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Evolution of Evolutionary Computation

Evolution of Evolutionary Computation. Xin Yao CERCIA and Natural Computation Group School of Computer Science The University of Birmingham, UK http://www.cercia.ac.uk. What Is CERCIA. The C entre of E xcellence for R esearch in C omputational I ntelligence and A pplications

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Evolution of Evolutionary Computation

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  1. Evolution of Evolutionary Computation Xin Yao CERCIA and Natural Computation Group School of Computer Science The University of Birmingham, UK http://www.cercia.ac.uk

  2. What Is CERCIA The Centre of Excellence for Research in Computational Intelligence and Applications • Focuses on applicationsof Nature Inspired Computation to real-worldbusiness problems • Knowledge transfer centre in the School of Computer Science, University of Birmingham • Established January, 2003 to bring cutting-edge technology to industry and businesses

  3. The Birmingham Triangle Applied Research and Knowledge Transfer: CERCIA Basic Research: Natural Computation Group Training and Teaching: MSc in Natural Computation

  4. Outline of My Talk • Evolutionary Optimisation • Evolutionary Learning • Theoretical Foundations • Other Applications • Concluding Remarks

  5. Evolutionary Optimisation • Numerical optimisation • Fast evolutionary algorithms • Hybrid local search and evolutionary algorithms • Constraint handling --- stochastic ranking • Combinatorial optimisation • Simulated annealing • Genetic annealing • Hybrid algorithms

  6. Fast Evolutionary Algorithms • Fast evolutionary programming (FEP), improved FEP (IFEP), and Levy EP (LEP) for unconstrained optimisation • Based on self-adaptive mixture of Gaussian, Cauchy and Levy mutation operators • Both analytical and experimental studies have shown their excellent performance on a wide range of benchmark functions. • X. Yao, Y. Liu and G. Lin, “Evolutionary programming made faster,” IEEE Transactions on Evolutionary Computation, 3(2):82-102, July 1999. • C. Y. Lee and X. Yao, “Evolutionary programming using the mutations based on the Levy probability distribution,” IEEE Transactions on Evolutionary Computation, 8(1):1-13, January 2004.

  7. Benchmark functions are fine for testing ideas and publishing papers. What about real applications?

  8. Discovering New Physical `Laws’ in Astrophysics --- Modelling Radial Brightness Distributions in Elliptical Galaxies • Empirical laws are widely used in astrophysics. • However, as the observational data increase, some of these laws do not seem to describe the data well. • Can EC evolve/discover new empirical laws that describe the data better?

  9. Galaxies • The galaxy is the basic building block of the universe • How galaxies form and evolve is not well understood • The study of the appearance of a galaxy might help answer the question (morphological classification) • One of the exercises in astronomy is to obtain a radial brightness profile of the galaxy • Two galaxy types: ellipticals and spirals

  10. Monochromatic (Negative) Images of Galaxies disk bulge A typical elliptical galaxy A typical spiral galaxy

  11. c2 = Current Approach • Pick a functional form in advance Drawbacks: ad hoc, difficult to determine and may only suit a smaller number of profiles • Apply fitting algorithms to find suitable parameters for the function. Usually adopt the non-linear reduced c2 minimization Drawbacks: difficult to set initial values and easily trapped in local minima where Iobs(i) is the individual observed profile value, Imodel(i) is the value calculated from the fitting function, u is the number of degrees of freedom, and d is the standard deviation of the data.

  12. Our Evolutionary Approach (1) Finding functional forms using GP : • A data-driven process without assuming a functional form in advance • A bottom up process which suits modelling a large number of galaxy profiles without any prior knowledge of them (2) Fitting parameters in the form found using FEP: • Not sensitive to initial setting values • More likely to find global minima J. Li, X. Yao, C. Frayn, H. G. Khosroshahi, S. Raychaudhury, ``An Evolutionary Approach to Modeling Radial Brightness Distributions in Elliptical Galaxies,'' Proc. of the 8th International Conference on Parallel Problem Solving from Nature (PPSN VIII), Lecture Notes in Computer Science, Vol. 3242, pp.591-601, Springer, September 2004.

  13. Well … It is debatable whether this is a real application. It is still in the scientific research domain, isn’t it? …

  14. Determining Unified Creep Damage Constitutive Equations in Aluminium Alloy Modelling • Creep bahaviours of different materials are often described by physically based unified creep damage constitutive equations. • Such equations are extremely complex. • They often contain undecided constants (parameters). • Traditional approaches are unable to find good near optima for the parameters. • EAs have been shown to be more effective.

  15. Example Equations

  16. Difficulties for Traditional Optimisation Algorithms • Large areas of approximate plateaus • Huge variation of gradients among different parameters, from 5.69E-6 to 8.23E15. • The objective functions have narrow ridges, somewhat similar to the Rosenbrock function. • Traditional methods often find a solution which is the same as the starting point!

  17. Evolutionary Parameter Calibration and Optimisation • Classical evolutionary programming (CEP), fast EP (FEP) and improved fast EP (IFEP) can be used to find parameters in a complex and non-differentiable space. B. Li, J. Lin and X. Yao, “A novel evolutionary algorithm for determining unified creep damage constitutive equations,” International Journal of Mechanical Sciences,44 (2002) 987–1002.

  18. Experimental Results

  19. Model with Evolved Parameters by IFEP

  20. IFEP Worked Well • Evolutionary algorithms can find near optimal parameter values for the constitutive equations. • Evolutionary algorithms can deal with complex and hard-to-differentiate functions. • Evolutionary algorithms can be used to discover models and optimise their parameters.

  21. But … • My problem has lots of constraints. • Existing constraint handling algorithms look very complicated. • Any simple yet effective method?

  22. Stochastic Ranking for Constraint Handling • Replace the selection method in an EA by stochastic ranking, you will get a constrained optimisation algorithm! • Stochastic ranking is very simple to implement. It’s basically a stochastic bubble sort algorithm. • It’s very effective. • T. P. Runarsson and X. Yao, “Stochastic Ranking for Constrained Evolutionary Optimization,” IEEE Transactions on Evolutionary Computation, 4(3):284-294, September 2000. • T. Runarsson and X. Yao, ``Search Bias in Constrained Evolutionary Optimization,'' IEEE Transactions on Systems, Man, and Cybernetics, Part C, 35(2):233-243, May 2005.

  23. I wish … The world is simple, but my problem is really difficult, complicated, complex, … Everything I’ve tried so far has failed. … If only I have simple problems all the time!

  24. Wish Granted, at Least Partially • How about making a difficult problem simpler before solving it? • Landscape approximation using a quadratic function • Local search + EAs • K.-H. Liang, X. Yao and C. Newton, “Evolutionary search of approximated N-dimensional landscapes,” International Journal of Knowledge-Based Intelligent Engineering Systems, 4(3):172-183, July 2000.

  25. All Sound Very Interesting, … • But I’m dealing with combinatorial optimisation problems, not numerical ones. …

  26. Similar Ideas Can Be Applied to CO • EP algorithm for cutting stock problems, where knowledge-based mutation operators were used • K.-H. Liang, X. Yao, C. S. Newton and D. Hoffman, ``A New Evolutionary Approach to Cutting Stock Problems With and Without Contiguity,'' Computers and Operations Research, 29(12):1641-1659, Oct. 2002. • Materialised view selection in data warehousing using a discrete variant of stochastic ranking for constraint handling • C. Zhang, X. Yao and J. Yang, ``An Evolutionary Approach to Materialized Views Selection in a Data Warehouse Environment,'' IEEE Transactions on Systems, Man and Cybernetics, Part C, 31(3):282-294, August 2001. • J. X. Yu, X. Yao, C.-H. Choi, and G. Gou, ``Materialized view selection as constrained evolutionary optimization,'' IEEE Transactions on Systems, Man and Cybernetics, Part C, 33(4):458-467, November 2003.

  27. Real World Applications?Gritting Truck Route Optimisation • H. Handa, L. Chapman and X. Yao, ``Dynamic Salting Route Optimisation using Evolutionary Computation,'' Proc. of the 2005 Congress on Evolutionary Computation (CEC'05), Vol.~1, 2-5 September 2005, IEEE Press, Piscataway, NJ, USA, pp.158-165. South Gloucestershire Road Network

  28. OK, OK, … • You’ve made your points: there are novel EAs that are very good. • But all your results are experimental. There are no theories behind them … • Are you sure you know what you are talking?

  29. Hmmm …. Maybe a Small Clue? • While this might be true a few years ago, it is less so now. • Not only can we prove convergence of EAs, we can now analyse EA’s computation time (scalability) for a given class of combinatorial problems. • J. He and X. Yao, ``Time Complexity Analysis of an Evolutionary Algorithm for Finding Nearly Maximum Cardinality Matching,'' Journal of Computer Science and Technology, 19(4):450-458, July 2004. • J. He and X. Yao, ``From an Individual to a Population: An Analysis of the First Hitting Time of Population-Based Evolutionary Algorithms,'' IEEE Transactions on Evolutionary Computation, 6(5):495-511, October 2002. • J. He and X. Yao, ``Drift Analysis and Average Time Complexity of Evolutionary Algorithms,'' Artificial Intelligence, 127(1):57-85, March 2001.

  30. Some Theoretical Results • We can show the necessary and sufficient conditions, under which an EA will need no more than a polynomial time (or no less than an exponential time) to find a global optimum for a given problem class • The particular analytical tool we used is: drift analysis • J. He and X. Yao, ``A study of drift analysis for estimating computation time of evolutionary algorithms,'' Natural Computing, 3(1):21-35, January 2004. • J. He and X. Yao, ``Towards an analytic framework for analysing the computation time of evolutionary algorithms,'' Artificial Intelligence, 145(1-2):59-97, April 2003.

  31. EA-Hard Problems • There are two and only two types of EA-hard problems: • The “wide-gap” problems; and • The “long-path” problems.

  32. Wait a Minute! Optimisation is important, but I’m more interested in learning! Learning, adaptation, autonomy, … These are trendy words that attract attentions (e.g., funding).

  33. Evolutionary Learning • Evolving neural network ensembles • Negative correlation learning • Artificial speciation and niching • Multi-objective approaches • Co-evolution • Iterated prisoner’s dilemma games • Co-evolving neural networks

  34. Evolutionary Learning in a Picture

  35. Fitness Evaluation

  36. Learning is Different From Optimisation • In optimisation, the fitness function reflects what is needed. The optimal value is always better than the second optimal one. • In learning, it is hard to quantify generalisation exactly in practice. Why select the “best” individual in a population as the final output? • X. Yao, Y. Liu and P. Darwen, ``How to make best use of evolutionary learning,'' Complexity International: An Electronic Journal of Complex Systems Research (ISSN 1320-0682), Vol. 3, July 1996.

  37. Use Populations! Instead of selecting the best individual as the evolved solution, more (or even all) individuals should be selected and combined to form the final solution

  38. The Simplest Approach • Do nothing during the evolution • Then combine all the individuals from the last generation • X. Yao and Y. Liu, “Making use of population information in evolutionary artificial neural networks,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, 28(3):417-425, June 1998.

  39. Speciation by Fitness Sharing or Negative Correlation • Introduce diversity generation and maintenance methods, such as fitness sharing or negative correlation, during evolution (or gradient descent training) • The aim is to form a population of diverse specialists (species) automatically • Md. Monirul Islam, X. Yao and K. Murase, “A constructive algorithm for training cooperative neural network ensembles,” IEEE Transactions on Neural Networks, 14(4):820-834, July 2003. • Y. Liu, X. Yao and T. Higuchi, “Evolutionary Ensembles with Negative Correlation Learning,” IEEE Trans. on Evolutionary Computation, 4(4):380-387, 2000. • P. J. Darwen and X. Yao, ``Speciation as automatic categorical modularization,'' IEEE Transactions on Evolutionary Computation, 1(2):101-108, 1997.

  40. Multi-objective Approaches • Two-objective evolutionary learning : • Accuracy: minimising quadratic/mean square error; • Diversity: minimising mutual information — the negative correlation penalty term. • A. Chandra and X. Yao, “Ensemble learning using multi-objective evolutionary algorithms,” Accepted by Journal of Mathematical Modelling and Algorithms, May 2005. • A. Chandra and X. Yao, “DIVACE: Diverse and Accurate Ensemble Learning Algorithm,” Proc. of the Fifth International Conference on Intelligent Data Engineering and Automated Learning (IDEAL’04), Lecture Notes in Computer Science, Springer, Vol. 3177, pp.619-625, August 2004.

  41. Co-evolutionary Learning of Iterated Prisoner’s Dilemma (IPD) Game Strategies • IPD with more than 2 players • IPD with more than two choices • IPD with reputation • IPD with mistakes/noises • Representations and genotype-phenotype mapping

  42. N-player IPD Games

  43. Group Size

  44. Multiple Choices

  45. More Choices Discourage Cooperation

  46. Reputation Helps

  47. Noises/Mistakes • Low noise may promote cooperation • While high noise discourages cooperation

  48. Other Applications • Evolutionary computation has “invaded” into many other domains: • Search-based software engineering (SBSE) • Games and entertainment in general • Creative design • EPSRC (EP/C514297/1). Nature Inspired Creative Design. • http://www.nature-inspired.org/ • More information: www.cercia.ac.uk

  49. Concluding Remarks • Evolutionary computation (EC) is evolving in four major areas: optimisation, learning, design and theory. • EC is much richer more than any single algorithms. Never think EC is just a genetic algorithm. • EC is a problem solving approach as well as a discovery engine. • This talk has only scratched the surface of EC.

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