The Use of Cuckoo Search in Estimating the Parameters of...

S P I R A L Software Process Improvement and Reliability Assurance Leb.

The Use of Cuckoo Search in

Estimating the Parameters of

Software Reliability Growth Models

2013. 8. 7

Taehyoun Kim

Dr. Najla Akram AL-Saati and Marwa Abd-ALKareem Software Engineering Dept.

College of Computer Sciences & Mathematics, Mosul, Iraq

International Journal of Computer Science and Information Security

(IJCSIS), 2013

Software Process Improvement and Reliability Assurance Lab.

Outlines

Introduction

Related Work

Cuckoo Search (CS)

Experiments

Conclusion & Future Work

Discussion


Introduction

Software Reliability

The probability of failure-free software operation for a specified

period of time in a specified environment (ANSI/IEEE, “Standard Glossary of Software Engineering Terminology”, STD-729-1991, 1991)

Software Reliability Growth Models (SRGMs)

The theoretical models for estimating software reliability growth

based on failure detection phenomenon during testing phase (S. Yamada and S. Osaki, “Software Reliability Growth Modeling: Models and Applications”, TSE, 1991)

Figure 1. Basic concept of SRGMs 1/21

Actual Failure data


Parameter Estimation of SRGM

Traditional SRGMs have some parameters which

have physical interpretations. Ex) Goel-Okumoto Model Cumulative failure function

𝑚 𝑡 = 𝑎 1 − 𝑒−𝑟𝑡

• a : the number of total failures

• r : failure detection rate

Time (Weeks)

The

num

ber

of

fail

ure

Figure 2. cumulative failure function

a = 120, b= 0.04

a = 120, b= 0.02

a = 80, b= 0.04

a = 80, b= 0.02

Failure data

Optimal

2/21


Classical Estimation Techniques

There are two of the most popular estimation techniques.

Maximum Likelihood Estimation (MLE)

Least Square Estimation (LSE)

However, these techniques are not effective to estimate

parameters of complicated function like non-linear function.

SRGMs are non-linear functions. (L. Shanmugam and L. Florence, “An Improved ACO Technique for Parameter Estimation”, European Journal of

Scientific Research, 2012)

The interest in heuristic algorithm began to have effect in

solving this problem.

There are many nature inspired algorithms.

3/21


Related Work

Genetic Algorithm (GA) Approach : Survival of the genetically fittest (T. Minohara et al., “Parameter estimation of Hyper-

Geometric distribution Software Reliability Growth

model by Genetic Algorithm”, ISSRE, 1995)

Particle Swarm Optimization

(PSO) approach : Flock migration (Zhang Ke- han et al., “Estimating parameters of

software reliability models using PSO” Computer

Engineering and Applications, 2008)

Ant Colony Optimization (ACO)

approach : Shortest path to food source (Changyou Zheng et al., A parameter Estimation Method

for Software Reliability Models, Procedia Engineering,

2011)

4/21


Cuckoo’s Inspiring Behavior (1/2)

Behavior 1. They have a strange habit of laying their eggs in

public nests.

Behavior 2. They remove other’s eggs to boost the hatching

probability of their own eggs.

Behavior 3.When the first cuckoo baby bird is hatched, he

instinctively throw out host eggs to increase his share of food.

5/21


Cuckoo’s Inspiring Behavior (2/2)

6/21


Cuckoo Search

①

②

③

④

⑤

(X.S. Yang and S. Deb, “Cuckoo Search via Levy Flights”, Nature & Biologically Inspired Computing (NaBIC) 2009) 7/21


Basic Steps of Cuckoo Search (1/5)

Step1. Generate initial population of n host nests. Ex) Goel-Okumoto model

𝑚 𝑡 = 𝑎 1 − 𝑒−𝑟𝑡

𝑎1 𝑟1

𝑛𝑒𝑠𝑡1

𝑎2 𝑟2

𝑛𝑒𝑠𝑡2

𝑎𝑛 𝑟𝑛

𝑛𝑒𝑠𝑡𝑛

• (𝑎𝑖 , 𝑟𝑖) : a candidate for optimal parameters

8/21



Step2. Lay the egg (𝑎𝑘′, 𝑏𝑘′) in the k nest. K nest is randomly selected.

Cuckoo’s egg is very similar to host egg.

𝑎𝑘′ = 𝑎𝑘 + 𝑅𝑎𝑛𝑑𝑜𝑚𝑤𝑎𝑙𝑘(L𝑒 vy flight)𝑎𝑘

𝑟𝑘′ = 𝑟𝑘 + 𝑅𝑎𝑛𝑑𝑜𝑚𝑤𝑎𝑙𝑘(L𝑒 vy flight)𝑟𝑘

𝑎𝑘 𝑟𝑘

𝑛𝑒𝑠𝑡𝑘

𝑎𝑘′ 𝑟𝑘′

Cuckoo’s egg

9/21



Step3. Compare the fitness of cuckoo’s egg with the

fitness of the host egg. Root Mean Square Error (RMSE)


𝑎𝑘 𝑟𝑘


Which egg is better? 𝑅𝑀𝑆𝐸 = 1

𝑛 𝑚 𝑡 − 𝑚𝑡

2

𝑛

𝑡=1

• 𝑚 𝑡 : the number of predicted failures by time t • 𝑚𝑡 : the number of actual failures by time t

10/21



Step4. If the fitness of cuckoo’s egg is better than

host egg, replace the egg in nest k by cuckoo’s egg.


𝑎𝑘 𝑟𝑘


ith generation



𝑏𝑘

i+1th generation

𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑐𝑢𝑐𝑘𝑜𝑜′𝑠 𝑒𝑔𝑔≥ 𝑓𝑖𝑡𝑛𝑒𝑠𝑠(ℎ𝑜𝑠𝑡 𝑒𝑔𝑔)

𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑐𝑢𝑐𝑘𝑜𝑜′𝑠 𝑒𝑔𝑔< 𝑓𝑖𝑡𝑛𝑒𝑠𝑠(ℎ𝑜𝑠𝑡 𝑒𝑔𝑔)

𝑎𝑘 𝑟𝑘


11/21



Step5. If host bird notice it, the nest is abandoned

and new one is built. (p <0.25)

(to avoid local optimization)

Iterate steps 2 to 5 until termination criterion is met.

𝑛𝑒𝑤 𝑛𝑒𝑠𝑡𝑘

𝑎𝑘′′ 𝑏𝑘′′


𝑏𝑘 𝑎𝑘′ 𝑏𝑘′

12/21

New egg

Cuckoo’s egg


Experimental Set-up (1/2)

Comparison with other techniques

reference Parameter estimation techniques Data Set

A. Sheta’s [1] Particle Swarm Optimization (PSO) Data Set 1

Data Set 2

Data Set 3

L. Shanmugam et al.’s [2] Ant Colony Optimization (ACO) Musa Data 1*

Musa Data 2*

Musa Data 3* L. Shanmugam et al.’s [3] Extended Ant Colony Optimization

(Ex-ACO)

[1] A. Sheta, “Reliability Growth Modeling for Software Fault Detection Using Particle Swarm Optimization”, IEEE Congress on

Evolutionary Computation, 2006

[2] L. Shanmugam and L.A. Florence, “Comparison of Parameter Best Estimation Method for Software Reliablity Models”,

International Journal of Software Engineering & Applications (IJSEA), 2012

[3] L. Shanmugam and L. Florence, “An Improved ACO Technique for Parameter Estimation”, European Journal of Scientific

Research, 2012

* John D. Musa, Software Reliability Data, Cyber Security and Information Systems Information Analysis Center, January 1980.

Table1. Estimation techniques and data sets

13/21


Experimental Set-up (2/2) SRGMs for the experiments

Parameter settings for the cuckoo search

SRGMs Mean value function

(cumulative failure function)

Goel-Okumoto (GO) model 𝑚 𝑡 = 𝑎 1 − 𝑒−𝑟𝑡

Power (POW) model 𝑚 𝑡 = 𝑎𝑡𝑟

Yamada Delayed S-Shaped (DSS) model 𝑚 𝑡 = 𝑎 1 − (1 + 𝑟𝑡)𝑒−𝑟𝑡

Musa-Okumoto (M-O) model 𝑚 𝑡 = 𝑎𝑙𝑛(1 + 𝑟𝑡)

Parameters Value

Lower and Upper bound for parameter a [0.00001 ~ 2000]

Lower and Upper bound for parameter r [0.00001 ~ 1]

Number of Nests 10

Number of iterations(Generations) 100

Table2. SRGMs for the experiments

Table3. Parameter settings for cuckoo search 14/21


The impact of training and testing data

A balance point is training 70% and testing 30%.

Table4. The impact of training and testing

percentage

(a) data set 1, (b) data set 2, (c) data set 3

(a)

(c)

(b)

15/21


Comparison with other techniques (1/4)

PSO vs. Cuckoo Search (Data set 1)

Training 70% Testing 30%

PSO CS PSO CS

G-O 20.2565 34.0933 119.4374 16.8945

POW 22.2166 44.8663 152.9372 33.6623

DSS 15.9237 32.6376 26.3015 10.9945

Table5. Comparison with PSO using Data set 1

Figure3. Comparison with PSO using Data set 1

16/21

(A. Sheta, “Reliability Growth Modeling for Software Fault Detection Using Particle Swarm Optimization”, IEEE Congress on

Evolutionary Computation, 2006 )





PSO CS PSO CS

G-O 24.9899 33.2311 80.8963 14.2998

POW 32.355 47.0571 149.9684 56.6807

DSS 20.8325 27.9159 17.0638 11.8833



17/21





PSO CS PSO CS

G-O 12.8925 13.5404 13.6094 8.9523

POW 11.9446 13.0886 14.0524 13.4669

DSS 18.5807 13.6634 47.4036 15.1916



18/21



ACO vs. Ex-ACO vs. Cuckoo Search

Musa Data Set 1 - Training 100%

ACO EX-ACO CS

G-O 60.0371 28.5891 41.7971

POW 52.8854 34.0521 45.9783

DSS 52.8854 33.0461 42.2256

M-O 26.0385 17.359 41.7732


ACO EX-ACO CS

G-O 71.5489 34.0709 21.7256

POW 57.5801 47.5814 15.5885

DSS 57.5801 48.4914 22.4944

M-O 36.1891 24.126 19.5448


ACO EX-ACO CS

G-O 71.4015 35.0007 25.7682

POW 53.2234 34.2645 28.1951

DSS 53.2234 35.2635 25.7294

M-O 33.1728 22.1152 26.4575

Table8. Comparison with ACO and

Extended ACO

(a) musa data set 1,

(b) musa data set 2,

(c) musa data set 3

(a)

(c)

(b)

19/21

(L. Shanmugam and L.A. Florence, “Comparison of Parameter Best Estimation Method for Software Reliablity Models”, International Journal of Software

Engineering & Applications (IJSEA), 2012)

(L. Shanmugam and L. Florence, “An Improved ACO Technique for Parameter Estimation”, European Journal of Scientific Research, 2012)


Conclusion & Discussion

Conclusion

Cuckoo Search can be successfully applied to find

acceptable solutions to problem of parameter estimation

of SRGM.

Future work

Other swarm intelligent methods can be applied and

compared. Ex) Harmony Search, Firefly algorithm, Accelerated Particle Swarm

Optimization(APSO), etc..

20/21


Discussion

Cons.

New heuristic algorithm was applied to estimate the

parameters of SRGM.

The results are obtained very quickly and accurately.

Pros.

Experiments were not proper to compare cuckoo search

with other heuristics.

21/21


Q&A

Thank you


Least Square Estimation (LSE) (1/2)

Minimize the sum of square of the deviations

between actual data and expected data

Ex) parameter estimation of function 𝑓 𝑥 = 𝑎𝑥 + 𝑏

Figure 2. Basic concept of LSE

𝐸 𝑎, 𝑏 = 𝑦𝑖 − 𝑎𝑥𝑖 + 𝑏2

𝑛

𝑖=1

When 𝑑 𝐸 𝑎,𝑏

𝑑𝑎 = 0,

𝑑 𝐸 𝑎,𝑏

𝑑𝑏 = 0,

The values of a and b are the best estimates of a and

b.

a

b

E(a,b)

Optimal Point


Least Square Estimation (LSE) (2/2)

Ex) Goel-Okumoto Model

𝑚 𝑡 = 𝑎 1 − 𝑒−𝑟𝑡

𝐸 𝑎, 𝑏 = (𝑦𝑖 − 𝑎(1 − 𝑒−𝑟𝑡𝑖))2

𝑛

𝑖=1

When 𝑑 𝐸 𝑎,𝑏

𝑑𝑎 = 0,

𝑑 𝐸 𝑎,𝑏

𝑑𝑏 = 0,

The values of a and b are the best estimates of

a and b.

a b

E(a,b)


L𝑒 vy flight (1/2)

A random walk in which the step-lengths have a probability

distribution that is heavy-tailed (to avoid local optimization)

Current point

Step Size

Step Size * random()

Figure6. the basic concept of random walk (L𝑒 vy flight)

Step Size * random()

- Normal Distribution - Heavy tail distribution


L𝑒 vy flight (2/2)

Normal distribution VS. Heavy tail distribution

Figure7. an example of Brownian motion

(Normal distribution)

Figure8. an example of L𝑒 vy flight

(Heavy tail distribution)

Date post:	21-Mar-2020
Category:	Documents
Upload:	others
View:	0 times
Download:	0 times

The Use of Cuckoo Search in Estimating the Parameters of...

Documents