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 Centre of Excellence for Research in Computational Intelligence and Applications

• Focuses on applications of Nature Inspired Computation to real-world business 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

The Birmingham Triangle

Basic Research:

Natural Computation Group

Training and Teaching:

MSc in Natural Computation

Applied Research and Knowledge Transfer:

CERCIA

Outline of My Talk

Evolutionary Optimisation

Theoretical Foundations

Evolutionary Learning

Other Applications

Concluding Remarks

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

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.

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

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?

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

Monochromatic (Negative) Images of Galaxies

A typical elliptical galaxy A typical spiral galaxy

bulge disk

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

i

obsm iIiI2

2

odel )]()([1

2 =

where Iobs(i) is the individual observed profile value, Imodel(i) is the value calculated from the

fitting function, is the number of degrees of freedom, and is the standard deviation of the data.

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.

Well …

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

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.

Example Equations

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!

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.

Experimental Results

Model with Evolved Parameters by IFEP

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.

But …

My problem has lots of constraints. Existing constraint handling

algorithms look very complicated. Any simple yet effective method?

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.

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!

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.

All Sound Very Interesting, …

But I’m dealing with combinatorial optimisation problems, not numerical ones. …

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.

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

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?

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.

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.

EA-Hard Problems

There are two and only two types of EA-hard problems:

1. The “wide-gap” problems; and 2. The “long-path” problems.

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).

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

Evolutionary Learning in a Picture

Fitness Evaluation

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.

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

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.

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.

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.

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

N-player IPD Games

Group Size

Multiple Choices

More Choices Discourage Cooperation

Reputation Helps

Noises/Mistakes

Low noise may promote cooperation While high noise discourages cooperation

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

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.