Differential evolution

1
Differential evolution

• Martti Kylmälä 0086379
• Santosh Kumar Kalwar 0331927
• Lappeenranta University of Technology
• 28-Jan-2008, Evolutionary Algorithms

2
Overview

• Introduction
• History
• Control parameters
• Selection scheme
• Schemes
• Handling integer valued variables
• Constraints
• How DE is used in our project
• Applications

3
Introduction

• Differential evolution (DE) is a mathematical
  global optimization method for solving
  multidimensional functions.
• Main idea is to generate trial parameter vectors.
• Kenneth Price and Rainer Storn first introduced
  this algorithm,1994
• Using vector differences for perturbing the
  vector population

4
History

• Genetic Annealing was the beginning of DE
  algorithms.
• Kenneth Price was interested in solving the
  Tchebychev polynomial fitting problem by Genetic
  Annealing
• Price modified the algorithm using floating-point
  instead of bit-string encoding and arithmetic
  vector operations instead of logical ones.
• The differential mutation procedure was
  discovered.

5
History

• Differential mutation discrete recombination
  pair-wise selection remove the need for an
  annealing factor
• Era of Differential Evolution algorithms evolved.
• "Differential Evolution -- a simple and efficient
  adaptive scheme for global optimization over
  continuous spaces, 1995

6
(No Transcript)
7
Control parameters

• F and CR are DE control parameters
• F is a real-valued factor in the range (0.0,1.0
• Upper limit on F has been empirically determined.
• CR is a real-valued crossover factor in range
  0.0,1.0
• CR controls the probability that a trial vector
  parameter will come from the randomly chosen
  noise vector

8
Control parameters

• Optimal values are dependent both on objective
  function characteristics and on the population
  size, NP
• Practical advice on how to select control
  parameters NP, F and CR can be found in the
  literature

9
Selection Scheme

• DEs selection scheme also differs from other
  evolutionary algorithms
• Current population is PG --population for the
  next generation, PG1, is selected from the child
  population based on objective function value

10
Selection Scheme

• Each individual of the temporary population is
  compared with its counterpart in the current
  population
• Trial vector is only compared to one individual,
  not to all the individuals in the current
  population.

11
Schemes of DE

• Several different schemes of DE exist
• Differences in target vector selection and
  difference vector creation

12
Handling Integer Valued Variables

• DE is only capable of handling continuous
  variables
• Very easy, simple modification needed.
• Integer values should be used to evaluate the
  objective function

13
Handling Integer Value Variables

• INT() function is used.
• Converting a real value to an integer value is
  done by rounding it downwards
• Only for purposes of evaluating trial vectors And
  handling boundary constraints

14
Handling Integer Value Variables

• Evaluate objective function value with rounded
  value in case of integer valued variable

15
Handling constraints

• Boundary Constraints---ensure that parameter
  values lie inside their allowed ranges after
  reproduction.
• Constraint Functions--penalty function methods
  have been applied with DE for handling constraint
  functions

16
How DE is used in Our Project ?

• Optimization of computer players performance in
  Slicks 'n Slide game.
• Scheme used is DE/rand/1
• Integer Valued Variables used.
• Control Parameters F0.9, CR0.9, NP10 and D12
• Where D is number of computer guidance points.
• Using DE algorithm, Tracks are modified.
• We assume that the game runs identical tracks in
  identical time. Randomization might cause minor
  problems.

17
Slicks n Slide
18
Application of DE

• Multiprocessor synthesis
• Power minimisation
• Neural network learning.
• Crystallographic characterization
• Synthesis of modulators
• Heat transfer parameter estimation in a trickle
  bed reactor

19
Application of DE

• Optimal Design of Shell-and-Tube Heat Exchangers
• Optimization of Thermal Cracker Operation
• Optimization of Non-Linear Chemical Processes
• Optimization of Water Pumping System
• Radio Network Design
• Etc

20
Conclusion

• Powerful algorithm- multidimensional functions
• Easy applicable to various problems.
• Widely used.
• Materials available

21
References

• Lampinen, J. and Zelinka, I. (2000). On
  Stagnation of the Differential Evolution
  Algorithm.In Omera, P. (ed.) (2000).
  Proceedings of MENDEL 2000, 6th Int. Conf. On
  Soft Computing, June 7.9. 2000, Brno University
  of Technology, Brno, Czech Republic,pp. 7683.
  ISBN 80-214-1609-2. Available via
  Internethttp//www.lut.fi/jlampine/MEND2000.ps
  .
• Price, K.V. (1999). An Introduction to
  Differential Evolution. In Corne, D., Dorigo,M.
  and Glover, F. (eds.) (1999). New Ideas in
  Optimization, pp. 79108. McGraw-Hill, London.
  ISBN 007-709506-5.
• Storn, R. and Price, K.V. (1995). Differential
  evolution - a Simple and Efficient Adaptive
  Scheme for Global Optimization Over Continuous
  paces. Technical Report TR-95-012, ICSI, March
  1995. Available via Internet ftp//ftp.icsi.berke
  ley.edu/pub/techreports/1995/tr-95-012.ps.Z .
• Storn, R. and Price, K.V. (1997). Differential
  Evolution a Simple and Efficient Heuristic for
  Global Optimization over Continuous Spaces.
  Journal of Global Optimization,11(4)341359,
  December 1997. Kluwer Academic Publishers.
• (C) Slick n Slide Version 1.29, Timo Kauppinen
  5/1995
• http//www.it.lut.fi/kurssit/05-06/Ti5216300/sourc
  es.html cited on 25th January, 2008Availaible
  Online
• Lampinen, J. ,Multi-Constrained Nonlinear
  Optimization by the Differential Evolution
  Algorithm,

22
Questions ???
23
Thank you !