TrussStructureOptimizationBasedonImproved …downloads.hindawi.com/journals/ace/2019/6902428.pdf · 2019. 10. 11. · hens,andseveralchicks. (2) e chicken swarm divides several subchicken

Research ArticleTruss Structure Optimization Based on ImprovedChicken Swarm Optimization Algorithm

Yancang Li 1 Shiwen Wang 2 and Muxuan Han 2

1College of Water Conservancy and Hydroelectric Power Hebei University of Engineering Handan 056038 China2College of Civil Engineering Hebei University of Engineering Handan 056038 China

Correspondence should be addressed to Shiwen Wang tumuwangshiwen163com

Received 23 May 2019 Revised 26 July 2019 Accepted 27 August 2019 Published 13 October 2019

Academic Editor Dimitris Rizos

Copyright copy 2019 Yancang Li et al -is 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

To improve the efficiency of the structural optimization design in truss calculation an improved chicken swarm optimizationalgorithmwas proposed for truss structure optimization-e chicken swarm optimization is a novel swarm intelligence algorithmIn the basic chicken swarm optimization algorithm the concept of combining chaos strategy and reverse learning strategy wasintroduced in the initialization to ensure the global search ability And the inertia weighting factor and the learning factor wereintroduced into the chick position update process so as to better combine the global and local search Finally the overallindividual position of the algorithm was optimized by the differential evolution algorithm-e improved algorithm was tested bymultipeak function and applied to the truss simulation experiment -e study provided a new method for the trussstructure optimization

1 Introduction

Engineering structure optimization is a problem that hasplagued scholars for many years Mechanical constraints andoptimization methods are combined in engineering struc-ture optimization According to the different engineeringrequirements some parameters in the project are involved inthe optimization calculation of the engineering structure inthe form of variables thus forming a solution domain of theoptimized structure -en based on the constraints of theproject the mathematical model is established and themathematical solution is used to find the most reasonabledesign scheme in accordance with the design requirementsIn 1974 Schimit and Farshi proposed an approximationproblem in structural optimization [1] After that with theapplication of computer technology modern structure op-timization become a real possibility

-e traditional structural optimization method had cer-tain defects -ere was no effective optimization designmethod At first it was judged by people directly such as thelimit stress method and the ultimate strain method -esemethods were difficult to find the best results and there was

no corresponding theoretical basis Later as the time passedthe corresponding mathematical theory support appearedbut it only existed in mathematical theory and it still cannotdescribe the actual engineering structure problem Faced withcomplex engineering optimization problems more and morescholars had proposed the theory of bionic intelligent algo-rithms based on the habit of biological evolution and survivalin nature -e optimization of structure was mainly focusedon reducing the total quality of the structure improving thedesign rationality and reducing the engineering cost [2ndash5]for example improving the application of artificial fish swarmalgorithm in truss structure optimization the truss optimi-zation of artificial bee colony algorithm and the application offirefly algorithm in truss structure optimization [6ndash8]

After years of research and development intelligentoptimization algorithms had been widely used in variousfields Fiore et al proposed an improved differential evo-lution algorithm to optimize the structure of flat steel trusses-e weight of the steel truss was designed as the minimumobjective function and the square hollow section was used asthe calculation variable -e design optimization involvedsize optimization shape optimization and topology

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 6902428 16 pageshttpsdoiorg10115520196902428

optimization [9] Karaboga et al proposed an improvedartificial bee colony algorithm (ABC) based on chaos theorywhich was applied to the truss structure example to verify theeffectiveness of the improved algorithm for truss engi-neering structure optimization [10] Kayabekir explored anew intelligent algorithm the flower pollination algorithm(FPA) and discussed its practical application in civil en-gineering mechanical engineering electronic communica-tion and chemistry In the civil engineering field the FPAalgorithm was applied to the 25-bar truss structure to op-timize the structure and the feasibility of the algorithm wasverified [11] Chen et al proposed a hybrid particle swarmoptimization (PSO) algorithm based on the improvedNelderndashMead algorithm (NMA) -e improved NMA se-lected a part of the n-simplex subplane for optimizationusing modal strain energy -e index (MSEBI) to locate thedamage effectively improved the convergence speed andaccuracy of the PSO algorithm and greatly improved thecomputational efficiency in the field of structural damagedetection (SDD) [12] Andrea Caponio et al proposed ametaheuristic algorithm based on population distributiontheory for the application of practical engineering structureoptimization -e proposed algorithm can converge wellwhen faced with nonlinear and indistinguishable optimi-zation problems -e optimization process was stable andprovides a new way of thinking [13]

In 2014 Chinese scholar Meng proposed the chickenswarm optimization (CSO) [14] which was a group-basedstochastic optimization algorithm -e advantage was thatthe implementation was simple-e disadvantage was that itwas easy to fall into the local optimal solution convergesslowly and is low in precision Scholars had done a lot ofresearch on this optimization algorithm In 2015 Fei et alproposed an improved chicken swarm optimization (CSO)which analyzed the weighting factors in the reference par-ticle swarm optimization algorithm-e adaptive weight wasintroduced in the process of updating the individual positionof the chicken which solved the problem that the optimalsearch solution was easy to skip due to the large search spacein the early stage of the algorithm the late search space wassmall the convergence was slow and the learning part of theindividual with the cock was added-is allowed the chick toenjoy a comprehensive learning mechanism [15] Yu et alimproved the chicken swarm optimization (CSO) in 2016using a variety of hybrid methods -e reverse directionlearning method was used to initialize the population in-dividuals to improve the quality of the population and thevariation idea was introduced in the boundary processing toenhance the diversity of the population improving theglobal optimization ability of the algorithm Finally the ideaof simulated annealing was used to accept the inferior so-lution with a certain probability which enhanced the abilityof the algorithm to jump out of local optimum [16] -eseimproved algorithms effectively improved the optimizationperformance of the algorithm and the results of its functionoptimization proved that the improved algorithm was ef-fective-e existing research showed that the chicken swarmoptimization (CSO) had been successfully applied to re-source scheduling [17] engineering optimization design

[14] cluster analysis and optimization of classifier co-efficients [18 19] In 2016 Hafez et al proposed a featureselection system based on chicken swarm optimization(CSO) which was used to select features in a wrapper modeto search for feature space for the best combination offeatures thus maximizing classification performance whileminimizing the number of selected features [20] Shayokhet al used the chicken swarm optimization (CSO) to solvethe wireless sensor network (WNS) node location problem[21] In 2016 Roslina et al proposed an improved chickenswarm optimization (CSO) for ANFIS performance whichcan more accurately solve the ANFIS network trainingclassification problem [22] In 2017 Awais et al combinedthe chicken swarm optimization (CSO) with energy opti-mization for home users enabling home users to reducepower costs power consumption and peak-to-average ratio[23 24] Ahmed et al improved the chicken swarm opti-mization (CSO) search ability by applying logistic and tendchaotic mapping to help the chicken swarm optimization(CSO) better explore search space [25] -ese successfulapplications show that the chicken swarm optimization(CSO) has a good development and application prospectsHowever in these application studies the chicken swarmalgorithm (CSO) is also imperfect For example the algo-rithm is not initialized the chicken position update does notprevent the individual from being out of bounds and thealgorithm has no overall individual optimization

Based on the above research this paper improved thechicken swarm optimization and applied to truss structureoptimization the concept of combining chaos strategy andreverse learning strategy was introduced in the initializationto ensure the global search ability And the inertia weightingfactor and the learning factor were introduced into the chickposition update process so as to better combine the globaland local search Finally the overall individual position ofthe algorithm was optimized by the differential evolutionalgorithm -e improved algorithm was tested by multipeakfunction and applied to the truss simulation experiment

2 Chicken Swarm Optimization Algorithm

-e traditional chicken swarm optimization mainly treatsthe optimization problem as the process of chickensrsquosearching for food -e whole chicken swarm is divided intoseveral chicken flocks each of which has a cock several hensand several chicks -ere is a competition between eachchicken swarm and the best cluster individuals are obtainedthrough competitions -e process of simplifying is asfollows

(1) In each chicken swarm there are many subchickenswarms each of which included one cock severalhens and several chicks

(2) -e chicken swarm divides several subchickenswarms and determines the fitness value of in-dividuals on which cocks hens and chicks dependSeveral individuals with the best fitness values can actas cocks Each cock is a leader of a chicken swarm-e worst fitness can be used as a chicken and the

2 Advances in Civil Engineering

rest can be hens -e hens randomly follow a cockand the relationship between the hen and the chick israndomly formed

(3) -e dominance relationship hierarchy and mother-child relationship in the chicken swarm are un-changed chickens regroup and update roles every Ggeneration

(4) -e subchicken swarms look for food with the cockthe chicks look for food around the hens and theindividual has an advantage in finding food -ecocks hens and chicks in the chicken swarmsperform different ways of optimizing

Individuals in the chicken swarm move according totheir own rules until they find the best position -ereforethe individual position in the chicken swarm correspond to asolution to the optimization problem and finding the bestposition is the optimal solution to the optimization problemIn the whole chicken swarm optimization the number ofindividuals in all flocks is set to N and the position of eachchicken swarm individual is represented by xij(t) and itsmeaning indicate the position obtained in the t-th iterationof the i-th flock individual in the j-th dimension -ereforethere are different positions for the three different types ofchickens in the chicken swarm optimization that is theposition update of the individual flocks is changed withdifferent positions depending on the type of chicken -ecock has the best fitness value in each subgroup and it canfind and locate food in a wide range of spaces

-e position corresponding to the cock is updated asfollows

xij(t + 1) xij(t)lowast 1 + Rand n 0 σ21113872 11138731113872 1113873

σ2

1 fi lefk

expfk minus fi

fi

11138681113868111386811138681113868111386811138681113868 + ε

1113888 1113889 fi gtfk

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)

where Rand n(0 σ2) produces a mean of 0 and Gaussiandistribution random number with standard deviation σ ε isan extremely small number to prevent the denominatorfrom being zero fi is the fitness value of individual i and fk

is the fitness value of the individual k Individual k israndomly selected from the rooster population and kne i

-e location of the hen is updated as follows

xij(t + 1) xij(t) + c1lowast randlowast xr1j(t) minus xij(t)1113872 1113873

+ c2lowast randlowast xr2j(t) minus xij(t)1113872 1113873

c1 expfi minus fr1( 1113857

abs f1( 1113857 + ε1113888 1113889

c1 exp fr2 minus fi( 1113857

(2)

where rand is a random number between 0 and 1 r1 is thespouse cock of the i-th hen r2 is any individual of all cocksand hens in the flock and r1ne r2

-e location corresponding to the chick is updated asfollows

xij(t + 1) xij(t) + Flowast xmj(t) minus xij(t)1113872 1113873 (3)

where m represents the hen corresponding to the i-th chickand F is the follow-up coefficient which means that thechick follows the hen to find food

3 Improved Chicken SwarmOptimization Algorithm

31 Initial Selection As can be seen from above thepopulation described in the traditional chicken swarmoptimization is not initialized which brought disadvan-tages to the traditional algorithm and there is no guaranteethat the optimal solution of the algorithm can evenlydistribute your distribution in the search space whichlimits the efficiency of the algorithm and reduces theperformance of the algorithm Chaos strategy and reverselearning strategy were combined in the initialization of thealgorithm [26ndash28] Firstly the chaotic strategy was used tomake the state nonrepetitive and ergodic and then thereverse learning strategy was used to reduce the blindnessof the algorithm to expand the initial search range of thewhole population the global detection capability of thealgorithm is ensured so as not to fall into local optimum-e process was as follows

(1) Select the chicken swarm optimization populationNP1 x1(t) x2(t) xN(t)1113864 1113865 and each individ-ual in the population was xi(t)

(xi1(t) xi2(t) xiD(t)) i isin N(2) Generate chaotic sequences by model iterations and

describe the logistic mapping of equation (4)NP2 x1(t)lowast x2(t)lowast xN(t)lowast1113864 1113865

xi(t)lowast

μlowastxi(t)lowast 1 minus xi(t)( 1113857 (4)

where the parameter μ 4(3) Find the inverse solution corresponding to NP2

individual by equation (5) 1113957xi(t) ( 1113958xi1(t) 1113958xi2(t)

1113958xiD(t)) thus the inverse populationNPop 1113957x1(t) 1113957x2(t) 1113958xN(t)1113864 1113865 was obtained

1113958xiD(t) Klowast xi + yi( 1113857 minus xiD(t) (5)

where xiD(t) isin [xi yi] [xi yi] is the dynamicboundary of the search space and K isin [0 1] is arandom number subject to uniform distribution

(4) NP2cup NPop and choose the best fitness for xbestcalculate xmean (x1 + x2 + middot middot middot x2N)2N and finallyget the inverse optimal solution as follows

xopbest xbest f xbest( 1113857lt f xmean( 1113857

xmean f xbest( 1113857ge f xmean( 1113857

⎧⎨

⎩ (6)

Advances in Civil Engineering 3

By introducing chaos strategy and reverse learningstrategy the chicken swarm optimization could findthe optimal solution in a larger search space and canguide the individual to evolve to the optimal solutionso that the overall convergence speed is improved

32ChickLocationUpdate In the traditional chicken swarmoptimization the position update of the chick is only relatedto the position of the hen but not to the position of the cockwith the best fitness in the algorithm [29 30] It can cause thealgorithm to fall into local optimum to a certain extentresulting in a lower overall efficiency It is not difficult to seethat the chicks in the chicken swarm optimization and theparticles in the particle swarm optimization have similarities[31ndash33] In order to improve the position update of thechicks we referred to the particle swarm optimization toobtain the position of the particles locally and globally sothat the chicks can obtain the local position in the henrsquos sideand the optimal position in the whole cock-guided group Inthis paper the inertia weight value ω and the learning factorφ in the particle swarm optimization algorithm were used toimprove the chick position update Equation (3) was im-proved as follows

xij(t + 1) ω(t)lowastxij(t) + φ1 lowast xmj(t) minus xij(t)1113872 1113873

+ φ2 xrj(t) minus xij(t)1113872 1113873(7)

where m is the individual in the subgroup and the individualcorresponding to the hen r is the individual of the cockcorresponding to the chick in the subgroup φ1 and φ2 arethe two learning factors respectively indicating the degreeof learning of the chick to the hen and the cock and ω(t) isthe weight value

321 Setting the Weight Value -e setting of the weightvalue is related to whether the algorithm can better achievelocal and global search which is related to the diversity of thealgorithm population in the later stage -is paper in-troduced a nonlinear inertia weight value ω(t) as follows

ω(t) floor ωmax minus ωmin( 1113857lowast exp3 minus 2lowast tTmax( 1113857( 1113857 + ωmin1113872 1113873

(8)

where ωmax is the maximum inertia weight ωmin is theminimum inertia weight Tmax is the maximum number ofiterations and floor is the rounding function in order toensure that ω(t) is an integer

After introducing the nonlinear weight value it canensure the global search of the individual chicken in the earlystage of the algorithm thereby improving the accuracy of thealgorithm and strengthening the local search later

322 Setting the Learning Factor -e learning factors φ1and φ2 appearing in the chick position update indicate thedegree of learning of chicks to hens and cocks to someextent just like the individual learning factors and sociallearning factors in the particle swarm optimization [33]From the learning factor in the particle swarm optimization

it can be inferred that in the initial stage of the search thelarger φ1 makes the chicks search for a greater probabilityaround the hen and more is to find the optimal solutionglobally in the later stages of the search the larger φ2 makesthe chicks search for a greater chance around the cockswhich is a local search near the optimal solution [34] -ispaper introduced a nonlinear learning factor that allowedchicks to perform local and global searches -e formula wasas follows

φ1 13 + 12lowast cos tπTmax( 1113857

φ2 2 minus 12lowast cos tπTmax( 1113857(9)

33 Select the Best Individual In the selection of the optimalposition of the chicken swarm optimization a differentialalgorithm was used which consists of three processesvariation intersection and selection [35 36] -e mainformula was as follows

(1) Variation Process Two bodies xr1j(t) and xr2j(t) ofthe same iteration number were randomly selectedand the mutation operation was performedaccording to the following equation

vij(t + 1) xij(t) + Flowast xr1j(t) minus xr2j(t)1113872 1113873 (10)

where vij(t + 1) is the mutated individual and F is arandom factor of [0 1] which controls the degree ofexpansion of the check score vector

(2) Cross Process -e cross-probability factor P wasintroduced and the cross operation was performedaccording to the following equation

kij(t) vij(t + 1) P isin [0 1]

xij(t) otherwise⎧⎨

⎩ (11)

(3) Selection Process For comparing the fitness functionvalues of two individuals select individuals withlarge function values to perform mutation andcrossover operations and compare the generated newindividuals with the previous generation If theformer was larger than the latter enter the next it-eration otherwise remain unchanged

34 Improved Chicken Swarm Optimization Steps and FlowChart -e steps to improved chicken swarm optimizationare described as follows

Step 1 set relevant parameters of the algorithmpopulation size cock hen chick scale factor updateiteration number etcStep 2 initialize the population by combining chaosstrategy and reverse learning strategyStep 3 determine the fitness value of the individual theratio of cock hen and chicken grouping and variousrelationships record the current global optimal fitnessvalue that is the optimal individual position


Step 4 enter the iterative update to determine whetherthe update condition is met the order of the flock themother-child relationship and the partnership areupdated the position of the cock hen and chick isupdated and the boundary is processedStep 5 select the optimal individual through three stepsmutation intersection and selectionStep 6 when the number of iterations is less than themaximum number of iterations go to step (4) tocontinue execution otherwise perform step (7)Step 7 the individual who chooses the best position isthe optimal solution

-e flow chart of the improved chicken swarm opti-mization is shown in Figure 1

4 Multipeak Function Tests

-e experimental environment in this paper used 35GHzCPU 4GB memory 64 bit operating system Windows 10Professional and the programming environment is MAT-LAB R2017b

To verify the effectiveness of the improved chickenswarm optimization and to analyze the improved conver-gence and performance of the improved chicken swarmoptimization five well-known test functions which areadopted from the IEEE CEC competitions were applied inthe experiments [37ndash40] and compared with the traditionalchicken swarm optimization (CSO) bat algorithm (BA) andparticle swarm optimization (PSO) [14 41] -e settingparameters of the algorithm are shown in Table 1 -especific forms of the test functions are shown in Table 2

Among them the dimension of the test function was setto 30 and the number of iterations was 200 -e calculationresults are shown in Table 3 and Figures 2ndash6 are iterativediagrams of the test function

It can be seen from Table 3 and the iterative graph of thetest function that the improved chicken swarm optimizationis more powerful than three other optimization algorithmsregardless of the convergence accuracy of the algorithm andthe ability to find the optimal value or the robustness of thealgorithm and it is better than the traditional chicken swarmoptimization in the optimization accuracy and convergencespeed -us after the multipeak function test it shows thatimproved chicken swarm optimization has great advantages

5 Engineering Applications

In industrial production the cross-sectional area of the trussmembers is generally standardized that is the cross-sec-tional area is selected from a given set of discrete realnumbers Due to different conditions and different re-quirements truss structure optimization can have multipleoptimization objectives such as minimum total mass ofstructure minimum displacement of specified nodes andmaximum natural frequency In this paper the optimalcross-sectional area of the member was found under thecondition of the stress constraint of the member so that thetruss mass was minimized and the node displacement was

minimized -e n-bar truss structure system was studied-e basic parameters of the system (including elasticmodulus material density maximum allowable stress andmaximum allowable displacement) were known Under thegiven load conditions the optimal cross-sectional area of theN-bar truss was found to minimize the mass

Four typical truss optimization examples were chosen todemonstrate the efficiency and reliability of the improvedchicken swarm optimization for solving the shape and size oftrusses with multiple frequency constraints

51 Optimization Design of Cross Section of the 25 Bar SpaceTruss Structure Figure 7 shows the 25 bar space trussstructure model [42] -e known material density is

Start

Initial (chaos strategy andreturn learning strategy)

Determine the individualrsquosfitness value and record the

optimal value

Flock role update condition

(level relationship)

Cock individual location update

Hen individual position update

Chick individual location update

Optimize the population bymutating and cross-

selecting

Maximum numberof iterations

Output optimal results

End

Rearrange the fitnessfunction

Reallocation

Subgroup partitioning

Yes

No

No

Yes

Figure 1 Flow chart of improved chicken swarm optimization


ρ 2786 kgm3 elastic modulus E 68974MPa stressconstraint [minus 2758 2758] MPa and L 635mm themaximum vertical displacement of nodes 1 and 2 does notexceed dmax 8899mmanddmax 8899mm Accordingto the symmetry 25 rods are divided into 8 groups and thedesign variable is 8 -e control parameters of the algorithmare set as follows the maximum number of iterations is 500the search space dimension is 10 We compared improvedchicken swarm optimization with improved particle swarmoptimization (IPSO) improved fruit fly optimization al-gorithm (IFFOA) and improved genetic algorithm (IGA)[43ndash45] -e node loads are shown in Table 4 and the barsare grouped in Table 5

Results after optimization are shown in Table 6

It can be concluded from Table 6 that under the sameconstraints the improved chicken swarm optimization al-gorithm was used to optimize the 25 bar truss structure -eoptimized total mass of the structure is 21148 kg which islighter than the improved particle swarm optimization al-gorithm and the quality is reduced to (21938 minus 21148)21148 374 compared with the improved genetic algo-rithm the quality is reduced to (22249 minus 21148)21148 520 the quality of the results obtained with theimproved fruit fly optimization algorithm is reduced to(21611 minus 21148)21148 219 and the optimization re-sults are improved -e four algorithm optimization itera-tion curves are shown in Figure 8 As can be seen fromFigure 8 the improved chicken swarm optimization can

Table 1 -e related parameter value

Algorithm ParameterPSO c1 c2 149445 w 0729BA α c 09 fmin 0 fmax 2 A0 isin [0 2] r0 isin [0 1]

CSO RN 02lowastN HN 06lowastN CN N minus RN minus HN

MN 01lowastN G 10 FL isin [04 1]

Improved chicken swarm optimization RN 02lowastN HN 06lowastN CN N minus RN minus HN MN 01lowastN G 10 FL isin [04 1] ωmax 09 ωmin 04 K 200

Table 2 Test function

Function form Bounds Optimum

f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2

i minus 10 cos(2πxi) + 10] [minus 6 6] 0

f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0

f5(x) 1113936Nminus 1i1 [100(xi+1 minus x2

i )2 + (1 minus xi)2] [minus 2 2] 0

Table 3 Optimal calculation results

Function Algorithm Best Mean Worst

f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0

Improved chicken swarm optimization 0 0 0

f2(x)

PSO 58349 874784 105953BA 08076 89964e+ 006 35767e+ 008CSO 11279e minus 07 553881e minus 07 10343e minus 06


f3(x)

PSO 864687 114428e+ 02 146842e+ 02BA 8844729 12199296 16760654CSO 33739e minus 08 55749e minus 02 183e minus 02


f4(x)

PSO 08973 106072 11596BA 0004 282906 1542094CSO 16567e minus 07 1092612e minus 02 2067e minus 01


f5(x)

PSO 71502e minus 10 278472e minus 06 43144e minus 06BA 238966 1018847 4629705CSO 24298e minus 10 315851e minus 06 186591e minus 06



Particle swarmoptimizationBat algorithm

Chicken swarmoptimizationImproved chicken swarmoptimization

20 40 60 80 100 120 140 160 180 2000Iteration number

0

50

100

150

200

250

300

350

400

450

Fitn

ess

Figure 4 -e experimental result of f3(x) with 30 dimensions



0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x

Figure 7 Schematic diagram of the 25 bar space truss structure


search for the global optimal solution It has higher con-vergence precision and convergence speed and the effect isobvious

52 Optimization Design of Cross Section of the 52 Bar PlaneTruss Structure As shown in Figure 9 the space 52 truss

structure model is established and the bars are divided into12 groups according to the force of the members [44] -especific grouping situation is shown in Table 7 We com-pared improved chicken swarm optimization with improvedparticle swarm optimization (IPSO) improved fruit flyoptimization algorithm (IFFOA) and improved genetic

Table 4 25 bar space truss load

Node number Fx(kN) Fy(kN) Fz(kN)

1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0

Table 5 25 bar space truss classification

Group number Rod number1 A12 A2simA53 A6simA94 A10simA115 A12simA136 A14simA177 A18simA218 A22simA25

Table 6 Comparison of optimization results for 25 bar space truss

NumberingRod cross-sectional area (mm2)

IPSO [43] IFFOA [44] IGA [45] ICSO1 7933 6252 6579 75552 18654 19155 23457 197553 214595 219154 222955 2178554 32657 6652 6432 286165 84812 108677 122062 984146 37565 61516 50025 410697 45432 39809 9115 420168 227564 218355 256785 219441Weight (kg) 21938 21611 22249 21148

Improved geneticalgorithmImproved particleswarm optimization

Improved fruit flyoptimization algorithmImproved chickenswarm optimization

200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200

Figure 8 Four algorithms for finding the iterative curve of 25 bars

50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x

Figure 9 Schematic diagram of the 52 bar plane truss structure

Table 7 52 bar plane truss structure grouping

Group number Rod numberA1 1 2 3 4A2 5 6 7 8 9 10A3 11 12 13A4 14 15 16 17A5 18 19 20 21 22 23A6 24 25 26A7 27 28 29 30A8 31 32 33 34 35 36A9 37 38 39A10 40 41 42 43A11 44 45 46 47 48 49A12 50 51 52


algorithm (IGA) [43ndash45] -e optimization results of eachalgorithm are shown in Table 8 -e structural members areall made of the same material material density isρ 78600 kgm3 the elastic modulus E 207 times 105 MPathe lateral load Px 100 kN and the vertical loadPy 200 kN -e allowable stress of each member in thestructure is plusmn 180MPa

It can be concluded from Table 8 that under the sameconstraints the improved chicken swarm optimizationwas used to optimize the 52-bar truss structure and thetotal mass of the optimized structure is 189545 kgCompared with the improved particle swarm algorithmthe quality is reduced to (193836 minus 189545)189545 226 compared with the improved geneticalgorithm the quality is reduced to (191261 minus 189545)

189545 091 compared with the improved fruit flyoptimization algorithm the quality is reduced to(190037 minus 189545)189545 026 and the optimiza-tion results have been improved very well -e four al-gorithm optimization iteration curves are shown inFigure 10 As can be seen from Figure 10 the improvedchicken swarm optimization can search for the globaloptimal solution Compared with the other three opti-mization algorithms it has a higher convergenceprecision and convergence speed and the effect isobvious

53 Optimization Design of Cross Section of the 72 Bar SpaceTruss Structure -e 72 bar space truss structure is shown in

Table 8 Comparison of optimization results of the 52 bar plane truss structure


IPSO [43] IFFOA [44] IGA [45] ICSO1 465606 464806 465215 4650552 116429 114129 116515 1160293 51645 45419 36023 363264 332322 333322 330632 3303225 94800 92000 94314 935266 48419 49019 48615 494197 227032 221871 220516 2210398 102839 102839 101018 1005599 226032 47419 38212 38838610 155548 125387 128617 12805911 106516 118129 116013 11546612 50145 49019 78615 792256Weight (kg) 193836 190037 191261 189545

0 50 100 150 200 250 300 350 400 450 500Iteration number

1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)

Improved particleswarm optimizationImproved geneticalgorithm

Improved chickenswarm optimizationImproved fruit flyoptimization algorithm

198019601940192019001880

205 210 215



Figure 11 [46] -e structure considers two load conditions-e specific working conditions are shown in Table 9According to the force of the rod the 72 rods in the structureare divided into 16 groups -e specific grouping of the rodsis shown in Table 10-e rods are made of the samematerialthematerial density is ρ 2 678 kgm3 the elastic modulus isE 68950MPa the maximum displacement variation rangeof each joint of the rods in each direction is plusmn 635mm theallowable stress range is [minus 172375 172375] we comparedthe results with the improved particle swarm optimizationalgorithm (IPSO) the improved fruit fly optimization al-gorithm (IFFOA) and the improved genetic algorithm(IGA) [43ndash45] and the optimized results are shown inTable 11

It can be concluded from Table 11 that under the sameconstraints the improved chicken swarm optimization wasused to optimize the design of the 72 bar truss structure andthe total mass of the optimized structure is 17024 kg

7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25



NodeWorking condition 1 Working condition 2

Fx(kN) Fy(kN) Fz(kN) Fx(kN) Fy(kN) Fz(kN)

1 22250 22250 minus 22250 0 0 minus 222502 0 0 minus 222503 0 0 minus 222504 0 0 minus 22250


Group number Rod numberA1 1 2 3 4A2 5 6 7 8 9 10 11 12A3 13 14 15 16A4 17 18A5 19 20 21 22A6 23 24 25 26 27 28 29 30A7 31 32 33 34A8 35 36A9 37 38 39 40A10 41 42 43 44 45 46 47 48A11 49 50 51 52A12 53 54A13 55 56 57 58A14 59 60 61 62 63 64 65 66A15 67 68 69 70A16 71 72


Compared with the improved particle swarm algorithm thequality is reduced to (18243 minus 17024)17024 716compared with the improved genetic algorithm the qualityis reduced to (19156 minus 17024)170241252 and com-pared with the improved fruit fly optimization algorithmthe results are optimized (17237 minus 17024)17024125-e optimization results have been improved very well -efour algorithm optimization iteration curves are shown inFigure 12 It can be seen from Figure 12 that the improvedchicken swarm optimization can search for the global op-timal solution Compared with the improved genetic

algorithm (IGA) the improved particle swarm optimizationalgorithm (IPSO) and the improved fruit fly optimizationalgorithm (IFFOA) it has higher convergence precision andconvergence speed and the effect is obvious

54 Optimization Design of Cross Section of the 200 Bar PlaneTruss Structure -e structure of the 200 bar truss is shownin Figure 13 [47] -e grouping of the structural members isshown in Table 12 -e specific optimization results areshown in Table 13 -e modulus of elasticity is

Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)

Improved particle swarmoptimizationImproved geneticalgorithm


50 100 150 200 250 300 350 400 450 5000

200

180

160200 250




IPSO [43] IFFOA [44] IGA [45] ICSO1 18574 16126 10134 95342 35128 37097 34554 325543 20021 27927 26426 244264 30069 38199 36729 357295 32593 15651 32691 318916 35070 33046 33548 326487 5852 6052 6452 62538 5852 6052 6452 62539 82023 71398 82587 8108710 31826 37381 33213 3211311 5852 6052 6452 625212 5852 6052 6452 625213 117800 133002 122407 12040714 31044 32488 33077 3357715 5853 6052 6452 625416 5853 6052 6452 6254Weight (kg) 18243 17237 19156 17024


E 21 times 1011Nm2 and the density of the rod material isρ 7860 kgm3 -e minimum allowable cross-sectionalarea of the truss member is set to 01 cm2 -e structure freepoint is given a nonstructural mass of 50 kg -e designvariable has 29 dimensions and is a relatively complexstructural optimization problem We compared the im-proved chicken swarm optimization with the results of theimproved gravitational search algorithm (IGSA) improvedgenetic algorithm (IGA) and improved fruit fly optimiza-tion algorithm (IFFOA) [44 47 48]

It can be concluded from Table 13 that under the sameconstraints the improved chicken swarm optimization wasused to optimize the 200 bar truss structure and the opti-mized total mass of the structure is 214792 kg Compared

with the improved gravitational search algorithm thequality is reduced to (215564 minus 214792)214792 359Compared with the improved genetic algorithm the qualityis reduced to (229615 minus 214792)214792 690 com-pared with the improved fruit fly optimization algorithmthe optimization results are optimized to(215673 minus 214792)214792 410 and the optimizationresults are improved

It can be seen from Figure 14 that the improvedchicken swarm optimization can find the global optimalsolution after iteration for about 170 times -e gravi-tational search algorithm is iterated about 210 times andthe genetic algorithm is iterated about 220 times to findthe global optimal solution and the improved fruit fly

11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m




Group number Rod numberA1 1 2 3 4A2 5 6 7 8 9 10 11 12 13 14 15 16 17A3 19 20 21 22 23 24A4 18 25 56 63 94 101 132 139 170 177A5 26 29 32 35 38A6 6 7 9 10 12 13 15 16 27 28 30 31 33 34A7 39 40 41 42A8 43 46 49 52 55A9 57 58 59 60 61 62A10 64 67 70 73 76

A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199


NumberingRod cross-sectional area (cm2)

IGSA [47] IGA [48] IFFOA [44] ICSO1 0239 0293 0289 02652 0466 0556 0488 04453 0120 0295 0100 01004 0120 0190 0100 01005 0479 0834 0499 04846 0864 0645 0804 08457 0115 0177 0103 01458 1353 1479 1377 13719 0112 0449 0100 011210 1544 1458 1698 168211 1141 1123 1156 114212 0121 0273 0131 013513 3032 1865 3261 302114 0114 0117 0101 010215 3254 3555 3216 326416 1646 1568 1621 162517 0227 0265 0209 014818 5152 5165 5020 416419 0124 0659 0133 015420 5485 4987 5453 568421 2907 1843 2113 2123


optimization algorithm is iterated about 180 times to findthe global optimal solution For the quality problem ofthe optimal global solution the improved chicken swarmoptimization is better than other three optimizationalgorithms It is proved that in the process of optimizingin the face of complex optimization problems the im-proved chicken swarm optimization is stable and not easyto fall into the local optimal solution It can be seen thatthe improved chicken swarm optimization is effective

6 Conclusion

Structure optimization is more and more important incivil engineering In order to find more effective opti-mization method the chicken swarm optimization wasintroduced For the NP hard problems the chickenswarm optimization performs better than common al-gorithms It has the shortcoming of the premature So weimproved the algorithm and applied to truss structure

optimization the concept of combining chaos strategyand reverse learning strategy was introduced in the ini-tialization to ensure the global search ability And theinertia weighting factor and the learning factor wereintroduced into the chick position update process so as tobetter combine the global and local search Finally theoverall individual position of the algorithm was opti-mized by the differential evolution algorithm -e mul-tipeak function was used to prove its validity Finally theimproved chicken swarm optimization was applied to thetruss structure optimization design -e mathematicalmodel of the truss section optimization was given -eexample verification shows that the improved chickenswarm optimization has a faster convergence speed whichmakes the results more optimal

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Table 13 Continued


IGSA [47] IGA [48] IFFOA [44] ICSO22 0659 1789 0723 071223 7658 8175 7724 715424 0144 0325 0182 018925 8052 10597 7971 789426 2788 2986 2996 296327 10477 10598 10206 1045928 21325 20559 20669 2016429 10511 18648 11555 11459Weight (kg) 215564 229615 215673 214792


2000

2500

3000

3500

4000

4500

Wei

ght (

kg)

Improved geneticalgorithmImproved gravitationalsearch algorithm


2300225022002150

210 215 220



Acknowledgments

-is work was supported by the Project of Scientific Re-search Program of Colleges and Universities in HebeiProvince (no ZD 2019114) and the Fund of Hebei Engi-neering Technology Research Centre for Water ResourcesHigh Efficiency Utilization

References

[1] L A Schmit and B Farshi ldquoSome approximation concepts forstructural synthesisrdquo AIAA Journal vol 12 no 5 pp 692ndash699 1973

[2] V J Savsani G G Tejani and V K Patel ldquoTruss topologyoptimization with static and dynamic constraints usingmodified subpopulation teaching-learning-based optimiza-tionrdquo Engineering Optimization vol 48 no 11 p 11 2016

[3] A Shakya P Nanakorn and W Petprakob ldquoA ground-structure-based representation with an element-removal al-gorithm for truss topology optimizationrdquo Structural andMultidisciplinary Optimization vol 58 no 2 pp 657ndash6752018

[4] A Asadpoure J K Guest and L Valdevit ldquoIncorporatingfabrication cost into topology optimization of discretestructures and latticesrdquo Structural and MultidisciplinaryOptimization vol 51 no 2 pp 385ndash396 2015

[5] S Bobby A Suksuwan S M J Spence and A KareemldquoReliability-based topology optimization of uncertain build-ing systems subject to stochastic excitationrdquo Structural Safetyvol 66 pp 1ndash16 2017

[6] Z Zhang KWang L Zhu and YWang ldquoA Pareto improvedartificial fish swarm algorithm for solving a multi-objectivefuzzy disassembly line balancing problemrdquo Expert Systemswith Applications vol 86 pp 165ndash176 2017

[7] J-Y Park and S-Y Han ldquoTopology optimization for non-linear structural problems based on artificial bee colony al-gorithmrdquo International Journal of Precision Engineering andManufacturing vol 16 no 1 pp 91ndash97 2015

[8] S L Tilahun and J M T Ngnotchouye ldquoFirefly algorithm fordiscrete optimization problems a surveyrdquo KSCE Journal ofCivil Engineering vol 21 no 2 pp 535ndash545 2017

[9] A Fiore G C Marano R Greco and E MastromarinoldquoStructural optimization of hollow-section steel trusses bydifferential evolution algorithmrdquo International Journal ofSteel Structures vol 16 no 2 pp 411ndash423 2016

[10] D Karaboga B Gorkemli C Ozturk and N Karaboga ldquoAcomprehensive survey artificial bee colony (ABC) algorithmand applicationsrdquo Artificial Intelligence Review vol 42 no 1pp 21ndash57 2014

[11] A E Kayabekir G Bekdas S M Nigdeli and X-S Yang ldquoAcomprehensive review of the flower pollination algorithm forsolving engineering problemsrdquo Nature-Inspired Algorithmsand Applied Optimization vol 40 no 7 pp 171ndash188 2018

[12] Z Chen and L Yu ldquoAn improved PSO-NM algorithm forstructural damage detectionrdquo Advances in Swarm andComputational Intelligence pp 124ndash132 2015

[13] A Cincin B Ozben and O Erdogan ldquoMemetic algorithms inengineering and designrdquo Handbook of Memetic Algorithmspp 241ndash260 Springer Berlin Heidelberg 2012

[14] X Meng Y Liu X Gao and H Zhang ldquoA new bio-inspiredalgorithm chicken swarm optimizationrdquo Lecture Notes inComputer Science pp 86ndash94 2014

[15] D Wu K Fei W Gao Y Shen and Z Ji ldquoImproved chickenswarm optimizationrdquo in Proceedings of the Paper presented at

the IEEE International Conference on Cyber Technology inAutomation Shenyang China June 2015

[16] W Yu X Qu and Y Bo ldquoImproved chicken swarm opti-mization method for reentry trajectory optimizationrdquoMathematical Problems in Engineering vol 2018 Article ID8135274 13 pages 2018

[17] S Torabi and F Safi-Esfahani ldquoA dynamic task schedulingframework based on chicken swarm and improved ravenroosting optimization methods in cloud computingrdquo Journalof Supercomputing vol 74 no 6 pp 2581ndash2626 2018

[18] H Hu J Li and J Huang ldquoEconomic operation optimizationof micro-grid based on chicken swarm optimization algo-rithmrdquo High Voltage Apparatus vol 53 no 1 pp 119ndash1252017

[19] N Irsalinda I T R Yanto H Chiroma and T Herawan ldquoAframework of clustering based on chicken swarm optimiza-tionrdquo Advances in Intelligent Systems and Computingvol 549 pp 336ndash343 2016

[20] A I Hafez H M Zawbaa E Emary H A Mahmoud andA E Hassanien ldquoAn innovative approach for feature selec-tion based on chicken swarm optimizationrdquo in Proceedings ofthe 2015 7th International Conference of Soft Computing andPattern Recognition (SoCPaR) Japan 2015

[21] M A Shayokh and S Y Shin ldquoBio inspired distributed WSNlocalization based on chicken swarm optimizationrdquo WirelessPersonal Communications vol 97 no 4 pp 5691ndash5706 2017

[22] Roslina M Zarlis I T R Yanto and D Hartama ldquoAframework of training ANFIS using chicken swarm optimi-zation for solving classification problemsrdquo in Proceedings ofthe 2016 International Conference on Informatics and Com-puting (ICIC) Mataram Indonesia October 2016

[23] M Awais Z U Abadeen T Bilal Z Faiz M Junaid andN Javaid ldquoHome Energy Management Using EnhancedDifferential Evolution and Chicken Swarm OptimizationTechniquesrdquo Advances in Intelligent Networking and Col-laborative Systems vol 8 pp 468ndash478 2017

[24] Z Faiz T Bilal M Awais Pamir S Gull and N JavaidldquoDemand side management using chicken swarm optimiza-tionrdquo Advances in Intelligent Networking and CollaborativeSystems vol 8 pp 155ndash165 2017

[25] K Ahmed A E Hassanien and S Bhattacharyya ldquoA novelchaotic chicken swarm optimization algorithm for featureselectionrdquo in Paper presented at the Fird InternationalConference on Research in Computational Intelligence ampCommunication Networks Kolkata India 2017

[26] M A Ahandani and H Alavi-Rad ldquoOpposition-basedlearning in shuffled frog leaping an application for parameteridentificationrdquo Information Sciences vol 291 pp 19ndash42 2015

[27] S Y Park and J J Lee ldquoStochastic opposition-based learningusing a beta distribution in differential evolutionrdquo IEEETransactions on Cybernetics vol 46 no 10 pp 2184ndash21942016

[28] B Bentouati S Chettih R Djekidel and R A-A El-SehiemyldquoAn efficient chaotic cuckoo search framework for solvingnon-convex optimal power flow problemrdquo InternationalJournal of Engineering Research in Africa vol 33 pp 84ndash992017

[29] M Abdollahi A Bouyer and D Abdollahi ldquoImprovedcuckoo optimization algorithm for solving systems of non-linear equationsrdquo Journal of Supercomputing vol 72 no 3pp 1ndash24 2016

[30] D Chitara K R Niazi A Swarnkar and N Gupta ldquoCuckoosearch optimization algorithm for designing of a


multimachine power system stabilizerrdquo IEEE Transactions onIndustry Applications vol 54 no 4 pp 3056ndash3065 2018

[31] M R Bonyadi and Z Michalewicz ldquoImpacts of coefficients onmovement patterns in the particle swarm optimization al-gorithmrdquo IEEE Transactions on Evolutionary Computationvol 21 no 3 pp 378ndash390 2017

[32] Y-p Chen and P Jiang ldquoAnalysis of particle interaction inparticle swarm optimizationrdquo Feoretical Computer Sciencevol 411 no 21 pp 2101ndash2115 2010

[33] B Nasiri M R Meybodi and M M Ebadzadeh ldquoHistory-driven particle swarm optimization in dynamic and uncertainenvironmentsrdquo Neurocomputing vol 172 no 3 pp 356ndash3702016


[35] A Orlandi ldquoDifferential evolutionary multiple-objective se-quential optimization of a power delivery networkrdquo IEEETransactions on Electromagnetic Compatibility vol 99pp 1ndash7 2018

[36] A W Mohamed ldquoRDEL restart differential evolution al-gorithm with local search mutation for global numericaloptimizationrdquo Egyptian Informatics Journal vol 15 no 3pp 175ndash188 2014

[37] P N Suganthan J J Liang N Hansen et al ldquoProblemdefinitions and evaluation criteria for the CEC 2005 specialsession on real-parameter optimizationrdquo Technical Report2005005 Nanyang Tech Uni Singapore May 2005 andKanGAL Report IIT Kanpur India 2005

[38] A Auger N Hansen J M P Zerpa R Ros andM Schoenauer ldquoExperimental Comparisons of derivative freeoptimization algorithmsrdquo Experimental Algorithms pp 3ndash15Springer Berlin Heidelberg 2009

[39] U K Chakraborty S Rahnamayan H R Tizhoosh andM M A Salama ldquoOpposition-based differential evolutionrdquoin Studies in Computational Intelligence Springer BerlinHeidelberg 2008

[40] P W Tsai J S Pan P Shi and B Y Liao ldquoA new frameworkfor optimization based-on hybrid swarm intelligencerdquo inHandbook of Swarm Intelligence vol 23 pp 421ndash449Springer Berlin Heidelberg 2011

[41] Z Wang and C Yin ldquoChicken swarm optimization algorithmbased on behavior feedback and logic reversalrdquo Journal ofBeijing Institute of Technology vol 27 no 3 pp 34ndash42 2018

[42] A Mortazavi V Togan and A Nuhoglu ldquoWeight minimi-zation of truss structures with sizing and layout variablesusing integrated particle swarm optimizerrdquo Journal of CivilEngineering ampManagement vol 23 no 8 pp 985ndash1001 2017

[43] L J Li Z B Huang F Liu andQ HWu ldquoA heuristic particleswarm optimizer for optimization of pin connected struc-turesrdquo Computers amp Structures vol 85 no 7-8 pp 340ndash3492007

[44] Y Li and S Lian ldquoImproved fruit fly optimization algorithmincorporating Tabu search for optimizing the selection ofelements in trussesrdquo KSCE Journal of Civil Engineeringvol 22 no 12 pp 4940ndash4954 2018

[45] F Erbatur O Hasanccedilebi I Tutuncu and H Kılıccedil ldquoOptimaldesign of planar and space structures with genetic algo-rithmsrdquo Computers amp Structures vol 75 no 2 pp 209ndash2242000

[46] H Assimi A Jamali and N Nariman-Zadeh ldquoMulti-ob-jective sizing and topology optimization of truss structuresusing genetic programming based on a new adaptive mutant

operatorrdquo Neural Computing amp Applications vol 23 no 24pp 1ndash21 2018

[47] M Khatibinia and S Sadegh Naseralavi ldquoTruss optimizationon shape and sizing with frequency constraints based onorthogonal multi-gravitational search algorithmrdquo Journal ofSound and Vibration vol 333 no 24 pp 6349ndash6369 2014

[48] T Xu W Zuo T Xu G Song and R Li ldquoAn adaptive re-analysis method for genetic algorithm with application to fasttruss optimizationrdquo Acta Mechanica Sinica vol 26 no 2pp 225ndash234 2010


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Submit your manuscripts atwwwhindawicom

optimization [9] Karaboga et al proposed an improvedartificial bee colony algorithm (ABC) based on chaos theorywhich was applied to the truss structure example to verify theeffectiveness of the improved algorithm for truss engi-neering structure optimization [10] Kayabekir explored anew intelligent algorithm the flower pollination algorithm(FPA) and discussed its practical application in civil en-gineering mechanical engineering electronic communica-tion and chemistry In the civil engineering field the FPAalgorithm was applied to the 25-bar truss structure to op-timize the structure and the feasibility of the algorithm wasverified [11] Chen et al proposed a hybrid particle swarmoptimization (PSO) algorithm based on the improvedNelderndashMead algorithm (NMA) -e improved NMA se-lected a part of the n-simplex subplane for optimizationusing modal strain energy -e index (MSEBI) to locate thedamage effectively improved the convergence speed andaccuracy of the PSO algorithm and greatly improved thecomputational efficiency in the field of structural damagedetection (SDD) [12] Andrea Caponio et al proposed ametaheuristic algorithm based on population distributiontheory for the application of practical engineering structureoptimization -e proposed algorithm can converge wellwhen faced with nonlinear and indistinguishable optimi-zation problems -e optimization process was stable andprovides a new way of thinking [13]

In 2014 Chinese scholar Meng proposed the chickenswarm optimization (CSO) [14] which was a group-basedstochastic optimization algorithm -e advantage was thatthe implementation was simple-e disadvantage was that itwas easy to fall into the local optimal solution convergesslowly and is low in precision Scholars had done a lot ofresearch on this optimization algorithm In 2015 Fei et alproposed an improved chicken swarm optimization (CSO)which analyzed the weighting factors in the reference par-ticle swarm optimization algorithm-e adaptive weight wasintroduced in the process of updating the individual positionof the chicken which solved the problem that the optimalsearch solution was easy to skip due to the large search spacein the early stage of the algorithm the late search space wassmall the convergence was slow and the learning part of theindividual with the cock was added-is allowed the chick toenjoy a comprehensive learning mechanism [15] Yu et alimproved the chicken swarm optimization (CSO) in 2016using a variety of hybrid methods -e reverse directionlearning method was used to initialize the population in-dividuals to improve the quality of the population and thevariation idea was introduced in the boundary processing toenhance the diversity of the population improving theglobal optimization ability of the algorithm Finally the ideaof simulated annealing was used to accept the inferior so-lution with a certain probability which enhanced the abilityof the algorithm to jump out of local optimum [16] -eseimproved algorithms effectively improved the optimizationperformance of the algorithm and the results of its functionoptimization proved that the improved algorithm was ef-fective-e existing research showed that the chicken swarmoptimization (CSO) had been successfully applied to re-source scheduling [17] engineering optimization design

[14] cluster analysis and optimization of classifier co-efficients [18 19] In 2016 Hafez et al proposed a featureselection system based on chicken swarm optimization(CSO) which was used to select features in a wrapper modeto search for feature space for the best combination offeatures thus maximizing classification performance whileminimizing the number of selected features [20] Shayokhet al used the chicken swarm optimization (CSO) to solvethe wireless sensor network (WNS) node location problem[21] In 2016 Roslina et al proposed an improved chickenswarm optimization (CSO) for ANFIS performance whichcan more accurately solve the ANFIS network trainingclassification problem [22] In 2017 Awais et al combinedthe chicken swarm optimization (CSO) with energy opti-mization for home users enabling home users to reducepower costs power consumption and peak-to-average ratio[23 24] Ahmed et al improved the chicken swarm opti-mization (CSO) search ability by applying logistic and tendchaotic mapping to help the chicken swarm optimization(CSO) better explore search space [25] -ese successfulapplications show that the chicken swarm optimization(CSO) has a good development and application prospectsHowever in these application studies the chicken swarmalgorithm (CSO) is also imperfect For example the algo-rithm is not initialized the chicken position update does notprevent the individual from being out of bounds and thealgorithm has no overall individual optimization

Based on the above research this paper improved thechicken swarm optimization and applied to truss structureoptimization the concept of combining chaos strategy andreverse learning strategy was introduced in the initializationto ensure the global search ability And the inertia weightingfactor and the learning factor were introduced into the chickposition update process so as to better combine the globaland local search Finally the overall individual position ofthe algorithm was optimized by the differential evolutionalgorithm -e improved algorithm was tested by multipeakfunction and applied to the truss simulation experiment

2 Chicken Swarm Optimization Algorithm

-e traditional chicken swarm optimization mainly treatsthe optimization problem as the process of chickensrsquosearching for food -e whole chicken swarm is divided intoseveral chicken flocks each of which has a cock several hensand several chicks -ere is a competition between eachchicken swarm and the best cluster individuals are obtainedthrough competitions -e process of simplifying is asfollows

(1) In each chicken swarm there are many subchickenswarms each of which included one cock severalhens and several chicks

(2) -e chicken swarm divides several subchickenswarms and determines the fitness value of in-dividuals on which cocks hens and chicks dependSeveral individuals with the best fitness values can actas cocks Each cock is a leader of a chicken swarm-e worst fitness can be used as a chicken and the








σ2

1 fi lefk

expfk minus fi

fi

11138681113868111386811138681113868111386811138681113868 + ε

1113888 1113889 fi gtfk

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)







abs f1( 1113857 + ε1113888 1113889


(2)










xi(t)lowast










⎧⎨

⎩ (6)





+ φ2 xrj(t) minus xij(t)1113872 1113873(7)




(8)














⎩ (11)

















Start



optimal value







selecting



End


Reallocation


Yes

No

No

Yes













f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2


f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0


i )2 + (1 minus xi)2] [minus 2 2] 0



f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0


f2(x)



f3(x)



f4(x)



f5(x)







0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








σ2

1 fi lefk

expfk minus fi

fi

11138681113868111386811138681113868111386811138681113868 + ε

1113888 1113889 fi gtfk

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(1)







abs f1( 1113857 + ε1113888 1113889


(2)










xi(t)lowast










⎧⎨

⎩ (6)





+ φ2 xrj(t) minus xij(t)1113872 1113873(7)




(8)














⎩ (11)

















Start



optimal value







selecting



End


Reallocation


Yes

No

No

Yes













f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2


f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0


i )2 + (1 minus xi)2] [minus 2 2] 0



f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0


f2(x)



f3(x)



f4(x)



f5(x)







0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





+ φ2 xrj(t) minus xij(t)1113872 1113873(7)




(8)














⎩ (11)

















Start



optimal value







selecting



End


Reallocation


Yes

No

No

Yes













f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2


f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0


i )2 + (1 minus xi)2] [minus 2 2] 0



f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0


f2(x)



f3(x)



f4(x)



f5(x)







0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia














Start



optimal value







selecting



End


Reallocation


Yes

No

No

Yes













f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2


f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0


i )2 + (1 minus xi)2] [minus 2 2] 0



f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0


f2(x)



f3(x)



f4(x)



f5(x)







0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












f1(x) 1113936Ni1(1113936

ij1xj)

2 [minus 100 100] 0

f2(x) 1113936Ni1|x| + 1113937

Ni1|x| [minus 10 10] 0

f3(x) 1113936Ni1[x2


f4(x) (14000)1113936Ni1x

2i minus 1113937

Ni1cos(xi

i

radic) + 1 [minus 600 600] 0


i )2 + (1 minus xi)2] [minus 2 2] 0



f1(x)

PSO 0 0 0BA 18674 29419 41871CSO 0 0 0


f2(x)



f3(x)



f4(x)



f5(x)







0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0

50

100

150

200

250

300

350

400

450

Fitn

ess




0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450

Fitn

ess





0

50

100

150

200

250

300

350

400

450Fi

tnes

s



11

2

33

65

5

4

7

810

9

9 8

2 671210

4

13 1123

18151422

20

2125 16 17 19

24

3l

3l

3l

4l

4l

8l

8l

y

z

x








1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







1 4445 4445 minus 22232 0 4445 minus 22233 2223 0 06 2667 0 0








200

400

600

800

1000

1200

1400

1600

Wei

ght (

kg)


230220210

185 190 195 200


50

44 45

51

46 47

52

48 49

40 41 42 43

37 38 3931 32 33 34 35 36

14 15 16

14 15 16

12

20

27 28 29 30

10 1124 25 26

18 19 20 21 22 23

17

7 8611

5 612

7 813

9 10

1

1

2

2

3

3

4

4

Py Py Py Py

Px Px Px Px

2m 2m 2m

3m

3m

3m

3m

17

13

9

5

y

x













1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










1500

2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



198019601940192019001880

205 210 215





7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




7

3

4

1

5

9

13

17

18

19

15

11

10

1420

16

6

2

12

8

1516

417

18

533

2

14 731

34

6 13

2231

8

26

32 25












Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Iteration number

150

200

250

300

350

400

450

Wei

ght (

kg)



50 100 150 200 250 300 350 400 450 5000

200

180

160200 250










11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






11

22

33

44

55

6

6

7

7

8

8

9

9

10

10

11

11

12

12

13

13

14

14

15

15

16

16

17

17

18

18

19

19

20

20

21

21

22

22

23

23

24

24

25

25

26

26

27

27

28

28

29

29

30

30

31

31

32

32

33

33

34

34

35

35

36

36

37

37

38

38

39

39

40

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77 78 79 80

81 82 83 84 85 86 87 88 89 90

151 152153 154 155 156

157 158 159 160 161 162 163 164 165 166 167 168 169170 171 172 173 174 175 176 177

178 179 180 181 182 183 184 185 186 187 188 189 190

91 92 93

94 95 96 97 98 99 100

191 192 193 194

195 196 197 198 199 200

101

102 103 104 105 106 107 108 109 110 111 112 113 114115 116 117 118

119 120 121 122 123 124 125 126 127 128 129 130 131

132 133 134 135 136 137 138 139

140 141 142 143 144 145 146 147 148 149 150

4 times 610m

10times

366

m9

144m





A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




A1144 45 47 48 50 51 53 54 65 66 68 69 71 72 74

75A12 77 78 79 80A13 81 84 87 90 93A14 95 96 97 98 99 100A15 102 105 108 111 114

A1682 83 85 86 88 89 91 92 103 104 106 107 109

110 112 113A17 115 116 117 118A18 119 122 125 128 131A19 133 134 135 136 137 138A20 140 143 146 149 152

A21120 121 123 124 126 127 129 130 141 142 144

145 147 148 150 151A22 153 154 155 156A23 157 160 163 166 169A24 171 172 173 174 175 176A25 178 181 184 187 190

A26158 159 161 162 164 165 167 168 179 180 182

183 185 186 188 189A27 191 192 193 194A28 195 197 198 200A29 196 199






6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



6 Conclusion





Table 13 Continued




2000

2500

3000

3500

4000

4500

Wei

ght (

kg)



2300225022002150

210 215 220



Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Acknowledgments


References
























































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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