance is that it looks or richer placeson the earth and captures adequate nutrition then survivesand reproduces. Here richer places mean the places where liehas better biological living condition. Here, biological livingcondition is reerred to as living space inormation.

In nature, each lies lietime is different, and its processo reproducing offspring is different too. For the ease o

simulation, a simplied dynamic model is extracted rom thetwo principles o lie cycle and survival o the ttest and romthe combination with the consideration o lies living spaceinormation, which is named as living space evolution (LSE),as shown in Algorithm .

From Algorithm , we can see that there are ve assump-tions in the LSE dynamic model.

() A lie acquires nutrition in itsliving space or subspace.

() A lie that captures adequate nutrition survives; oth-erwise, it dies.

() One surviving lie can reproduce multiple offspringat the same time. Afer reproducing one generation ooffspring, the parental lie dies immediately.

() Te offspring inherit and share their parental livingsubspaces only.

() All lives reproduce offspring in a synchronous man-ner.

From the LSE dynamic model, we can know that itsrunning process can be described as ollows: lie reproducesits multiple offspring rom generation to generation, but onlythe offspring that capture adequate nutrition in their livingspaces can survive; other offspring with their living spacesare eliminated. By this way, lie living spaces continually

evolve. In other words, in order to survive, the offspring olie concentrate and evolve continuously towards the richerliving spaces or ever and never stopped.

3. Description of LSE Algorithm

.. Basic Concepts. First o all, the ollowing concepts shouldbe dened in order to describe LSE algorithm.

Denition (lie). Lie is an abstract entity. Living spaceand living condition, here, namely, nutrition, are the twobasic surviving elements that lie depends on. Lies spatialcoordinates are dened at the midpoint in its living space.

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Step .InitializationSet initial swarm o lie.Set initial living space.

Step .Divide the initial living space to each lie in the initial swarm o lie, namely, assign living space or each lie.Step .Each lie gets nutrient in its living space.Step .For each lie, do:

{Step ..Acquires nutrition in its living space.Step ..Te lie that capture adequate nutrition survives, otherwise dies.Step ..Te surviving lie reproduces its multiple offspring in its living spaces.Step ..Te offspring inherit and share their parental lies living spaces, namely, assign living subspace or each offspring.Step ..Te parental lie die afer reproduction.Step ..Each offspring gets nutrient in its living subspace.}Step .For each offspring, do:{Step ..Te offspring that capture adequate nutrition survives, otherwise dies.Step ..Te surviving offspring reproduces its multiple new offspring in its living subspaces.Step ..Te new offspring inherit and share their parental offsprings living subspaces, namely, assign living subspace or eachnew offspring.

Step ..Te parental offspring die afer reproduction.Step ..Each new offspring gets nutrient in its living subspace.}Step .Go to Step

A : LSE dynamic model.

Denition (living space). Living space denotes the spatialrange where a lie is located in. Lie monopolizes its livingspace. When lie reproduces offspring, its offspring inherit

and share its living space.Denition (nutrition). Nutrition represents the resourcethat lie depends on. Here, the size o nutrition is supposedto be a xed distribution in living space.

Denition (threshold nutrition). Treshold nutrition isdened as a basic amount o nutrition; a lie that acquiresnutrition bigger than or equal to threshold nutrition survives;otherwise, it dies.

Denition (richer living space). Richer living space standsor the living space with richer nutrition. Tere are twocases: or maximum optimizations, richer living space meansthe living space with bigger tness, whereas, or minimumoptimizations, it means the living space with smaller tness.

.. Basic Assumptions. o create LSE algorithm, the ollow-ing assumptions should be introduced too.

Assumption (reproduction). When the acquired nutritionis bigger than or equal to the threshold nutrition, lie canreproduce offspring, whereas i the acquired nutrition issmaller than the threshold nutrition, lie cannot reproduceoffspring.

Assumption (asexual reproduction). Lie reproduces off-spring by asexual means.

Assumption (multiple offspring reproduction). One lie canreproduce multiple offspring within one generation.

Assumption (inheritance and share). Offspring inherit andshare their parental lies living space. But the living spacewhere lie cannot reproduce offspring will be naturally dis-carded because no offspring can inherit and share the livingspace.

Assumption (survival o the ttest). When acquiring nutri-tion bigger than or equal to the threshold nutrition, liesurvives and reproduces offspring; otherwise, lie dies imme-diately.

Assumption (lie cycle). Tere are two cases or liestermination. Lie dies immediately while acquiring nutritionsmaller than threshold nutrition or dies immediately afer

reproducing one generations offspring.

Assumption (nutrition calculation). Te size o nutritionin living space is supposed to be a xed distribution andcalculated by means o itsdistribution unction marked as()with coordinates at midpoint in the living space.

.. Flow o LSE Algorithm. Based on the concepts denedand the assumptions introduced above and according to theLSE dynamic model in Algorithm , we can get the ow oLSE algorithm that is described in Algorithm .

In Algorithm , Step 1 nishes initialization or LSE algo-rithm, including setting the number o lives in initial swarm

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Step .Initialization.Set the number o lives in initial swarm o lie;Set the scope o initial living space;Set the number o offspring reproduced by each surviving lie;Set nutrition distribution unction().Set the maximum number o reproduction generations;

Step .Divide uniormly the initial living space to each lie in the initial swarm o lie, namely, assign uniormly living space oreach lie.Step .Each lie acquires nutrition in its living space, which is calculated by nutrition distribution unction()with coordinatesat midpoint o its living space.Step .For each lie, do:{Step ..Calculate threshold nutrition that is equal to the average o nutrition acquired by all l ives at present.Step ..Te lives that acquire nutrition bigger than or equal to threshold nutrition survive, otherwise die.Step ..Te surviving lives reproduce multiple offspring in their living spaces.Step ..Te offspring inherit and share uniormly their parental lies living spaces, namely, assign uniormly living subspaceor each offspring.Step ..Te parental lie dies afer reproduction.Step ..Each offspring acquires nutrition in its living subspace, which is calculated by nutrition distribution unction()withcoordinates at midpoint o its living subspace.

}Step .Judge whether the maximum number o reproduction generations is reached. I reached, go to Step .Step .For each offspring, do:{Step ..Calculate threshold nutrition that is equal to the average o nutrition acquired by all offspring at present.Step ..Te offspring that acquire nutrition bigger than or equal to threshold nutrition survive, otherwise die.Step ..Te surviving offspring reproduce its mutiple new offspring in its living subspaces.Step ..Te new offspring inherit and share uniormy their parental offsprings living subspaces,namely, assign uniormly living subspace or each new offspring.Step ..Te parental offspring die afer reproduction.Step ..Each new offspring acquires nutrition in its living subspace, which is calculated by nutrition distribution unction()with coordinates at midpoint o its living subspace.}Step .Go to Step Step .Te end

A : Flow o LSE algorithm.

o lie, the ranges o initial living spaces, the number o off-spring reproduced by each surviving lie, and the maximumnumber o reproduction generations and giving the nutritiondistribution unction(). Step2 assigns uniormly livingspace or each lie. In Step3, each lie acquires nutrition inits living space, calculated by nutrition distribution unction

()with coordinates at midpoint o its living space.

Step4 enters a loop or each lie, in which Step 4.1calculates threshold nutrition that is equal to the averageo nutrition acquired by all lives at present. In Step4.2,the lives that acquire nutrition bigger than or equal to thethreshold nutrition survive; otherwise, they die. In Step4.3, the surviving lives reproduce its multiple offspring intheir living spaces. In Step4.4, the offspring inherit andshare uniormly their parental lies living spaces; namely,they assign uniormly living subspace or each offspring. InStep4.5, the parental lie dies afer reproduction. In Step4.6, each offspring acquires nutrition in its living subspace,which is calculated by nutrition distribution unction()with coordinates at midpoint o its living subspace.

Step5judges whether the maximum number o repro-duction generations is reached. I it is reached, go to Step8that ends the LSE algorithm.

Step6 enters a loop or each offspring, in which itsprocedures and operations are same as Step4. Step7goes toStep5. Step8is the end o the LSE algorithm.

We need to pay special attention to the act that Steps

4 and6 accomplish living space evolution and multipleoffspring reproduction, respectively. On the one hand, withinthe course o living space evolution, a portion o lives withtheir livingspaces are eliminated.On the other hand, multipleoffspring reproduction can continuously supplement reshlives in order to maintain a certain number o ones. Tere-ore, multiple offspring reproduction is the prerequisite andguarantee or achieving living space evolution.

.. Implementation o LSE Algorithm. Pseudocodes o LSEalgorithm are summarized as shown in Pseudocode .

In Pseudocode , or ease o computer programing, thenumber o lives in initial swarm is set to be equal to and

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Step . InitializationSet initial-dimensional living space as = {| }, = 1, . . . ,, +Set the number o lives in initial swarm equal to, +,is the number o dimensions o living space.Set the number o offspring reproduced by each surviving lie equal to

next

,next

+,is the number o dimensions o livingspace.Set the nutrition distribution unction in living space equal to(1, 2, . . . , ), , = 1, . . . , , +Set the adjustment coefficient = 1Set the initial value o present reproduction generation = 1Set the maximum number o reproduction generations equal toStep . Share living spaceSet the coordinates o lives inth dimensional living space marked as.= (| ), = 1, . . . ,, = 1, . . . ,Set the interval o sharing evenlyth dimensional living space marked as.= ( )// Interval o sharing uniormlyth dimensional living space /Set= + (1/2)| = 1and(+1)= + | 1/ Relationship o coordinates o lives inth dimensional living space.Te coordinate range o each lie inth dimensional living subspace is [ (1/2),+ (1/2)], and its length is /Where = 1, . . . , , = 1,2 , . . . ,Step . Acquire nutritionCalculate(1, 2, . . . , )or all lives with coordinates at midpoints in their living subspaces.Step . Calculate threshold nutrition

Set threshold nutrition marked. = ((1, 2, . . . , )/)/ Calculate threshold nutrition, which is dened as an average o all(1, 2, . . . , )multiple /Step . Survival o the ttestFor each lieI(1, 2, . . . , ) / Compare(1, 2, . . . , )with /Write its coordinates and nutrition [,(1, 2, . . . , )] into a( + 1)-dimensional linked list Linkedlist / Surviving livesare recorded in Linkedlist, while other lives are dead, which are not recorded into Linkedlist. /End iEnd orSet the length o Linkedlist marked as1.Calculate1rom Linkedlist.Step . Output and Exit loopI Search the maximum o(1, 2, . . . , )rom Linkedlist and output its coordinates and nutrition [, max (1, 2, . . . , )]Output Maximum number of reproduction generations is reached. Exit loop .ExitEnd IStep . ReproductionStep .. Inherit and share living spaceSet the number o offspring reproduced by each surviving lie equal to

next

/ Te coordinate range o offspring inth dimensionalliving space, inherited orm their parent, is[ (1/2),+ (1/2)], and its length is. /For = 1 : 1Readrom Linkedlist / Lives recorded in Linkedlist reproduce offspring. /Set the interval o sharing evenlyth dimensional living space marked as= /next/ Interval o sharing uniormlyth dimensional living space /Set= (1/2)+ (1/2)| = 1and(+1)= + | 1/ Relationship o coordinates o offspring inth dimensionalliving space. Te coordinate range o each offspring inth dimensional living subspace is [ (1/2),+ (1/2)], and itslength is. /Where,

= 1, . . . ,,

= 1,2 , . . . ,,

= 1,2 , . . . ,next

End ForStep .. Acquire nutritionCalculate(1, 2, . . . , )or all offspring with coordinates at midpoints in their living subspaces, and write [,(1, 2, . . . , )]into a ( + 1)-dimensional linked list LinkedlistStep .. Calculate threshold nutritionSet the length o Linkedlist marked as2.2= next1/ Length o Linkedlist / = ((1, 2, . . . , )/2)rom Linkedlist / Calculate threshold nutrition rom Linkedlist, which is dened anaverage o all(1, 2, . . . , )multiple /Step .. Survival o the ttestFor each offspringI(1, 2, . . . , ) / Compare(1, 2, . . . , )with /

P : Continued.

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Write its coordinates and nutrition [,(1, 2, . . . , )] into a ( + 1)-dimensional linked list Linkedlist / Survivingoffspring are recorded in Linkedlist, while other offspring are dead, which are not recorded into Linkedlist. /End iEnd orSet the length o Linkedlist marked as3.Calculate3orm Linkedlist.Step . Lie cycleSet = + 1Linkedlist =/ Parents o the offspring are naturally dead. Teir coordinates and nutrition inormation are lostnaturally in the algorithm. /Linkedlist =/ Now all data o parents are o insignicance /Linkedlist = Linkedlist / Surviving offspring become parents or next generation /1= 3/ Length o linked list or next generation /= / Interval o sharing uniormlyth dimensional living space or next generation /Step . LoopGo to Step / Loop /

P : Pseudocodes o LSE algorithm.

the number o offspring reproduced by each surviving lie isset to be equal tonext, whereis the number o dimensionso living space and a lot o simulations have proved that this iseasible. In addition, offspring inherit andshare their parentallies living space and are to be set to be uniormly distributedin the living space.

Te sofware codes o the LSE algorithm are implementedin C on the platorm o Visual Studio .

.. Output o LSE Algorithm. Te outputo LSE algorithminPseudocode is the maximum o unction(1, 2, . . . , )and its coordinates at last generation.

I the optimality o all generations is going to be output,we can easily improve the LSEalgorithm by adding a unctionthat could output the optimality o each generation and thencompare them to get the optimality o all generations. But,in general, the optimality at last generation could representthe optimality o all generations, because the living space othe later generation is more superior to that o the previousgeneration.

It should be noted that i the comparison statement(1, 2, . . . , ) is turned into(1, 2, . . . , ) in Pseudocode , the output o LSE algorithm will becometo output the minimum o unction(1, 2, . . . , )and itscoordinates at the last generation.

4. Demonstration of LSE

By using the ollowing example, the procedure o LSE is goingto be digitally demonstrated.

.. Function and Parameter Setting. Te ollowing unctionis employed to demonstrate the procedure o LSE:

, = 100.2 3 5 exp 2 2 13exp (1 + )2 2 + 3 (1 )2

exp 2 1 + 2 .()

21

0

12

21

0 1 2

8

4

0

4

8

y-axis x-ax

is

z-axis

F : Graph o two-dimensional unction.

: Parameter setting o two-dimensional unction.

1,2 1,2 next

Te scope o variables, namely, initial living space, is 3 3, 3 3. Te objective is to calculate the minimumo(,). Te graph o the unction is shown in Figure .

Parameter setting is shown in able .

.. Procedure o LSE . Procedure o LSE or the unctionrom the rst generation to the tenth generation is shown inFigure . It is noted that, in Figure , each blue line visuallyrepresents each lie, one end o which stands or the positiono thelie located in itsliving space,while the other endstandsor the size o nutrition acquired by the lie.

In this demonstration, in order to calculate the minimumo the unction, the comparison statement(1, 2, . . . , ) in LSE algorithm should be turned into(1, 2, . . . , )

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(b)

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(d)

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(e)

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y-axis x-axis

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()

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z-axis

(g)

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(h)

F : Continued.

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(i)

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(k)

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(l)

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(m)

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(o)

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(p)

F : Continued.

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(q)

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(t)

F : Processes o LSE or the unction rom the rst generation to the tenth generation, where each blue line visually represents each lie,one end o which stands or the position o the lie located in its living space, while the other end stands or the size o nutrition acquired bythe lie. (a) Te rst generation data; (b) the rst generation survival data; (c) the second generation data; (d) the second generation survivaldata; (e) the third generation data; () the third generation survival data; (g) the ourth generation data; (h) the ourth generation survivaldata; (i) the fh generation data; (j) the fh generation survival data; (k) the sixth generation data; (l) the sixth generation survival data; (m)the seventh generation data; (n) the seventh generation survival data; (o) the eighth generation data; (p) the eighth generation survival data;(q) the ninth generation data; (r) the ninth generation survival data; (s) the tenth generation data; (t) the tenth generation survival data.

; by this way, the output o LSE algorithm is the minimumo the unction and its position.

Figure (a) shows the rst generation data, where all thelives (here, = 4, = 2, so the total number o lives isequal to = 42 = 16) are set to be uniormly distributedin the living space. Figure (b) shows the rst generationsurvival data, where some o the lives are discarded afer

the operation o the survival o the ttest. Figure (c) showsthe second generation data, where each lie reproduces ouroffspring (here,next= 2, = 2, so the number o offspringreproduced by each lie is equal to2next = 4) and theour offspring are set to be distributed uniormly in each liesubspace too. Te rest o the gures (Figures (d)(t)) canbe done in the same manner.

It is observed rom Figure that the living spaces o off-spring are gradually moving closer and closer to the positionwhere the minimum o(,)is located as the generation isincreased, which means that Figure has demonstrated theprocedure o LSE; namely, the lies living spaces can evoluteto the richer living spaces. In this demonstration, we should

note thatwe wantto calculate the minimum o(,), whichmeans the richer living space is the living space where the

value o unction is smaller.Te above procedure o LSE could also be simply

expressed as a graphical abstract shown in Figure , whichis a continuously evolving result rom the rst generation tothe tenth generation.

Why canthe lies living spacesevolve to the richer spaces?Te reasons can be explained as ollows. Firstly, in LSEalgorithm, the lives that acquire nutrition biggerthan or equalto the threshold nutrition survive, and their living spacesare inherited by their offspring and thereore preserved. Incontrast, the lives that acquire nutrition smaller than thethreshold nutrition die and their living spaces immediatelydisappeared. Here, richer living space stands or the livingspace with richer nutrition. Secondly, a lie could reproducemultiple offspring, which could on the one hand supplementresh lives and could on the other hand accelerate theprocedure o living space evolution to much richer livingspaces. Te procedure o LSE seems like that people move

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Living space evolution

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F : Graphical abstract o LSE.

continuously rom countryside to city and the population incity rapidly increases because the living space in city is muchricher than that in countryside.

5. Examples for LSEs Application

Here, two examples are employed or LSEs applications. Terst is the optimization or continuous unctions; the other isto apply LSE to routing protocol or sensor networks that is adiscrete problem in real world. Te critical question or LSEsapplications is the creation o living space. For continuousunction, living space is its variable space. But, or discreteproblem in real world, how to create its living space dependson specic issues.

.. Optimization or Continuous Functions

... Continuous Functions. Nine continuous unctionsincluding three unimodal unctions and six multimodalunctions are employed or the optimization or continuousunctions with the objective o computing the minimumo each unction. Teir mathematical models and threedimensional graphs are given and illustrated in able .

... Parameter Settings. Parameter settings o the ninecontinuous unctions are shown in able . In order to beconcise and get to the point, here only three-dimensional

variables o the unctions are calculated.

... Results o Optimization. We should note that in orderto calculate the minimum o these unctions the comparisonstatement(1, 2, . . . , ) in LSE algorithm should beturned into(1, 2, . . . , ) , so that the optimizationresult o which is to output the minimum o each unctionand its position.

Optimization results o the nine continuous unctions areshown in able , rom which the ollowing results could bedrawn.

For sphere, the minimum searched is equal to .through generations. For weighted sphere, the minimum

searched is equal to . through generations. ForSchweels, the minimum searched is equal to . through generations. For Rosenbrock, the minimum searched isequal to through generations. For Rastrigin, the min-imum searched is equal to . through gen-erations. For Griewank, the minimum searched is equalto9.17386 05 through generations. For Schweel,the minimum searched is equal to . through generations. For Ackley, the minimum searched is equalto . through generations; For Schaffers , theminimum searched is equal to5.143344 05 through generations. Furthermore, multiple coordinate points havethe same minimum or some unctions. For example,sphere has the same minimum o . at coordinate

points, namely, (0.01,0.01,0.01), (0.01,0.01,0.01),(0.01,0.01,0.01) ,(0.01,0.01, 0.01), (0.01,0.01,0.01),(0.01,0.01,0.01),(0.01, 0.01, 0.01), and(0.01,0.01, 0.01).Other unctions o multiple coordinate points are not listedhere.

Graphs that illustrate the convergence perormance orthe nine benchmark unctions are shown in Figure .

From Figure , it can be observed that or all unctionsthe minimum searched by the later generation is smaller thanthe previous generation, which indicates that living spacesare evolving towards much better ones. For Rosenbrock, theminimum o the unction is directly obtained, while theminima o other unctions searched by LSE are getting closer

and closer to the real minima o the unctions as the numbero generations is increased. Hence, LSE is effective or theoptimization o these unctions.

Why is LSE algorithm effective or the optimization othese unctions? Te success o an optimization methoddepends on a large extent on the careul balance o twoconicting goals, exploration and exploitation. While explo-ration is an important global search to ensure that everypart o the solution space is searched enough to provide areliable estimate o the global optimum, exploitation is animportant local search around the best solutions ound so arby searching their neighborhoods to reach better solutions[]. From the optimization course o these unctions, we can

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T:Benchmarkfunctions.

Name

Formula

Range

Optimalvalue

SketchinD

Sphere

()=

=1

2

[5.12,5.1

2]

min()=0

=0

40 20 0

5

5

0

0

5

5

Weightedsphere

()=

=1

2

[5.12,5.1

2]

min()=0

=0

5

5

0

0

55

80

60

40

20

0

Schwefels

()=

=1

=1

2

[5.12,5.1

2]

min()=0

=0

5

5

0

0

5

5

80

60

40

20 0

Rosenbrock

()=

1

=1

100

+1

2

2+

1

2

[2.048,2.048]

min()=0

=0

2

2

1

1

0

0

1 1

2 2

20

00

15

00

10

00

500 0

Rastrigin

()=

=1

2

10

cos

2

+10

[2.048,2.048]

min()=0

=0

2

2

1

1

0

0

1

1

2

2

4

0

3

0

2

0

1

0 0

Griewank

()=

14000

+1

2

=

1

cos

+1

[5.12,5.1

2]

min()=0

=0

5

5

0

05

5

2

.0

1

.5

1

.0

0

.5

0

.0

Schwefel

()=

=1

sin

+418.9829

[100.1

2,500.12]

min()=0

100

100

200

200

300

300

400 4

00

5

00

500

100

0

50

0 0

Ackley

()=20exp

0.2

1 =

1

2

exp

1

=1

cos

2

+20+

[5.12,5.1

2]

min()=0

=0

5 5

0 0

5

5

10 5 0

Schaffersf

()=

sin

=

1

2 2

0.5

1+0.001

=1

2

+0.5

[2.12.2.1

2]

min()=0

=0

2

2

1

1

0

0

1

1

2

2

1.0 0.

50

.0

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: Parameter settings o the test unctions.

Function Dimension Initialization

1,2,3 1,2,3 next Sphere . . Weighted sphere . . Schweels . . Rosenbrock . . Rastrigin . . Griewank . . Schweel . .

Ackley . . Schaffers . .

: Optimization results o continuous unctions.

Function Simulation results

1 2 3 Minimum

Sphere . . . .Weighted sphere . . . .Schweels . . . .Rosenbrock

Rastrigin . . . .Griewank . . . .ESchweel . . . .

Ackley . . . .Schaffers . . . .E

Note: some unctions have multiple coordinate points, but they are not listed here.

know that, at the beginning, all o the lives are uniormlydistributed in the whole living spaces, so their search isa global one. While the LSE algorithm goes ahead, theiroffspring evolve towards some richer spaces, and their searchbecomes a local one. Tereore, In LSE, its prophase isexploration and its anaphase is exploitation. Tat is to say,LSE has a special ability to balance the search process romexploration to exploitation gradually.

.. Application or Routing Protocol in Wireless SensorNetworks. In routing protocol or wireless sensor networks(WSNs), LEACH [, ] is a amous clustering protocolthat resolves the energy unbalancing problem among nodes

by reorming clusters once every period o time, called around, in order to rotate the role o the cluster header amongmembers in a cluster. LEACH randomly selects a portion onodes as cluster headers that gather the neighboring nodesto construct clusters. Each node orwards its sensed data to acluster header that collects and delivers data to the sink node.LEACH takes account o data usion and energy balancedamong nodes within a cluster, but it does not consider thedistance rom each cluster header to sink node, which wouldcause imbalanceo energy. o solve this problem, CPSOCH isproposed in [], where both energy balance and the distanceo each cluster header to sink node are to be considered.In this work, CPSOCH is improved by taking LSE as

a new approach o optimization instead o Chaos-PSO or theselection o cluster headers.

... Problem Description

() Network and Energy Model. Network model is assumed tobe as ollows.

() Tere aresensor nodes distributed in an interestedarea. Each node has a unique identity.

() All nodes are homogeneous in terms o initial energyandconstant transmissionrange. Te total energy in any nodeis limited.

() All sensor nodes can use power control to vary the

amount o transmit power in order to communicate with thesink node.

() A sink node is located at some convenient place out othe sensor eld, which has sufficient energy resource.

() Te sink node andthe sensornodesare stationaryaferdeployment. Teir locations are known by each other.

Energy model is assumed to be as ollows.Te radio o power, x(,), consumed by a transmitting

node to send a-bit message over distance m is

x(, )=

elec+ 2 < 0elec+ 4 0 .

()

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Minimum

0.0001

0.001

0.01

0.1

1

10

Minimum

2 3 4 5 6 7 81

Generation

(a)

0.0001

0.001

0.01

0.1

1

10

100

Minimum

Minimum

2 3 4 5 6 7 81

Generation

(b)

0.0001

0.001

0.01

0.1

1

10

100

Minimum

Minimum

2 3 4 5 6 7 81

Generation

(c)

0

2

4

6

8

10

12

14

16

Minim

um

Minimum

2 3 4 5 6 71

Generation

(d)

0.001

0.01

0.1

1

10

100

Minim

um

Minimum

2 3 4 5 6 71

Generation

(e)

0.00001

0.0001

0.001

0.01

0.1

1

Minim

um

Minimum

2 3 4 5 61

Generation

()

Minimum

0.001

0.01

0.1

1

10

100

Minimum

2 3 4 5 61

Generation

(g)

Minimum

2 3 4 5 6 7 8 91

Generation

0.01

0.1

1

10

Minimum

(h)

Minimum

0.00001

0.0001

0.001

0.01

0.1

1

Minimum

2 3 4 5 6 7 81

Generation

(i)

F : Convergence perormance. (a) Sphere; (b) weighted sphere; (c) Schweels; (d) Rosenbrock; (e) Rastrigin; () Griewank; (g) Schweel;

(h) Ackley; (i) Schaffers .

o receive this message, the radio o power()expends

Rx()= elec. ()o process this message, the radio o powerda-us()

expends

da-us()= da, ()

whereelec is energy consumption o sending circuits andreceiving circuits.da is energy consumption o processingdata.s andmpare energy consumption o power ampliersin ree space model and multipath ading model, respectively.0is threshold o transmission distance.() Objective or Clustering Routing. Te objective is to electcluster headers rom thesensor nodes to createclusters,which should meet the ollowing demands: the more the

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Step .Initialization.Set the number o nodes in initial sensor networks;Set the parameters o energy model according to (), () and ();Set the parameters o tness according to ();Set the maximum number o data transmission;

Step .Select cluster heads, set up clusters, create schedule and then transmit data according to the methods provided by LEACH;

Step .Judge whether the maximum number o data transmission is reached. I reached, go to Step ;Step .Cluster head selection optimized by LSE:Step ..Give a serial number to each node in the interesting area;Step ..Set the number o cluster heads;Step ..Set the maximum number o iterations according to computing capability o each node;Step ..Judge whether the maximum number o iterations is reached. I reached, go to Step ;Step ..Optimization by LSE according to Sections .. and .., where tness is computed by ();Step ..Issue the inormation o cluster headers;Step ..go to Step .;Step .Set up clusters, create schedule and then transmit data according to the methods provided by LEACH;Step .Goto Step Step .End

A : Clustering routing algorithm based on LSE.

optimization; the only difference is that the valueso the coor-dinate axesandare discrete ones instead o continuousones in LSE.

For example, in the discrete two-dimensional living spaceshown in Figure , the values o coordinate axesandallinto{1, 2, . . . , 100}with lower bound and upper bound ,where LSE is easy to be used.

... Clustering Routing Algorithm Based on LSE. Clusteringrouting algorithm based on LSE is described in Algorithm .

In the rst round, at the beginning o deployment, theremaining energy o all the nodes in the sensor networksis provided to be equivalent. Tereore, we can still employLEACH algorithm or the selection o cluster heads as shownin Step 2. From the second round, the remaining energy o allthe nodes in the sensor networks is no longer equivalent, andthe sink node should use the optimization methods based onLSE introduced in the paper or the selection o cluster headsas shown in Step4.

In Step4.5, the process o cluster head selectionoptimizedby LSE should be done according to the methods describedpreviously in Sections .. and ...

In Section ., LSE is used as an optimization tool or

routing protocol in wireless sensor network and its optimiza-tion methods and processes are described in detail, by whichwe can see that LSE is also applicable or the optimization orsome discrete problems in real world.

6. Conclusions

In this paper, a new computational intelligence approach,namely, living space evolution (LSE), is presented, which isinspired by lie cycle and survival o the ttest and combinedwith the consideration o living space inormation. LSEdynamic model, its ow, and pseudocodes are described indetail. A digital simulation has shown the procedure o LSE.

Furthermore, two applications o using LSE are employed todemonstrate its effectiveness and applicability. One is to applyit to the optimization or continuous unctions; the other is touse it as an optimization tool or routing protocol in wirelesssensor network that is a discrete problem in real world.

By means o simulations and discussions in the paper,conclusions could be summarized as ollows.

() Research has shown that LSE is effective or theoptimization or the continuous unctions and also applicableor the discrete problem in real world.

() LSE has reected two new ideas. One is living spaceevolution. Te other is multiple offspring reproduction. Mul-tiple offspring reproduction is the prerequisite and guaranteeor achieving living space evolution.

() Te critical question or LSEs applications is thecreation o living space. For continuous unction, living spaceis its variable space. But, or discrete problem in real world,how to create its living space depends on specic issues.

() In LSE, its prophase is exploration and its anaphaseis exploitation; in other words, LSE has a special abilityto balance search process rom exploration to exploitationgradually.

Conflict of InterestsTe author declares that there is no conict o interestsregarding the publication o this paper.

References

[] Z. Cui and R. Xiao, Bio-inspired computation: theory andapplications,Journal o Multiple-Valued Logic and Sof Comput-ing, vol. , no. , pp. , .

[] W. J. ang and Q. H. Wu, Biologically inspired optimization:a review, ransactions o the Institute o Measurement andControl, vol. , no. , pp. , .

7/25/2019 804512

16/17


[] A. P. Engelbrecht,Computational Intelligence: An Introduction,John Wiley & Sons, West Sussex, UK, nd edition, .

[] D. Zhao, Y. Dai, and Z. Zhang, Computational intelligence inurban traffic signal control: a survey, IEEE ransactions on Sys-tems, Man and Cybernetics C: Applications and Reviews, vol. ,no. , pp. , .

[] M. Danziger and M. A. A. Henriques, Computational intelli-gence applied on cryptology: a briereview, IEEELatin Americaransactions, vol. , no. , pp. , .

[] H. Zhang, Z. Wang, and D.Liu, A comprehensivereviewo sta-bility analysis o continuous-time recurrent neural networks,IEEE ransactions on Neural Networks and Learning Systems,vol. , no. , pp. , .

[] C. Cioffi-Revilla, K. de Jong, and J. K. Bassett, Evolutionarycomputation and agent-based modeling: biologically-inspiredapproaches or understanding complex social systems, Com-putational and Mathematical Organization Teory, vol. , no., pp. , .

[] S. K. Pal, S. Bandyopadhyay, and S. S. Ray, Evolutionarycomputation in bioinormatics: a review, IEEE ransactions

on Systems, Man, and Cybernetics, Part C: Applications andReviews, vol. , no. , pp. , .

[] A. M. Zungeru, L.-M. Ang, and K. P. Seng, Classical andswarm intelligence based routing protocols or wireless sensornetworks: a survey and comparison, Journal o Network andComputer Applications, vol. , no. , pp. , .

[] A. Khosravi, S. Nahavandi, D. Creighton, and A. F. Atiya,Comprehensive review o neural network-based predictionintervals and new advances, IEEE ransactions on NeuralNetworks, vol. , no. , pp. , .

[] J. Zhang, Z.-H. Zhang, Y. Lin et al., Evolutionary computationmeets machine learning: a survey,IEEE Computational Intelli-gence Magazine, vol. , no. , pp. , .

[] H. Chen, Y. Zhu, L. Ma, and B. Niu, Multiobjective RFIDnetwork optimization using multiobjective evolutionary andswarm intelligence approaches, Mathematical Problems inEngineering, vol. , Article ID , pages, .

[] N. A. Alrajeh and J. Lloret, Intrusion detection systemsbased on articial intelligence techniques in wireless sensornetworks, International Journal o Distributed Sensor Networks,vol. , Article ID , pages, .

[] X. Yao and D. Gong, Genetic algorithm-based test data gener-ation or multiple paths via individual sharing,ComputationalIntelligence and Neuroscience, vol. , Article ID , pages, .

[] D. Gong, J. Yan, and G. Zuo, A review o gait optimizationbased on evolutionary computation, Applied Computational

Intelligence and Sof Computing, vol. , Article ID , pages, .

[] S. Salcedo-Sanz, B. Saavedra-Moreno, A. Paniagua-ineo, L.Prieto, and A. Portilla-Figueras, A review o recent evolu-tionary computation-based techniques in wind turbines layoutoptimization problems,Central European Journal o ComputerScience, vol. , no. , pp. , .

[] P. Civicioglu, Backtracking search optimization algorithm ornumerical optimization problems,Applied Mathematics andComputation, vol. , no. , pp. , .

[] A. El-Fergany, Optimal allocation o multi-type distributedgenerators using backtracking search optimization algorithm,International Journalo ElectricalPower and Energy Systems, vol., pp. , .

[] J. Krause, G. D. Ruxton, and S. Krause, Swarm intelligence inanimals and humans,rends in Ecology and Evolution, vol. ,no. , pp. , .

[] B. Yao, R. Mu, and B. Yu, Swarm intelligence in engineering,Mathematical Problems in Engineering, vol. , Article ID, pages, .

[] Z. Cui and X. Gao, Teory and applications o swarm intel-ligence,Neural Computing and Applications, vol. , no. , pp., .

[] J. Kennedy and R. C. Eberhart, Particle swarm optimization,inProceedings o the IEEE International Conerence on NeuralNetworks, Piscataway, vol. , pp. , Piscataway, NJ,USA, December .

[] W. Elloumi, H. El Abed, A. Abraham, and A. M. Alimi, A com-parative study o the improvement o perormance using a PSOmodied by ACO applied to SP, Applied Sof ComputingJournal, vol. , pp. , .

[] H.-K. Hsin, E.-J. Chang, and A.-Y. Wu, Spatial-temporalenhancement o ACO-based selection schemes or adaptiverouting in network-on-chip systems, IEEE ransactions on

Parallel and Distributed Systems, vol. , no. , pp. ,.

[] D. Ruperez Canas, A. L. Sandoval Orozco, L. J. Garca Villalba,and P.-S. Hong, Hybrid ACO routing protocol or mobileAd hoc networks, International Journal o Distributed SensorNetworks, vol. , Article ID , pages, .

[] D. Karaboga, An idea based on honey bee swarm or numericaloptimization, ech. Rep. R, Erciyes University, Kayseri,urkey, .

[] J. D. Farmer, N. H. Packard, and A. S. Perelson, Te immunesystem, adaptation, and machine learning,Physica D, vol. ,no. , pp. , .

[] D. Dasgupta, S. Yu, and F. Nino, Recent advances in articialimmune systems: models and applications,Applied Sof Com-

puting, vol. , no. , pp. , .

[] R. Tangaraj, M. Pant, A. Abraham, and P. Bouvry, Particleswarm optimization: hybridization perspectives and experi-mental illustrations, Applied Mathematics and Computation,vol. , no. , pp. , .

[] W. R. Heinzelman, A. Chandrakasan, and H. Balakrish-nan, Energy-efficient communication protocol or wirelessmicrosensor networks, in Proceedings o the rd AnnualHawaii International Conerence on System Siences (HICSS ),p. , IEEE, Maui, Hawaii, USA, January .

[] W. B. Heinzelman, A. P. Chandrakasan, and H. Balakrish-nan, An application-specic protocol architecture or wirelessmicrosensor networks, IEEE ransactions on Wireless Commu-nications, vol. , no. , pp. , .

[] Z. Liiu, Z. Liu, and C. Li, A clustering protocol or wirelesssensor networks based on Chaos-PSO optimization, ChineseJournal o Sensors and Actuators, vol. , no. , .

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