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Evolutionary Computing - Genetic Algorithms - An Introduction
- 1. Blue Trail Software Evolutionary Computing Genetic Algorithms An Introduction Martín Pacheco
- 2. Overview of Topics 1. Biological inspiration 2. What is evolutionary computing (EC) 3. General outline of the evolutive algorithm (EA) 4. Genetic algorithm (GA) overview 5. SGA technical summary 6. SGA reproduction cycle 7. SGA operators 8. Practical Application Example: “It is not the strongest of the species that survives, nor the most intelligent, but the one most responsive to change.”
- 3. Biological Inspiration ● To understand biological processes properly, we must first have an understanding of the cell ● Human bodies are made up of trillions of cells ● Each cell has a core structure (nucleus) that contains your chromosomes ● Additionally, each of our 23 chromosomes are made up of tightly coiled strands of deoxyribonucleic acid (DNA) The Origin of Species (1859)
- 4. Biological Inspiration ● Reproduction involves recombination of genes from parents and then small amounts of mutation (errors) in copying ● The fitness of an organism is how much it can reproduce before it dies ● Here is an example of the passing of chromosomes within human reproduction
- 5. What is evolutionary computing (EC) ● Evolution of species: ○ Natural selection ○ Genetic operators ● Biological sciences provide inspiration and terminology
- 6. General Outline of EA Population Offspring Parents Parent selection Recombination Mutation Survivor selection Initialization Termination
- 7. Genetic algorithm (GA) overview ● Originally developed by John Holland (1975). ● Genetic Algorithm’s have 2 essential components: ○ “Survival of the fittest” ○ Genetic Diversity ● The genetic algorithm (GA) is a search heuristic that mimics the process of natural evolution. ● Attributed features: ○ Not too fast
- 8. Genetic algorithm (GA) overview ● Holland’s original GA is now known as the simple genetic algorithm (SGA). ● Other GAs use different: ○ Representations ○ Mutations ○ Crossovers ○ Selections mechanisms ● Applications: ○ Optimization and Search Problems
- 9. The Simple GA ● Has been subject of many (early) studies ○ Still often used as benchmark for novel GAs ● Shows many shortcomings, e.g. ○ Representation is too restrictive ○ Mutation & crossovers only applicable for bit-string & integer representations ○ Selection mechanism sensitive for converging populations with close fitness values ○ Generational population model (step 5 in SGA repr. cycle) can be improved with explicit survivor selection
- 10. SGA technical summary Representation Binary strings Recombination N-point or uniform Mutation Bitwise bit-flipping with fixed probability Parent selection Fitness-Proportionate Survivor selection All children replace parents speciality Emphasis on crossover
- 11. SGA reproduction cycle 1. Select parents for the mating pool (size of mating pool = population size) 2. Shuffle the mating pool 3. For each consecutive pair apply crossover with probability pc , otherwise copy parents 4. For each offspring apply mutation (bit-flip with probability pm independently for each bit) 5. Replace the whole population with the resulting offspring
- 12. SGA operators: Point crossover ● Choose a random point on the two parents ● Split parents at this crossover point ● Create children by exchanging tails ● Pc typically in range (0.6, 0.9)0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 Parents Children
- 13. SGA operators: Mutation ● Alter each gene independently with a probability pm ● pm is called the mutation rate ○ Typically between 1/pop_size and 1/ chromosome_length 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 1 1 0 0 0 1 0 1 1 0 0 1 Child Parent
- 14. SGA operators: Selection ● Main idea: better individuals get higher chance ○ Chances proportional to fitness ○ Implementation: roulette wheel technique ■ Assign to each individual a part of the roulette wheel ■ Spin the wheel n times to select n individuals A 3/6 = 50% B 1/6 = 17% C 2/6 = 33% fitness(A) = 3 fitness(B) = 1 fitness(C) = 2
- 15. N-Queen Problem ● N-Queen dates back to the 19th century (studied by Gauss) ● Classical combinatorial problem, widely used as a benchmark because of its simple and regular structure. ● Problem involves placing N queen on a N x N chessboard such that no queen can attack any other.
- 16. N-Queen Problem This problem contains three constraints: 1. No two queens can share a same row. 2. No two queens can share a same column. 3. No two queens can share a same diameter.
- 17. N-Queen Problem: Cycle Initialize Population Parent Selection Satisfy Constraints Children Mutation Insert Children Select The Best ThenElse n + 1 generation
- 18. N-Queen Problem: Representation 1 4 2 3 3 1 4 2
- 19. N-Queen Problem: Representation Genotypic space Codification Phenotypic space Decodification 1 4 2 3 Chromosome Gen Alelo
- 20. N-Queen Problem: Fitness [R1, R2, ..., Ri, Ri+1, ..., Rj, …, Rn] i - Ri = j - Rj o i + Ri = j + Rj || Ri - Rj || = || i-j ||
- 21. N-Queen Problem: Parent Selection 1 2 3 5 6 7 10 9 8 4 10 1 4 5 6 9 7 3 9 4 4 9 1th 2th
- 22. N-Queen Problem: Crossover 1 4 2 3 3 1 4 2 1 4 4 2
- 23. Take a look at ● N-Queen report ● N-Queen source code at GitHub. ● Eiben, A. E. y Smith, J. E., (2015), Introduction to Evolutionary Computing, Springer, 2da. Edición, ISBN: 978-3-540-40184-1 ● Mitchell, M., (2014), An Introduction to Genetic Algorithms, MIT Press ● Goldberg, D. E., (2007), Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publishing Company, Inc., 2007, ISBN: 0201157675.