Convergence Analysis and Parameter Selection of Pso Algorithm

7/27/2019 Convergence Analysis and Parameter Selection of Pso Algorithm

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Chan Shu Weng20769

Supervisor: Mdm Sharifah Masniah Wan Masra


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Introduction Problem Statement

Project Objectives

Methodology Results and Discussions

Conclusions

Recommendations


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Particle Swarm Optimization (PSO) is anevolutionary computation techniquemotivated by simulation of social behaviorwhich was developed by Kennedy and

Eberhart.


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velocityof the ithparticle

positiveconstant

positiveconstant

function inthe range

{0,1}

function inthe range

{0,1}

the best previous

position of ithindividual particle

over its flightpath

the best particleamong all theparticles in the

populationthe ith particle in

the D-dimensionalsearch space

InertiaWeight

vid

= w * vid

+c1

*rand( )*(pid

-xid

)+c2

*Rand( )*(pgd

-xid

)xid= xid + vid


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In order to improve the performance and theconvergence characteristic of PSO, thecorresponding strategy parametersconfiguration need to be analyzed and

adjusted to optimize the different problems.

Some parameters enhance the convergenceability; while some parameters enhance the

space exploration abilities (either helps inglobal exploration ability or local explorationability).


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To study the influence of inertia weight,population sizes, and the number ofmaximum iterations parameters of PSOalgorithms for different optimization

problems.

To analyze and provide guideline for tuning

PSO parameters for different optimizationproblems.


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StartInput Initializations:Population sizeNumber of iterationsNumber of trialsInertia weight valuesRange

Select testing

benchmark function

System searching forpgdSave the data for analysis

Show the data and the result graph

End

Are the displayed

settings as the user

intended?

Yes

No

Inertia Weight Testing Approach(static and time varying inertiaweight)

Population Sizes and The

Number of Maximum IterationsTesting Approach(Population size: 20,40,80 and

160Maximum iterations:

1000,1500,and 2000)

1. Schaffers f62. Spherical3. Rosenbrock4. Rastrigin5. Griewank


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Inertia Weight Testing Approach Results: Schaffers f6 function

Rosenbrock function

Function DimensionSize

Accelerate

CoefficientDynamic

RangeVmax=

XmaxThreshold

for successSchaffers f6, f0 2 c1=2, c2=2 (-100,100) 100 0.001

Spherical, f1 30 c1=2, c2=2 (-100,100) 100 0.01Rosenbrock, f2 30 c1=2, c2=2 (-30,30) 30 100

Rastrigin, f3 30 c1=2, c2=2 (-5.12,5.12) 5.12 100Griewank, f4 30 c1=2, c2=2 (-600,600) 600 1

Table 1: The parameter setting of PSO simulation


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No.Initial Weights, w

Time

varying0.9 0.8 0.7 0.6 0.5 0.4 01 2609 226 2035 2068 23 4272 375 102 1616 99 1216 2193 1828 1005 200 5074 2398 400 154 1451 748 143 4075 196 194 205 1404 2030 212 7086 678 830 913 926 2693 3807 974 209 159 97 2271 2508 2002 1458 851 44 56 2879 238 150 466 74 2163 560

10 410 117 641 36711 1345 598 131 801 26312 1558 3363 653 193 140813 2522 245 3983 72414 586 247 503 25715 403 125 187 267 52316 2975 855 184 96 317 27317 297 2300 981 1526 80918 1434 1171 169 82 61 16019 1005 862 154 256 141320 3051 3926 256 62 361 81521 3872 1638 714 63322 1504 1309 59 25223 1713 266 114 71 770 35624 868 368 189 45 1480 59025 1830 495 1340 90 91926 488 3377 1568 3400 107 79927 1044 590 2333 516 1789 66628 718 135 190 38 61 346 47929 2385 1727 359 1285 982 459 97330 1378 1503 2213 257 471 480

Avg 1959.6 1236 970.76 607.84 507.86 748.53 1026.5 575.27

0

5

10

15

20

25

0.9 0.8 0.7 0.6 0.5 0.4 0 Time

varying

No

.ofFailure

Inertia Weight, w

Schaffer's f6 Function


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No. Initial Weights, w Timevarying0.7 0.6 0.55 0.5 0.4 0.3 0

1 1464 725 1259 374 1347 25522 1032 14133 772 917 511 313 1257 26094 1538 868 508 403 293 1530 25755 1469 888 493 1709 26096 823 853 761 419 27067 783 893 426 319 239 1506 28188 1019 2031 684 2973 27639 714 618 599 490 2085

10 1821 757 512 446 710 276511 1056 640 677 973 790 272612 868 816 563 331 282213 2052 689 475 2877 264914 1012 995 507 439 287615 2836 694 790 1898 275516 792 694 409 413 158717 1296 937 912 427 383918 1434 650 663 346 288119 1063 633 424 569 1294 259220 1519 883 1912 652 271521 896 507 336 257422 1255 607 577 479 263923 1260 747 763 537 319824 1330 925 479 463 418 255325 646 514 397 271226 948 1457 832 339 2346 289827 597 535 102928 863 937 1278 2613 380829 856 650 531 394530 1600 967 798 478 200 1396

Avg 1267 859 711.14 690.32 438.57 1804.45 2864.16

0

5

10

15

20

25

30

35

0.7 0.6 0.55 0.5 0.4 0.3 0 Time

varying

No.ofFailure

Inertia Weight, w

Rosenbrock Function


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Population Sizes and The Number ofMaximum Iterations Testing ApproachResults: Spherical Function

Function DimensionSize AccelerateCoefficient

Asymmetric

Initialization

RangeVmax=

Xmax Thresholdfor successSchaffers f6, f0 2 c1=2, c2=2 (50,100) 100 0.001

Spherical, f1 30 c1=2, c2=2 (50,100) 100 0.01

Rosenbrock, f2 30 c1=2, c2=2 (15,30) 30 100

Rastrigin, f3 30 c1=2, c2=2 (2.56,5.12) 5.12 100

Griewank, f4 30 c1=2, c2=2 (300,600) 600 1

Table 2: The parameter setting of PSO simulation


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Population Size Generation Mean BestFitness

201000 1713.44541500 0.83142000 0.0009

401000 451.37181500 0.04222000 0.0000

80 1000 157.80221500 0.00082000 0.0000

1601000 66.52471500 0.00012000

0.0000

Table 3: Mean best fitness values for the Spherical function


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Table 4: Best fitness values for the Spherical function with populationsizes = 20 and 40, each with three different maximum iterations


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Table 5: Best fitness values for the Spherical function with populationsizes = 80 and 160, each with three different maximum iterations


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The PSO with static inertia weight in the range{0.7, 0.8} for the Schaffers f6 function, {0.4,0.55} for Rosenbrock function, will have betterperformance.

It is showed that only the Schaffers f6benchmark saw much improvement from linearlydecreasing inertia weight. The other fourbenchmark functions are suffered from decreasefor the performance of PSO.

It is concluded that the selection for linearlydecreasing inertia weight for improving theperformance of PSO may be problem-dependent.


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The performance of PSO is not too sensitiveto population sizes.

The number of maximum iteration generationcan improve the performance of the PSO as itconverges to a closer position to the globaloptimum.


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To fully justify the advantages of selectingthe inertia weight parameter, it is suggestedthat an increasing inertia weight can befurther tested on other benchmark functions.


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Documents

Convergence Analysis and Parameter Selection of Pso Algorithm