Estimation of fCOCOMO Model Parameters Using Optimization Techniques

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Estimation of f-COCOMO Model Parameters Using
Optimization Techniques

• University of Alabama at Birmingham
• Birmingham, Alabama, USA
• Leonard J. Jowers
• Dr. James J. Buckley
• Dr. Kevin D. Reilly

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Introduction

• This presentation is concerned with promoting use
  of optimization methods to estimate COCOMO model
  parameters.
• We briefly describe fuzzy COCOMO, showing how
  fuzzy arithmetic is applied to the model.
• We describe the issue which may be addressed
  using this technique.
• We provide an example and note future work.

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University of Alabama at Birmingham
Department of Computer and Information Sciences
LEONARD J. JOWERS Bachelor of Sciences, 1969,
University of Alabama. Master of Arts, 1972,
University of Alabama. PhD candidate, University
of Alabama at Birmingham.
2003-pres. Doctorial student. UAB
2002-pres. President. AuditSoft, Inc.
Birmingham, Alabama, USA. 2001-2002 Executive
Vice-President. Imaging Business Machines,
LLC. 1982-2001 President. Computer Utilization
Services Corporation. 1974-1982 VP of
Operations. AOM Corporation, Birmingham, Alabama,
USA. 1972-1974 Unit Supervisor systems analyst,
LTV Aerospace, Langley AFB, Virginia, USA.
1970-1972 Head of Software Department systems
analyst, Applied Computer Data Services,
Tuscaloosa, AL 1967-1970 Programmer, UNIVAC,
Bluebell, Pennsylvania, USA. 1965-1968 Student
programmer, University Of Alabama Computing
Center, Tuscaloosa, Alabama, USA Publications on
simulating fuzzy systems, numerical computing.
Latest book Simulating Continuous Fuzzy Systems
(Springer), jointly with Dr. Buckley.
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University of Alabama at Birmingham
Department of Computer and Information Sciences
Department of Mathematics
KEVIN D. REILLY, Ph.D. Math Biol. (Th. Biol.
Biophy.) U. of Chicago in 1966.
JAMES J. BUCKLEY, Ph.D. Mathematics Georgia Tech
in 1970
1966-1970 Information Scientist,
Institute of Library Research,
UCLA 1968-1970 Lecturer, Computer Science,
School of Engineering,
UCLA 1969-1970 Senior Lecturer, School of
Business, University of Southern
California 1970-Pres. Professorial staff,
Computer Information Sciences, UAB Numerous
publications on simulating fuzzy systems.
1970-1976 Mathematics Department at University
of South Carolina. 1976-pres. Mathematics
Department at U. of Alabama at
Birmingham. Numerous publications in fuzzy
sets/fuzzy logic and 9 books.
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Origins of Fuzzy Logic

• Lotfi Zadeh founded fuzzy logic in 1965.
• A basic principle of fuzzy logic is, Everything
  is a matter of degree.
• Whereas Boolean logic postulates the concept of
  truth as a function from a linguistic expression
  onto the set 0, 1, fuzzy logic postulates the
  concept of truth as a function from a linguistic
  expression onto the interval 0,1.

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Fuzzy Numbers
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Fuzzy Arithmetic
Using a-cuts, create membership functions for C
A B CacL,cR aL,aR bL,bR aLbL,
aRbR. C A - B CacL,cR aL,aR -
bL,bR aL-bR, aR-bL. C A B CacL,cR
aL,aR bL,bR bL, bR. Where bL
minaL bL, aL bR, aR bL, aR bR. bR
maxaL bL, aL bR, aR bL, aR bR. and if 0 is
not in the support of B, C A / B CacL,cR
aL,aR/bL,bR aL, aR (1/bR),(1/bL.
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f-COnstructive COst MOdel

• Start with classical COCOMO.
• Making one or more parameters into a fuzzy
  variable causes the result to be a fuzzy
  variable.
• Use definitions and tables for COCOMO, but allow
  specific uncertainty in one or more parameters.

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Motivation

• At the start of a project, some schedule and
  budget requirements are known.
• Values for f-COCOMO project parameters may be
  generated from expert experience or data.
• However, project resources and methods may not be
  fixed.
• One or more fuzzy parameters may be optimized to
  meet the schedule or budget.
• By improving the estimation of parameters,
  management may make adjustments to improve the
  project.

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Optimization to Solve Inverse Problems

• An inverse problem is one for which an answer is
  known but the question is not.
• Such problems are sometimes difficult to solve by
  analytical methods.
• Optimization techniques such as Monte Carlo
  methods or Genetic Algorithms are available for
  such problems.

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Method a Simple Example

• Consider a Nominal project of Size 5K for which
  a budget of 16 PM has been decreed (but
  PM17.26!).
• PM A x SizeE lt 16.
• EB0.01 x SSFj
• Allow a couple of Scale Factors more freedom.
• TEAM nominal to Very High
• PMAT nominal to Very High
• Use Fuzzy Monte Carlo to optimize TEAM and PMAT
  for
• ln(PM) ln(A x SizeE)lt ln(16).
• ln(PM) 0.0161 x TEAM 0.0161 x PMAT lt 0.0526.

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Method a Simple Example (Contd.)

• It is determined that it is possible to meet the
  decreed budget by raising TEAM and PMAT (lowering
  their nominal values) to less than Very High.
• TEAM 1.43/1.51/2.62
• PMAT 1.62/1.76/2.99
• Also
• Other constraints may be put into the
  optimization such as, limits on costs of
  improving a Scale Factor.
• Effort Multipliers can be handled as fuzzy
  variables also.
• With specification of a defuzzification of
  compounded results, additional understanding may
  be possible.

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Summary

• Starting with crisp COCOMO, one may represent
  linguistic parameters as fuzzy variables to
  create a fuzzy COCOMO.
• Fuzzy arithmetic is such that operational using
  fuzzy variables tends to increase fuzziness in
  results.
• Using decreed limitations on person-months, one
  may use optimization techniques to determine
  fuzzy values for parameters.

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Future Work

• Computer sources will be available on request
  from jowersl_at_cis.uab.edu after publication of
  Monte Carlo Studies with Fuzzy Random Numbers, to
  appear Sringer-Verlag, 2007.
• On-going research into extending this method to
  multi-objective f-COCOMO.

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Major References
Barry W. Boehm, Chris Abts, A. Windsor Brown,
Sunita Chulani, Bradford K. Clark, Ellis
Horowitz, Ray Madachy, Donald Reifer, and Bert
Steece, Software Cost Estimation with COCOMO II,
Prentice Hall PTR, Upper Saddle River, NJ,
2000. J.J. Buckley and L.J. Jowers, Simulating
continuous fuzzy systems, Springer-Verlag,
Heidelberg, Germany, 2005. George J. Klir and Bo
Yuan, Fuzzy sets and fuzzy logic Theory and
applications, Prentice-Hall, Inc., Upper Saddle
River, NJ, USA, 1995. Petr Musilek, Witold
Pedrycz, Giancarlo Succi, and Marek Reformat,
Software cost estimation with fuzzy models,
SIGAPP Appl. Comput. Rev. 8 (2000), no. 2,
24-29. L. Zadeh, Fuzzy sets, Inf. Control 8
(1965), 338-353. Lotfi A. Zadeh, Computing with
Words and Its Application to Information
Processing, Decision and Control, The 2003 IEEE
International Conference on Information Reuseand
Integration (2003), Keynote speech. Toward a
Generalized Theory of Uncertainty (GTU)An
Outline, January 20, 2005, To appear in
Information Sciences, http//www.bisc.cs.berkeley.
edu/BISCSE2005/Zadeh2005.pdf.
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Questions?