Investigation on the Inversion of the Atmospheric Duct Using the

Research ArticleInvestigation on the Inversion of the AtmosphericDuct Using the Artificial Bee Colony Algorithm Based onOpposition-Based Learning

Chao Yang1 Jian-Ke Zhang1 and Li-Xin Guo2

1School of Science Xirsquoan University of Posts and Telecommunications Xirsquoan 710121 China2School of Physics and Optoelectronic Engineering Xidian University Xirsquoan 710071 China

Correspondence should be addressed to Chao Yang yang chaomail163com

Received 14 January 2016 Accepted 21 March 2016

Academic Editor Sotirios K Goudos

Copyright copy 2016 Chao Yang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The artificial bee colony (ABC) algorithm is a recently introduced optimization method in the research field of swarm intelligenceThis paper presents an improved ABC algorithm named as OGABC based on opposition-based learning (OBL) and global bestsearch equation to overcome the shortcomings of the slow convergence rate and sinking into local optima in the process ofinversion of atmospheric duct Taking the inversion of the surface duct using refractivity from clutter (RFC) technique as anexample to validate the performance of the proposed OGABC the inversion results are compared with those of the modifiedinvasive weed optimization (MIWO) and ABC The radar sea clutter power calculated by parabolic equation method using thesimulated and measured refractivity profile is utilized to carry out the inversion of the surface duct respectively The comparativeinvestigation results indicate that the performance of OGABC is superior to that of MIWO and ABC in terms of stability accuracyand convergence rate during the process of inversion

1 Introduction

The lower atmospheric duct commonly encountered inmarine boundary layer is an abnormal electromagnetic envi-ronment due to the sharp variations of atmospheric tempera-ture and humidity above the sea surface In the ducting envi-ronment the performance of radar system and communica-tion system can be significantly changed such as the maxi-mumoperation range creation of radar holes where the radaris practically blind and strengthened sea surface clutter [1 2]Therefore it is of great importance to infer the atmosphericduct owing to its considerable effect on the radar and com-munication system that are designed to work under standardatmospheric conditionswith a typical slope of 0118M-unitss[3]

In general the atmospheric duct is represented by themodified refractivity profile The traditional methods ofdetermining the atmospheric duct include radiosondes rock-etsondes microwave refractometers and lidar Nevertheless

the traditional measurement methods have the drawbacks ofhigh cost and containing many restrictive factors RecentlyRFC technique [4 5] has been a promising method to inferthe atmospheric duct It uses the propagation characteristicsof radar sea clutter signal to infer the modified refractiv-ity profile information of atmospheric duct And the RFCtechnique has the advantages of simple devices and easyimplementation

Inversion of atmosphere duct from the RFC techniquehas been an important research subject over the past severaldecades owing to its important applications in radar systemand communication system More attention is paid to thestudy of inversion model and optimization model in RFCtechnique The detailed procedures of RFC technique aregiven by Gerstoft et al [4] and the inversion of the rangedependent and independent atmospheric duct using RFCtechnique is implemented by genetic algorithm Karimianet al [5] published a review paper on the latest researchdevelopments and the direction of future work to be done

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 2749035 10 pageshttpdxdoiorg10115520162749035

2 International Journal of Antennas and Propagation

about RFC technique Zhao et al [6 7] derive the inversiontheoretical framework of adjoint method from parabolicequation model and the feasibility of the adjoint method isvalidated by numerical simulations As is known to all esti-mation of atmosphere duct using RFC technique is an inverseproblem Taking the nonlinear relation between the forwardpropagation model and atmospheric duct parameters intoconsideration the investigation on the optimization modelswith high performance is one of the most important researchtopics in the field of inversion of the atmospheric ductfrom radar sea clutter For instance the least square supportvector machine the particle swarm optimization (PSO)the simulated annealing algorithm and the ABC algorithmhave been applied to infer the atmospheric duct using RFCtechnique [8ndash11]

The ABC algorithm [12] is one of the most recentlyproposed swarm intelligence algorithms which simulatesthe intelligent behavior of honeybee swarm In ABC theoptimization procedures are implemented by simulating theintelligent foraging behavior of a honeybee swarm to shareinformation of bees for the purpose of finding the optimalsolution Currently the ABC algorithm has been applied tothe design of antenna and electromagnetic devices [13ndash15]In addition the ABC algorithm has been used to infer theatmospheric duct from RFC technique [11] and the compar-ative study results demonstrate that the performance of ABCis superior to that of the PSO for the inversion of atmosphericduct However the ABC also has the drawbacks of easilyfalling into local optima and slower convergence rate Toovercome this issue the improvedABChas been proposed byupdating the search equation to enhance its optimization per-formance and the improved ABC is validated by benchmarkfunction [16 17] In recent years the OBL was introducedby Rahnamayan et al [18] and has been proven to be auseful strategy to enhance the accuracy and convergence rateof the optimization algorithm such as differential evolutionand PSO

In this paper the OGABC is proposed by incorporatingthe OBL strategy and global best search equation into theABC to enhance the performance of ABC in the inversion ofatmospheric duct In OGABC the OBL is used to acceleratethe convergence rate and the global best search equation isadopted to balance the local and global search ability

2 The Propagation Model andObjective Function

21 Parabolic Equation Method Considering that theparabolic equation method has the advantages of highstability and accuracy it has been extensively utilized toinvestigate the tropospheric electromagnetic wave propa-gation In rectangular coordinates the parabolic equationcan be represented as

1205972119906

1205971199112+ 21198941198960

120597119906

120597119909+ 1198962

0(1198992minus 1) 119906 = 0 (1)

where 119899 is the refractive index and 1198960is the free space wave

number

If the initial field is provided the split step Fouriersolution of parabolic equation method at different range canbe easily obtained by [19]

119906 (1199090+ Δ119909 119911)

= 119890(11989411989602)[119899

2minus1]Δ119909

119865minus1119890(119894Δ11990921198960)119901

2

119865 [119906 (1199090 119911)]

(2)

where 119865 and 119865minus1 are the Fourier transform and inverse

Fourier transform respectively 119901 is the transform variableΔ119909 is the distance interval and 119906(119909

0 119911) is the initial field It

should be pointed out that this researchmainly focuses on theinversion of atmospheric duct more detailed information onthe propagation problemwith parabolic equationmethod canbe found in [19]

22 Radar Sea Clutter Power In RFC technique the objec-tive function is described by the radar sea clutter powerat different propagation distances Taking the influence ofatmosphere condition into account the received radar seaclutter power based on radar equation can be expressed indB by [4]

119875119888(m) = minus2119871 + 120590

∘+ 10 lg (119903) + 119862 (3)

where 119871 is the propagation loss calculated by the parabolicequationmethod120590∘ is the radar cross section obtained by theGIT sea clutter model [20] 119903 is the propagation distance 119862 isa constant that includes wavelength transmitter power andantenna gain and m is the parameter vector of the atmo-spheric duct

In this paper the surface based duct is described by thefollowing four-parameter model [2]

119872(119911) = 1198720

+

1198881119911 119911 lt ℎ

1

1198881ℎ1+ 1198882(119911 minus ℎ

1) ℎ

1le 119911 le ℎ

2

1198881ℎ1+ 1198882ℎ2+ 0118 (119911 minus ℎ

1minus ℎ2) 119911 gt ℎ

2

(4)

where 1198720is the base refractivity and 119888

1and ℎ

1stand for

the slope and thickness of the base layer whereas 1198882and ℎ

2

represent the slope and thickness of the inversion layerrespectively

23 The Objective Function In the process of inversion thecommonly used least squares objective function is given by[4]

119891 (m) = eTe

e = Pobs119888

minus P119888(m) minus

= Pobs119888

minus P119888(m)

(5)

where Pobs119888

and P119888(m) stand for the observed and received sea

clutter power at different ranges and Pobs119888

and P119888(m) denote

the average power of Pobs119888

and P119888(m) respectively

International Journal of Antennas and Propagation 3

3 The Proposed OGABC Algorithm

31TheOBL TheOBL strategy can improve the convergencerate and accuracy of optimization algorithm by simultane-ously evaluating the initial solution and opposite solution forthe population initialization and for the generation jumpingThe probability theory indicates that the opposite solutioncan increase the opportunity of approaching the global bestsolution in the search process The definitions of oppositenumber and opposite solution are given by [18]

Definition 1 Let119909 isin [119897 119906] be a real number Its correspondingopposite number is defined by

= 119897 + 119906 minus 119909 (6)

Definition 2 Let 119883 = (1199091 1199092 119909

119863) be a solution in 119863-

dimensional space where 119909119894isin [119897119894 119906119894] and 119897

119894 119906119894are lower

and upper bounds of the 119894th dimension The correspondingopposite solution = (

1 2

119863) is defined by

119894= 119897119894+ 119906119894minus 119909119894

119894 = 1 119863 (7)

In this paper the inversion of atmospheric duct is aminimization problem With the help of the definition ofopposite solution the OBL in the inversion of atmosphericduct can be described by the following if 119891() le 119891(119883) thenrandom solution 119883 can be replaced with otherwise wecontinue with 119883 Additionally according to a jumping ratethe better population for the next iteration can be obtainedby the generation jumping using the current and theircorresponding opposite population Evidently the randomsolution and opposite solution are simultaneously evaluatedto select the better solution in the search process

32 The Proposed OGABC and Its Implementation StepsThe ABC is one of the most recent swarm intelligenceoptimization algorithms proposed by Karaboga under theinspiration of the intelligent foraging behavior of honeybeeswarm In ABC there are three types of honeybees employedbees onlooker bees and scoutsThe position of a food sourcestands for a possible solution of the optimization problemand the nectar amount of a food source is employed toevaluate the quality of the solutionThe number of employedbees is equal to the number of food sources and the halfof the population size The employed bees undertake theresponsibility of searching for food sources and share theeffective information with onlooker bees The onlooker beestry to make a further selection of the excellent food sourcesbased on the information provided by employed bees Ifthe quality of food source cannot be improved through apredetermined condition the corresponding food sourcebecomes a scoutThen the scout begins to randomly generatea new food source at the neighborhood of the hive

In order to enhance the performance of ABC in theinversion of atmospheric duct the OGABC is presentedby incorporating the OBL strategy and global best searchequation into ABC algorithmThemain steps of OGABC aresummarized as follows

Step 1 (opposition-based population initialization) Step 1contains the following

Step 11 Randomly produce119863-dimensional population1198830of

119873 solutions by

1198830119894119895

= 119897119895+ rand (0 1) (119906

119895minus 119897119895)

119894 = 1 2 119873 119895 = 1 2 119863

(8)

Step 12 Generate the opposite population 1198741198830of1198830by

1198741198830119894119895

= 119897119895+ 119906119895minus 1198830119894119895

(9)

Step 13 Choose the119873 best solutions from [1198830 1198741198830] accord-

ing to the fitness value to produce the initial population

Step 2 (in employed bees stage) Step 2 contains the following

Step 21 Update the position of food sources using the globalbest search (10) [16] and evaluate the quality of the newposition of food sources

V119894119895= 119909119894119895+ 120601119894119895(119909119894119895minus 119909119896119895) + 120595119894119895(119910119895minus 119909119894119895)

(119894 119896 = 1 119873 119895 = 1 119863)

(10)

where the subscripts 119896 119894 and 119895 are randomly selected andsatisfy 119896 = 119894 119910

119895is the 119895th element of the global best solution

and 120601119894119895and 120595

119894119895are uniform random number in [minus1 1] and

[0 15] respectively

Step 22 Apply the greedy selectionmechanism to choose thebetter food source between the old and new food source

Step 3 Calculate the probability of each food source accord-ing to

119901119894=

fit119894

sum119873

119896=1fit119896

(11)

where fit119894represents the fitness value of the food source 119894

computed in employed bees stage

Step 4 (in onlooker bees stage) Step 4 contains the following

Step 41 Update the position of food sources using (10)according to the probability computed in Step 3

Step 42 Apply the greedy selection mechanism again tochoose the better food source

Step 5 Memorize the best solution so far

Step 6 In scouts stage decidewhether a food source becomesa scout or not if it exists the food source is replaced by a newrandom solution

Step 7 (opposition-based generation jumping) Step 7 con-tains the following


Opposition-based population initializationwith (8) and (9)

In employed bees stage update the positionof food sources using the global best search (10) and choose the better one

In onlooker bees stage update the position offood sources using the global best search (10) and choose the better one

Does scout exist

Terminal condition

No

End

Yes

Begin

Opposition-based generation jumpingaccording to the jumping rate

Replace the scout with a random solution

Yes

No

Figure 1 The flowchart of the proposed OGABC algorithm

Step 71 According to the jumping rate decide whetheropposition-based generation jumping appears or not if itappears the new opposite population 119874119883 of 119883 are producedby

119874119883119894119895= 119897

min119895

+ 119906max119895

minus 119883119894119895

119894 = 1 2 119873 119895 = 1 2 119863

(12)

where 119897min119895

and 119906max119895

are the minimum and maximum valueof the 119895th dimension in the current population

Step 72 Choose the119873 best solutions from [119883119874119883] accordingto the fitness value to generate the population for the nextiteration

Step 8 Repeat Step 2 to Step 7 until a terminating conditionis met

The flowchart of the proposed OGABC is shown inFigure 1

4 The Numerical Results and Discussions

In this section the inversion results are given to validatethe optimization performance of the proposed OGABC Inthe following we take the inversion of the four-parametersurface duct with RFC technique as an example to analyzethe performance of OGABC and the inversion results arecompared with those of the MIWO [21] and ABC

In fact the essence of the inversion of surface duct isto obtain its corresponding refractivity profile determined


005 01 015 02 0250

5

10

15O

ccur

renc

eO

ccur

renc

eO

ccur

renc

eO

ccur

renc

e

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus22 minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus22 minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus220

5

10

15

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

MIWO ABC OGABC

14 16 18 20 22 24 26 28 300

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)

Figure 2 The comparison of the histograms of the inversion results for different algorithms with the noise level of 0 dB

Table 1 The lower and upper search bounds of the parameters

Parameter Lower bound Upper bound Units1198881

00 025 M-unitsm1198882

minus35 minus10 M-unitsmℎ1

250 500 mℎ2

100 300 m

by (4) In other words the optimization problem can betranslated into the inversion of the parameters of the surfaceduct m = (119888

1 1198882 ℎ1 ℎ2) and the lower and upper bounds of

the surface duct parameters are shown in Table 1In numerical simulation the inversions are implemented

by the radar sea clutter power calculated by parabolic equa-tion method using the simulated and measured refractivityprofile respectively During the inversion the simulatedradar sea clutter power from 10Km to 50Km is regardedas the observed radar sea clutter power and the radarsystem operates at a frequency of 10GHz power of 914 dBmantenna gain of 528 dB antenna height of 7m beam widthof 07∘ 600m range bin and HH polarization In additionthe control parameters of OGABC are given as followsthe population size is 60 the number of food sources is30 the parameter limit is 25 the maximum number ofiterations is 120 and the jumping rate of OBL is 03 [18]the parameters settings for MIWO are given as follows theinitial population size is 30 the maximum population size is

40 the maximum number of iterations is 120 the nonlinearmodulation index is 3 theminimumandmaximumnumbersof seeds are 0 and 10 the initial and final value of standarddeviation are 100 and 00001 and the inversion results areobtained from 30 independent runs for each algorithm forthe simulated refractivity profile case For a fair comparisonbetween ABC and OGABC they are examined using thesame parameter settings and the settings of the radar systemremain unchanged in the process of inversions

For the simulated refractivity case the radar sea clutterpower computed by the parameters of the surface duct m =

(013 minus25 40 20) is utilized to the inversion of the surfaceduct Moreover the Gaussian noise with zero mean anddifferent standard deviations is added to the simulated radarsea clutter power to examine the stability of the algorithmsand the standard deviation is employed to represent thenoise level Also the histograms and convergence curves arepresented to analyze the accuracy and convergence rate indetail

Figures 2ndash5 give the comparison of the histograms ofthe inversions of the surface duct parameters for differentalgorithms at a specific noise level and the red lines denotethe actual parameter of surface duct It is obvious that thedistribution of inversion parameters obtained by theOGABCis more intensive than those of MIWO and ABC for differentnoise level In addition the inversion results of OGABCachieve the most occurrence at the vicinity of the actualparameter compared with those of theMIWO andABCThatis to say the proposed OGABC is the most stable algorithm


006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC

minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus22minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus22minus36 minus34 minus32 minus3 minus28 minus26 minus24 minus22

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


among the three algorithms It is likely due to the fact thatthe global best search equation not only enhances the globalsearch ability but also avoids falling into the local minimum

To study the convergence performance of the OGABCthe comparisons of the convergence curves of different

algorithms based on the inversion results given in Figures 2ndash5with the same noise level are demonstrated in Figure 6 It canbe seen that the convergence rate of OGABC is faster thanthat of the MIWO and ABC besides the OGABC has thesmallest meanminimum fitness at the end of the iteration for


0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


different noise levelThe convergence curves indicate that theOGABC is the best algorithm among the three algorithmsThis can be attributed to the fact that the OBL can produce arelatively excellent initial population in the initialization stageand a generation jumping to form a better population in thesearch process

The accuracy of the inversion of atmospheric duct is ofcrucial importance to exactly predict the marine electromag-netic environment Hence the comparisons of the differencebetween the inverted and actual radar coverage diagramsimulated by parabolic equation method for different noiselevel are shown in Figure 7 and the peaks of the parameterdistributions [20] in Figures 2ndash5 are treated as the invertedparameters of the surface duct to simulate their correspond-ing coverage diagram Nevertheless it is hardly possible toevaluate the quality of the algorithms according to the resultspresented in Figure 7 Thus a new quantitative evaluationcriterion named Mean Absolute Error (MAE) is given by

MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL

119886(119894 119895) represent the inverted and actual

propagation loss calculated at discrete point (119894Δ119909 119895Δ119910) and119873119909and 119873

119910are the sample points along the horizontal and

vertical direction respectively It is easy to see that the smallerthe MAE the higher the accuracy of the algorithm

The MAE of the three algorithms for different noise levelobtained by (13) are presented in Table 2 and the minimum

Table 2 The comparison of the MAE for different algorithms withdifferent noise level

Noise level AlgorithmsMIWO ABC OGABC

0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060

results are highlighted in bold It can be observed fromTable 2that the MAE of OGABC is the smallest one among the threealgorithms for different noise level namely the accuracy ofOGABC is superior to MIWO and ABC

Then in order to further test the performance ofOGABCthe radar sea clutter power generated bymeasured refractivityprofile [20] is also utilized for the inversion of the surfaceduct Figure 8 shows the comparison of the inverted profileobtained by the three algorithms with the measured profileand it is distinct that the inverted profile of OGABC is inexcellent agreement with the measured one

In addition Figure 9 presents the corresponding com-parison of the convergence curves of the MIWO ABC andOGABC It is observed that the three algorithms have thefaster convergence rate at the early stage of iterations andthe minimum fitness is hardly changed with iteration at themiddle and later stage of iterationsHowever theOGABChasthe smallest minimum fitness among the three algorithms


0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s

IterationsMIWOABCOGABC

Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)

Figure 6 The comparison of the convergence curves of different algorithms with the same noise level

That is to say the OGABC is superior to MIWO and ABCaccording to the accuracy and convergence rate

5 Conclusion

In this paper an improved ABC algorithm called OGABCis presented by simultaneously merging the OBL strategyand global best search equation into the standard ABCalgorithm to tackle its deficiency of slow convergence rateand falling into the local best during the process of inversionof atmospheric duct Taking the inversion of the surfaceduct using RFC technique as an example the propagation

characteristics of radar sea clutter obtained from the sim-ulated and measured refractivity profile are treated as theobserved sea clutter power to examine the performance ofOGABC respectively For the simulated refractivity profilecase the Gaussian noise is added to the simulated radarsea clutter power to investigate the stability of the proposedOGABC algorithm and the histograms and the convergencecurves are used to analyze the accuracy and convergencerate Further investigation using the radar sea clutter powergenerated by themeasured refractivity profile is also involvedand the accuracy and convergence rate of the algorithmsare discussed by comparing the inverted refractivity profilewith the measured one and analyzing their convergence


60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)

Figure 7 The comparison of the difference between the inverted and actual coverage diagram with different noise level (a) 0 dB (b) 1 dB(c) 2 dB and (d) 3 dB

290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC

OGABCMeasured profile

Figure 8 The comparison of the inverted profile with the measured profile


0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC

Figure 9 The comparison of the convergence curves of differentalgorithms

curves In addition the inversion results are also analyzed andcompared with those of the MIWO and ABC The obtainedresults verify that the proposed OGABC algorithm outper-forms MIWO and ABC in terms of stability accuracy andconvergence rate Future work will focus on the experimentalresearch and the improvement of the inversion model

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Science Fund forDistinguished Young Scholars of China (no 61225002) andthe Young Scientists Fund of the National Natural ScienceFoundation of China (no 61302050)

References

[1] C Yardim P Gerstoft andW S Hodgkiss ldquoEstimation of radiorefractivity from radar clutter using BayesianMonte Carlo anal-ysisrdquo IEEE Transactions on Antennas and Propagation vol 54no 4 pp 1318ndash1327 2006

[2] C Yardim P Gerstoft andW S Hodgkiss ldquoTracking refractiv-ity from clutter using Kalman and particle filtersrdquo IEEE Trans-actions on Antennas and Propagation vol 56 no 4 pp 1058ndash1070 2008

[3] C Yardim P Gerstoft andW S Hodgkiss ldquoSensitivity analysisand performance estimation of refractivity from clutter tech-niquesrdquo Radio Science vol 44 pp 1ndash16 2009

[4] P Gerstoft L T Rogers J L Krolik andW S Hodgkiss ldquoInver-sion for refractivity parameters from radar sea clutterrdquo RadioScience vol 38 pp 1ndash22 2003

[5] A Karimian C Yardim P Gerstoft W S Hodgkiss and AE Barrios ldquoRefractivity estimation from sea clutter an invitedreviewrdquo Radio Science vol 46 pp 1ndash16 2009

[6] X-F Zhao S-X Huang and H-D Du ldquoTheoretical analysisand numerical experiments of variational adjoint approach forrefractivity estimationrdquo Radio Science vol 46 no 1 pp 1ndash122011

[7] X F Zhao and S X Huang ldquoAtmospheric duct estimationusing radar sea clutter returns by the adjoint method withregularization techniquerdquo Journal of Atmospheric and OceanicTechnology vol 31 no 6 pp 1250ndash1262 2014

[8] R Douvenot V Fabbro P Gerstoft C Bourlier and J SaillardldquoA duct mapping method using least squares support vectormachinesrdquo Radio Science vol 43 pp 1ndash12 2008

[9] B Wang Z-S Wu Z-W Zhao and H-G Wang ldquoRetrievingevaporation duct heights from radar sea clutter using particleswarm optimization (PSO) algorithmrdquo Progress In Electromag-netics Research M vol 9 pp 79ndash91 2009

[10] X-F Zhao S-X Huang J Xiang andW-L Shi ldquoRemote sens-ing of atmospheric duct parameters using simulated annealingrdquoChinese Physics B vol 20 no 9 Article ID 099201 8 pages 2011

[11] C Yang ldquoEstimation of the atmospheric duct from radarsea clutter using artificial bee colony optimization algorithmrdquoProgress in Electromagnetics Research vol 135 pp 183ndash199 2013

[12] D Karaboga and B Basturk ldquoA powerful and efficient algo-rithm for numerical function optimization artificial bee colony(ABC) algorithmrdquo Journal of Global Optimization vol 39 no 3pp 459ndash471 2007

[13] J Yang W-T Li X-W Shi L Xin and J-F Yu ldquoA hybrid ABC-DE algorithm and its application for time-modulated arrayspattern synthesisrdquo IEEE Transactions on Antennas and Pro-pagation vol 61 no 11 pp 5485ndash5495 2013

[14] X Zhang X Zhang S Y Yuen S L Ho and W N Fu ldquoAnimproved artificial bee colony algorithm for optimal design ofelectromagnetic devicesrdquo IEEE Transactions on Magnetics vol49 no 8 pp 4811ndash4816 2013

[15] S K Goudos K Siakavara A Theopoulos E E Vafiadis andJ N Sahalos ldquoApplication of Gbest-guided artificial beecolonyalgorithm to passive UHF RFID tag designrdquo InternationalJournal of Microwave and Wireless Technologies 2015

[16] G Zhu and S Kwong ldquoGbest-guided artificial bee colonyalgorithm for numerical function optimizationrdquo Applied Math-ematics and Computation vol 217 no 7 pp 3166ndash3173 2010

[17] W-F Gao S-Y Liu and L-L Huang ldquoA novel artificialbee colony algorithm based on modified search equation andorthogonal learningrdquo IEEE Transactions on Cybernetics vol 43no 3 pp 1011ndash1024 2013

[18] R S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolutionrdquo IEEETransactions onEvolutionary Computation vol 12 no 1 pp 64ndash79 2008

[19] A E Barrios ldquoTerrain parabolic equation model for propaga-tion in the troposphererdquo IEEE Transactions on Antennas andPropagation vol 42 no 1 pp 90ndash98 1994

[20] A Karimian C Yardim W S Hodgkiss P Gerstoft and A EBarrios ldquoEstimation of radio refractivity using a multiple angleclutter modelrdquo Radio Science vol 47 pp 1ndash9 2012

[21] A Basak D Maity and S Das ldquoA differential invasive weedoptimization algorithm for improved global numerical opti-mizationrdquo Applied Mathematics and Computation vol 219 no12 pp 6645ndash6668 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



about RFC technique Zhao et al [6 7] derive the inversiontheoretical framework of adjoint method from parabolicequation model and the feasibility of the adjoint method isvalidated by numerical simulations As is known to all esti-mation of atmosphere duct using RFC technique is an inverseproblem Taking the nonlinear relation between the forwardpropagation model and atmospheric duct parameters intoconsideration the investigation on the optimization modelswith high performance is one of the most important researchtopics in the field of inversion of the atmospheric ductfrom radar sea clutter For instance the least square supportvector machine the particle swarm optimization (PSO)the simulated annealing algorithm and the ABC algorithmhave been applied to infer the atmospheric duct using RFCtechnique [8ndash11]

The ABC algorithm [12] is one of the most recentlyproposed swarm intelligence algorithms which simulatesthe intelligent behavior of honeybee swarm In ABC theoptimization procedures are implemented by simulating theintelligent foraging behavior of a honeybee swarm to shareinformation of bees for the purpose of finding the optimalsolution Currently the ABC algorithm has been applied tothe design of antenna and electromagnetic devices [13ndash15]In addition the ABC algorithm has been used to infer theatmospheric duct from RFC technique [11] and the compar-ative study results demonstrate that the performance of ABCis superior to that of the PSO for the inversion of atmosphericduct However the ABC also has the drawbacks of easilyfalling into local optima and slower convergence rate Toovercome this issue the improvedABChas been proposed byupdating the search equation to enhance its optimization per-formance and the improved ABC is validated by benchmarkfunction [16 17] In recent years the OBL was introducedby Rahnamayan et al [18] and has been proven to be auseful strategy to enhance the accuracy and convergence rateof the optimization algorithm such as differential evolutionand PSO

In this paper the OGABC is proposed by incorporatingthe OBL strategy and global best search equation into theABC to enhance the performance of ABC in the inversion ofatmospheric duct In OGABC the OBL is used to acceleratethe convergence rate and the global best search equation isadopted to balance the local and global search ability

2 The Propagation Model andObjective Function

21 Parabolic Equation Method Considering that theparabolic equation method has the advantages of highstability and accuracy it has been extensively utilized toinvestigate the tropospheric electromagnetic wave propa-gation In rectangular coordinates the parabolic equationcan be represented as

1205972119906

1205971199112+ 21198941198960

120597119906

120597119909+ 1198962

0(1198992minus 1) 119906 = 0 (1)

where 119899 is the refractive index and 1198960is the free space wave

number

If the initial field is provided the split step Fouriersolution of parabolic equation method at different range canbe easily obtained by [19]

119906 (1199090+ Δ119909 119911)

= 119890(11989411989602)[119899

2minus1]Δ119909

119865minus1119890(119894Δ11990921198960)119901

2

119865 [119906 (1199090 119911)]

(2)

where 119865 and 119865minus1 are the Fourier transform and inverse

Fourier transform respectively 119901 is the transform variableΔ119909 is the distance interval and 119906(119909

0 119911) is the initial field It

should be pointed out that this researchmainly focuses on theinversion of atmospheric duct more detailed information onthe propagation problemwith parabolic equationmethod canbe found in [19]

22 Radar Sea Clutter Power In RFC technique the objec-tive function is described by the radar sea clutter powerat different propagation distances Taking the influence ofatmosphere condition into account the received radar seaclutter power based on radar equation can be expressed indB by [4]

119875119888(m) = minus2119871 + 120590

∘+ 10 lg (119903) + 119862 (3)

where 119871 is the propagation loss calculated by the parabolicequationmethod120590∘ is the radar cross section obtained by theGIT sea clutter model [20] 119903 is the propagation distance 119862 isa constant that includes wavelength transmitter power andantenna gain and m is the parameter vector of the atmo-spheric duct

In this paper the surface based duct is described by thefollowing four-parameter model [2]

119872(119911) = 1198720

+

1198881119911 119911 lt ℎ

1

1198881ℎ1+ 1198882(119911 minus ℎ

1) ℎ

1le 119911 le ℎ

2

1198881ℎ1+ 1198882ℎ2+ 0118 (119911 minus ℎ

1minus ℎ2) 119911 gt ℎ

2

(4)

where 1198720is the base refractivity and 119888

1and ℎ

1stand for

the slope and thickness of the base layer whereas 1198882and ℎ

2

represent the slope and thickness of the inversion layerrespectively

23 The Objective Function In the process of inversion thecommonly used least squares objective function is given by[4]

119891 (m) = eTe

e = Pobs119888

minus P119888(m) minus

= Pobs119888

minus P119888(m)

(5)

where Pobs119888

and P119888(m) stand for the observed and received sea

clutter power at different ranges and Pobs119888

and P119888(m) denote

the average power of Pobs119888

and P119888(m) respectively





= 119897 + 119906 minus 119909 (6)

Definition 2 Let 119883 = (1199091 1199092 119909



119894 119906119894are lower


1 2


119894= 119897119894+ 119906119894minus 119909119894

119894 = 1 119863 (7)






119873 solutions by

1198830119894119895

= 119897119895+ rand (0 1) (119906

119895minus 119897119895)

119894 = 1 2 119873 119895 = 1 2 119863

(8)


1198741198830119894119895

= 119897119895+ 119906119895minus 1198830119894119895

(9)





V119894119895= 119909119894119895+ 120601119894119895(119909119894119895minus 119909119896119895) + 120595119894119895(119910119895minus 119909119894119895)

(119894 119896 = 1 119873 119895 = 1 119863)

(10)



and 120601119894119895and 120595


[0 15] respectively



119901119894=

fit119894

sum119873

119896=1fit119896

(11)













Does scout exist

Terminal condition

No

End

Yes

Begin



Yes

No



119874119883119894119895= 119897

min119895

+ 119906max119895

minus 119883119894119895

119894 = 1 2 119873 119895 = 1 2 119863

(12)

where 119897min119895

and 119906max119895









005 01 015 02 0250

5

10

15O

ccur

renc

eO

ccur

renc

eO

ccur

renc

eO

ccur

renc

e

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15


5

10

15

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

MIWO ABC OGABC

14 16 18 20 22 24 26 28 300

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




00 025 M-unitsm1198882


250 500 mℎ2

100 300 m










006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC


Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)






0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













= 119897 + 119906 minus 119909 (6)

Definition 2 Let 119883 = (1199091 1199092 119909



119894 119906119894are lower


1 2


119894= 119897119894+ 119906119894minus 119909119894

119894 = 1 119863 (7)






119873 solutions by

1198830119894119895

= 119897119895+ rand (0 1) (119906

119895minus 119897119895)

119894 = 1 2 119873 119895 = 1 2 119863

(8)


1198741198830119894119895

= 119897119895+ 119906119895minus 1198830119894119895

(9)





V119894119895= 119909119894119895+ 120601119894119895(119909119894119895minus 119909119896119895) + 120595119894119895(119910119895minus 119909119894119895)

(119894 119896 = 1 119873 119895 = 1 119863)

(10)



and 120601119894119895and 120595


[0 15] respectively



119901119894=

fit119894

sum119873

119896=1fit119896

(11)













Does scout exist

Terminal condition

No

End

Yes

Begin



Yes

No



119874119883119894119895= 119897

min119895

+ 119906max119895

minus 119883119894119895

119894 = 1 2 119873 119895 = 1 2 119863

(12)

where 119897min119895

and 119906max119895









005 01 015 02 0250

5

10

15O

ccur

renc

eO

ccur

renc

eO

ccur

renc

eO

ccur

renc

e

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15


5

10

15

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

MIWO ABC OGABC

14 16 18 20 22 24 26 28 300

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




00 025 M-unitsm1198882


250 500 mℎ2

100 300 m










006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC


Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)






0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Does scout exist

Terminal condition

No

End

Yes

Begin



Yes

No



119874119883119894119895= 119897

min119895

+ 119906max119895

minus 119883119894119895

119894 = 1 2 119873 119895 = 1 2 119863

(12)

where 119897min119895

and 119906max119895









005 01 015 02 0250

5

10

15O

ccur

renc

eO

ccur

renc

eO

ccur

renc

eO

ccur

renc

e

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15


5

10

15

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

MIWO ABC OGABC

14 16 18 20 22 24 26 28 300

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




00 025 M-unitsm1198882


250 500 mℎ2

100 300 m










006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC


Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)






0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










005 01 015 02 0250

5

10

15O

ccur

renc

eO

ccur

renc

eO

ccur

renc

eO

ccur

renc

e

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15


5

10

15

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

MIWO ABC OGABC

14 16 18 20 22 24 26 28 300

5

10

15

14 16 18 20 22 24 26 28 300

5

10

15

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




00 025 M-unitsm1198882


250 500 mℎ2

100 300 m










006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC


Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)






0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

006 008 01 012 014 016 0180

5

10

15

0

10

20

30

0

10

20

30

0

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

38 39 40 41 42 43 44 45 460

10

20

30

10 15 20 25 3005

101520

10 15 20 25 3005

101520

10 15 20 25 3005

101520

MIWO ABC OGABC


Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

Occ

urre

nce

c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)


005 01 015 02 0250

5

10

15

Occ

urre

nce

005 01 015 02 0250

5

10

15

005 01 015 02 0250

5

10

15

0

5

10

15

Occ

urre

nce

0

5

10

15

0

5

10

15

38 40 42 44 46 480

5

10

15

Occ

urre

nce

38 40 42 44 46 480

5

10

15

38 40 42 44 46 480

5

10

15

10 15 20 25 3005

101520

Occ

urre

nce

MIWO ABC OGABC

10 15 20 25 3005

101520

10 15 20 25 3005

101520


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)






0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 005 01 015 02 02505

101520

Occ

urre

nce

0 005 01 015 02 02505

101520

0 005 01 015 02 02505

101520

05

101520

Occ

urre

nce

05

101520

05

101520

36 38 40 42 44 4605

101520

Occ

urre

nce

36 38 40 42 44 4605

101520

36 38 40 42 44 4605

101520

15 20 25 300

5

10

Occ

urre

nce

MIWO ABC OGABC

15 20 25 300

5

10

15 20 25 300

5

10


c 1(M

-uni

tsm

)c 2

(M-u

nits

m)

h1

(m)

h2

(m)




MAE =

sum119873119909

119894=1sum119873119910

119895=1

1003816100381610038161003816PL119894 (119894 119895) minus PL119886(119894 119895)

1003816100381610038161003816

119873119909119873119910

(13)

where PL119894(119894 119895) and PL








0 dB 222 164 0091 dB 188 088 0752 dB 354 184 1053 dB 325 079 060





0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 0dB

(a)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 1dB

(b)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000

Mea

n m

inim

um fi

tnes

s


Noise level 2dB

(c)

0 20 40 60 80 100 1200

1000

2000

3000

4000

5000

6000M

ean

min

imum

fitn

ess

Iterations

MIWOABCOGABC

Noise level 3dB

(d)



5 Conclusion




60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










60

120

180

0 20 40 60 80 100

40

20

0

minus20

minus40

40

20

0

minus20

minus40

Hei

ght (

m)

60

120

180

Hei

ght (

m)

60

120

180

Hei

ght (

m)

Distance (km)0 20 40 60 80 100

Distance (km)0 20 40 60 80 100

Distance (km)

5

0

minus5

MIWO ABC OGABC

(a)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

40

20

0

minus20

minus40

MIWO ABC OGABC

(b)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

minus40

40

20

0

minus20

40

20

0

minus20

minus40

minus60

MIWO ABC OGABC

(c)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

60

120

180

0 20 40 60 80 100

Hei

ght (

m)

Distance (km)

40

20

0

minus20

40

20

0

minus20

50

0

minus50

MIWO ABC OGABC

(d)


290 295 300 305 310 315 3200

50

100

150

200

Hei

ght (

m)

M (M-units)

MIWOABC




0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20 40 60 80 100 1204000

5000

6000

7000

8000

Min

imum

fitn

ess

Iterations

MIWOABCOGABC



Competing Interests


Acknowledgments


References
























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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