Genetic Algorithms (GAs)

1. Genetic Algorithms (GAs) • Genetic Algorithms - Adaptive search and optimisation techniques based on the principles of nature evolution • Holland, 1975 - GAs as an attempt to explain algorithmically diversity of species and individuals - members of species - in the nature. • model of evolution processes where the basic operations are natural selection, crossover and mutation, • Schema Theorem - analysis of reproduction model • GAs are popular for their simplicity, effectiveness and robustness. • Applications: control, design, scheduling, resource allocation, image processing as well as in finance, medicine and political sciences. J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

2. Principal characteristics of GAs • GAs work with a coding of the parameter set not the task parameters themselves • GAs work with a population of individuals - built-in parallelism • GAs need to know only a prescription for evaluation of individuals • GAs use probabilistic transition rules J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

3. Standard Genetic Algorithm Begin t=0 Initialize P(t) Evaluate P(t) while (not termination-condition) do begin t=t+1 Select P(t) from P(t-1) Recombine Evaluate P(t) end End J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

4. The Effect of Parallelism J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

5. GAs: Terminology • allele, gene, chromosome, individual, • genotype, phenotype, • fitness • population, • selection, • crossover, mutation • generation J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

6. Representation • Very crucial step of the GA’s design - representation should satisfy the presumption that the whole chromosome is decomposable to building blocks • String of genes of given alphabet: • Binary • Float • Integer • More complex representation • matrices • rules • trees J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

7. Selection (Reproduction) • Models nature’s survival-of-the-fittest principle • Selection strategies: • Roulette wheel (proportionate) • Ranking • Tournament • Selection process: • determination of Expected values: EVi = fitnessi / fitnessavg • sampling algorithm - conversion of EVi to the actual number of individuals J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

8. Roulette Wheel Selection J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

9. Crossover • Provides random information exchange - works on couples of individuals • Simple 1-point crossover J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

10. Mutation • Mutation - preserves population diversity • works on single individual J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

11. Replacement Strategy • Replacement strategy defines: • how big portion of the old population will be replaced in each generation of the new population, and • the rule that determines which individuals from the old population will be replaced and which individuals will be placed in the new population • Generational - the old population is entirely rebuilt in each generation (short-lived species) • Steady-state - just a few individuals are replaced in each generation (longer-lived species) J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

12. Schemata and Schema Theorem • Schema - a template, which defines certain class of chromosomes • consists of 0s, 1s and #s (# could stand for either 0 or 1) • In binary representation - 2L strings, 3L schemata L = 7, S = (**0*1*1) - covers 24 strings Fitness of a schema - average fitness computed over all covered strings Schema order - number of fixed symbols; o(S) = 3 Defining length - distance between the first and last fixed symbol; d(S) = 4 J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

13. Theory of GAs • Schema theorem: Short, low-order, above average schemata receive exponentially increasing number of samples in subsequent generations. • Building Block Hypothesis: A genetic algorithm seeks near-optimal performance through the juxtaposition of short, low-order, high-performance schemata, called the building blocks. • Davidor [2]: “The whole GA theory is based on the assumption that one can state something about the whole only by knowing its parts”. The parts are the building blocks and the whole is the fitness value assessing the whole chromosome J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

14. Premature Convergence • The ratio of the best-fit individual’s reproduction rate to the average reproduction rate is too high - selection kills ‘worse’ individuals too early J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

15. Linear Scaling J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

16. Linear Scaling: Slow Finishing J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

17. Linear Scaling: Fixing Problems J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

18. Handling of Constraints • Constrained search space - mainly in discrete tasks • Three essential ways of constraint handling: • Penalties: illegal trial is deliberately made worse - works only with very simple constraints • Decoders and repair algorithms: special procedures that decode string representation of individuals to legal solutions, or repair an illegal representation to a ‘close’ legal trial solution - can be very expensive • Problem specific representation and special operators: promising, but very demanding approach, ad hoc representations J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

19. Initialisation of the First Population • Aspects affecting a performance of GA • how are the important fundamental schemata sampled in the initial population • Initialisation mechanisms • random - relies on “lucky sampling” of the whole solution space by limited number of samples • informed - uses prior knowledge of the desired solution shape • Pre-processing • runs several short pre-processing runs • samples the promising areas of the search space identified during the foregone pre-processing runs J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

20. Pre-processing Initialisation J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

21. Deceptive Problems • Deception • the lower order schemata lead the search away from the global optimum toward the false one called a deceptive attractor • the value of all lower order schemata instantiated by a local optimum is greater than their complementing schemata instantiated by the global optimum • The ways of handling those problems: • Dual GAs • messy GAs • Partially randomised Crossover operators J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

22. Deceptive Functions: Example J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

23. Partially Randomised Crossover J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

24. Statistical Evaluation of GA’s Performance • GAs must be evaluated in a statistical way due to its probabilistic fundamentals The same configuration of GA The same initial population Different found solutions + = • A number of experiment replications should be carried out in order to estimate the GA’s performance or influence of tested phenomenon on the GA’s performance J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

25. Applications of GAs • Variety of optimisation problems: • highly multimodal, multiobjective, when it is hard to determine the derivatives (discrete opt.), and even when the objective function is not defined analytically • Applications: • routing problems, • scheduling problems - optimal resources allocation, • layout planning, • automated design - shape optimisation • control and system identification • image processing • marketing, credit and insurance modelling problems, stock prediction, credit scoring, risk assessment etc. J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

26. Facial Recognition System Chromosome: 1011 | 0000 | 1101 | … | 1010 skull moust. eyes hairs • Choose a set of pictures at random • Repeat • Let the witness assess those pictures (YES, …, MAYBE, …, NO) • Generate a new population of chromosomes • Find those faces which best correspond to the chromosomes • Until the picture of the criminal is found J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

27. 6 -0.4 0.3 4 5 0.7 -0.3 0.2 -0.3 -0.1 1 0.8 2 3 Evolving Weights in Multi-Layer ANN Chromosome: (0.2 0.8 -0.3 -0.1 0.7 -0.3 0.3 -0.4) J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

28. JSSP: Example J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

29. JSSP: Example Optimal schedule of length 55: J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

30. TSP: Edge-Recombination Operator J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

31. Tree Representation in Genetic Programming Tree representation of a function XY: J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control

32. GP: Crossover J. Kubalík, Gerstner Laboratory for Intelligent Decision Making and Control