andrew cannon yuki osada angeline honggowarsito€¦ · knapsack, trading prediction in stock...
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Andrew CannonYuki Osada
Angeline Honggowarsito
ContentsWhat are Evolutionary Algorithms (EAs)?Why are EAs Important?Categories of EAsMutationSelf AdaptationRecombinationSelectionApplication
Evolutionary AlgorithmsSearch methods that mimic the process of natural
evolution
Principle of “Survival of the Fittest”
In each generation, select the fittest parents
Re‐combine those parents to produce new
offspring
Perform mutations on the new offspring
Why are EAs Important?Flexibility
Adaptable Concept to Problems
Problem examples: Travelling Salesman,
Knapsack, Trading Prediction in Stock Market,
etc.
Algorithms to solve those problems are either too
specialised or too generalised
Categories of EAsGenetic Algorithms
Evolutionary Strategies
Evolutionary Programming
Genetic Programming
More similarities than differences
Genetic AlgorithmsIn 1950s, Biologists used computers for biological
system simulation.
First introduced in 1960s by John Holland from the
University of Michigan
Modeling Adaptive Process
Designed to solve discrete/integer optimization
problem
Genetic AlgorithmsOperate on Binary Strings, binary as the
representation of individuals
Applying recombination operator with mutation as
background operator
Evolutionary StrategiesFirst developed by Rechenberg in 1973
Solved parameter optimization problems
Individuals represented as a pair of float‐valued vectors
Apply both recombination and self adaptive mutation
Evolutionary StrategiesSimilar to Genetic Algorithms in recombination and mutation processesDifferences with Genetic Algorithms
Evolutionary Strategies are better at finding local maximum while Genetic Algorithms are more suitable at finding global maximumThus, Evolutionary Strategies are faster than Genetic AlgorithmsEvolutionary Strategies are represented as real number vector while GAs are represented using bitstrings
Evolutionary ProgrammingDeveloped by Lawrence Fogel in 1962
Aimed at evolution of Artificial Intelligence in
developing ability to predict changes in
environment
Use Finite State Machine for prediction
Evolutionary ProgrammingPredict output of 011101 with
initial state C, produce
output of 110111
No recombination
Representation based on real‐
valued vectors
1/1
0/0
0/c
0/1
1/1
1/0
A
B
C
Genetic ProgrammingDeveloped by Koza to allow the program to
evolve by itself during the evolution process
Individuals are represented by Tree or Graphs
Genetic ProgrammingDifferent from GA,ES,EP where representation
is linear (bit strings and real value vectors),
Tree is non‐linear
Size depend on Depth and Width, while other
representations have a fixed size
Only requires crossover OR mutation
MutationBinary Mutation:
Flipping the bits, as there are only two states of
binary values : 0 and 1
Mutating (0,1,0,0,1) will produce (1,0,1,0,1)
MutationReal Value Mutation:
Randomly created value added to the variables
with some predefined mutation rate
Mutation rate and Mutation step need to be
defined
Mutation rate is inversely proportional to the
number of variables (dimensions)
Sources & ReferencesEiben A.E 2004, “What is Evolutionary Algorithm”, Available from: <http://www.cs.vu.nl/~gusz/ecbook/Eiben‐Smith‐Intro2EC‐Ch2.pdf>.[29 August 2012 ].Michalewicz, Z., Hinterding, R., and Michalewicz, M., Evolutionary Algorithms, Chapter 2 in Fuzzy Evolutionary Computation, W. Pedrycz (editor), Kluwer Academic, 1997. T. Bäck, U. Hammel, and H.‐P. Schwefel, “Evolutionary computation: comments on the history and current state”, IEEE Transactions on Evolutionary Computation 1(1), 1997X. Yao, “Evolutionary computation: a gentle introduction”, Evolutionary Optimization, 2002Whitley, D 2001, “An Overview of Evolutionary Algorithm: Practical Issues and Common Pitfalls”, Information and Software Technology, vol.43, pp. 817‐831
Self AdaptationDon’t know what values to assign to parameters – so let them evolve!Population consisting of real vectors x = (x1,x2,…,xn)We produce offspring by adding random vectors to them
Step SizeSchwefel (1981): add vectors whose components are Gaussian random variates with mean 0What standard deviation should be used?The standard deviation evolves as the algorithm is running
Step SizeRepresent entities as (x,s) – the individual itself (x) and a step vector (s)We start by producing an offspring s’ from s:
si’ = si exp(cn‐1/2N(0,1) + dn‐1/4Ni(0,1))n = generation number, c,d>0 constants
We produce an offspring x’ from x:xi’ = xi + si’Ni(0,1)
Self AdaptationOther parameters can evolve using similar ideasSources:Bäck T, Hammel, U & Schwefel, H‐P 1997, ‘Evolutionary computation: comments on the history and current state’, IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 3‐17. Available from: IEEE Xplore Digital Library [23rd August 2012].
Beyer, HG 1995, ‘Toward a Theory of Evolution Strategies: Self‐Adaptation’, Evolutionary Computation, vol. 3, no. 3, pp. 311‐348.
Saravanan, N, Fogel, DB & Nelson, KM 1995, ‘A comparison of methods for self‐adaptation in evolutionary algorithms’, BioSystems, vol. 36, no. 2, pp. 157‐166. Available from: Science Direct [26th August 2012].
Schwefel, H‐P 1981, Numerical Optimization of Computer Models, Wiley, Chichester.
RecombinationProduce offspring from 2 or more entities in the original populationMost easily addressed using bitstring representations
One Point CrossoverEntities are represented in the population as bitstrings of length nRandomly select a crossover point p from 1 to n(inclusive) Take the substring formed by the first p bits of the first string and append to it the last n‐p bits of the second string to give offspring
One Point CrossoverBitstrings of length 8:01011100 and 00001111Choose crossover point of 6Take the first 6 bits from 01011100Take the last 2 bits from 00001111Form the offspring 01011111
Uniform CrossoverForm a new offspring from 2 parents by selecting bits from each parent with a particular probabilityFor example, given strings: 11001011 and 01010101Select bits from the first string with probability ½
Uniform CrossoverRolled a die 8 times: 2, 3, 6, 6, 3, 1, 3, 5Whenever the result is 3 or less, take a bit from the first string, otherwise, take a bit from the second string:23663135 2366313511001011 and 01010101Produce offspring: 11011011
Other VariantsMultiple crossover pointsMultiple parentsProbabilistic application
Source:Bäck T, Hammel, U & Schwefel, H‐P 1997, ‘Evolutionary computation: comments on the history and current state’, IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 3‐17. Available from: IEEE Xplore Digital Library [23rd August 2012].
SelectionHow individuals and their offspring from one generation are selected to fill the next generationMay be probabilistic or deterministic
Proportional SelectionProbabilistic methodAssume that fitness f(x)>0 for every entity x in the populationp(y) = f(y) / (sum of f(x) for every x)
Tournament SelectionProbabilistic methodSelect q individuals randomly from the population with uniform probabilityThe best individual of this set goes into the next generationRepeat until the next generation is filled
(μ,λ)‐SelectionDeterministic methodFrom a generation of μ individuals, λ>μ offspring are producedThe next generation is produced from the μ fittest individuals of the λ offspringThe fittest member of the next generation may not be as fit as the fittest member of the previous generation
(μ+λ)‐SelectionDeterministic methodFrom a generation of μ individuals, λ offspring are producedThe next generation is produced from the μ fittest individuals from the μ+λ parents and offspringThe fittest members will always survive
SelectionBest method (or methods) will be problem specificSources:Bäck T 1994, ‘Selective pressure in evolutionary algorithms: a characterization of selection mechanisms’, Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 57‐62. Available from: IEEE Xplore Digital Library [28th August 2012].
Bäck T, Hammel, U & Schwefel, H‐P 1997, ‘Evolutionary computation: comments on the history and current state’, IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, pp. 3‐17. Available from: IEEE Xplore Digital Library [23rd August 2012].
Travelling Salesman Problem (TSP)Travelling salesman problem:This is a hard problem (NP‐hard, "at least as hard as the hardest problems in NP")The DP solution is O(n2.2n)Genes are a sequence representing the order that the cities are visited inExample: [0 5 3 4 8 2 1 6 7 9]
Crossover in TSPA possible crossover: The greedy crossover.
"Greedy crossover selects the first city of one parent, compares the cities leaving that city in both parents, and chooses the closer one to extend the tour. If one city has already appeared in the tour, we choose the other city. If both cities have already appeared, we randomly select a non‐selected city."
Sources:J. J. Grefenstetts, R. Gopal, B. Rosmaita, and D. Van Gucht. Genetic Algorithms for the Traveling Salesman problem. In Proceedings of an International Conference on Genetic Algorithms and Their Applications, pages 160–168, 1985.
Mutation in TSPA possible mutation: The greedy‐swap.
"The basic idea of greedy‐swap is to randomly select two cities from one chromosome and swap them if the new (swapped) tour length is shorter than the old one"Sources:S. J. Louis, R. Tang. Interactive Genetic Algorithms for the Travelling Salesman Problem. Genetic Adaptive Systems Lab, University of Neveda, Reno. 1999.
ApplicationsEAs are a very powerful computational toolEAs find application in:
bioinformaticsphylogeneticscomputational scienceengineeringeconomicschemistrymanufacturingmathematicsphysics and other fields
ApplicationsComputer‐automated design
Automotive designDesign composite materials and aerodynamic shapes to provide faster, lighter, more fuel efficient and safer vehiclesNo need to spend time in labs working with models
Engineering designOptimise the design of many tools/components ie. turbines
ApplicationsGame playing
Sequence of actions can be learnt to win a gameEncryption and code breakingTelecommunicationsDP problems:
Travelling salesman problemPlan for efficient routes and scheduling for travel planners.
Knapsack problem
SourcesT. Bäck, U. Hammel, and H.‐P. Schwefel, “Evolutionary computation: comments on the history and current state”, IEEE Transactions on Evolutionary Computation 1(1), 1997X. Yao, “Evolutionary computation: a gentle introduction”, Evolutionary Optimization, 2002