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Artificial Intelligence Search Methodologies

Artificial Intelligence Search Methodologies. Dr Rong Qu School of Computer Science University of Nottingham Nottingham, NG8 1BB, UK rxq@cs.nott.ac.uk Evolutionary Computation. EAs - framework. Based on the idea of evolution. Selection. Population. Parents. Reproduction. Replacement.

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Artificial Intelligence Search Methodologies

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  1. Artificial Intelligence Search Methodologies Dr Rong Qu School of Computer Science University of Nottingham Nottingham, NG8 1BB, UK rxq@cs.nott.ac.uk Evolutionary Computation

  2. EAs - framework • Based on the idea of evolution Selection Population Parents Reproduction Replacement Offsprings Metaheuristics – From Design to Implementation pp. 199 (Talbi, 2009) Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  3. EAs - framework • Template of an evolutionary algorithm Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  4. Genetic Algorithms Charles Darwin 1809 - 1882 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  5. Genetic Algorithms Charles Darwin 1859 Origin of the Species Survival of the Fittest Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  6. Genetic Algorithms John Holland 1975 Genetic Algorithms Artificial Survival of the Fittest Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  7. Genetic Algorithms David Goldberg 1989 Genetic Algorithms Foundations and Applications Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  8. Genetic Algorithms • Compared to exhaustive tree search techniques, modern heuristic algorithms quickly converge to sub-optimal solutions by searching a small fraction of the search space • Simulates the Darwinian evolution process in computer programs. • Populationsevolve by selective pressures, mating between individuals, and alterations such as mutations. • Genetic operators evolve solutions in the current population to create a new population Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  9. Generate Initial Population n = 1 Population Generation 'n' Crossover Population Mutate Population Final Population n = n + 1 Genetic Algorithms Flowchart (20 generations) Selection n<20? Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  10. Genetic Algorithms • Evolution of population(a set of solutions) into a new population, using operators: reproduction, mutationandcrossover • Can be implemented as three modules: the evaluation, the populationand the reproductionmodules Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  11. 1 1 2 2 Genetic Algorithm Operators Crossover A percentage of the population is selected for breeding and assigned random mates. A random crossover point is selected and a pair of new solutions are produced Adapted from Prof Graham Kendall’s G5BAIM lecture example

  12. Genetic Algorithm Operators Mutation In a small percentage of the population random changes are made. May be designed to conduct more complex operations (local search) accordingly. Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  13. Genetic Algorithm Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Crossover probability, PC = 1.0 Mutation probability, PM = 0.0 x can be represented using five binary digits Adapted from Dr Graham Kendall’s G5BAIM lecture example Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  14. Genetic Algorithm Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Generating random initial population Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  15. P3 P4 P2 P2 1 0 0 0 0 1 0 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 C1 C3 C2 C4 Genetic Algorithm Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Choose two parents (roulette selection) One point crossover (random position 1) Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  16. Genetic Algorithm Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 New generation Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  17. Genetic Algorithm Example I • Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 • 0 <= x <= 31 • Two generations • Mutation • What problem do you see with the populations? Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  18. Genetic Algorithm Example II • Traveling Salesman Problem (TSP) • a number of cities • costs of traveling between cities • a traveling sales man needs to visit all these cities exactly once and return to the starting city • What’s the cheapest route? Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  19. Genetic Algorithm Example II Traveling Salesman Problem Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  20. P1 P2 5 9 9 8 84 78 81 1 11 8 16 32 36 7 27 1 27 7 44 24 … … … 54 24 19 … 67 … … P30 Genetic Algorithm Example II Initial generation 6.5 7.8 … 6.0 Any idea of other ways to generate the initial population? Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  21. P2 C2 8 9 9 9 9 78 78 8 1 1 81 16 16 11 11 81 7 36 27 7 27 7 7 36 … … 44 24 24 … … 44 … … 19 24 … … 19 24 P30 C1 Genetic Algorithm Example II Choose pairs of parents 6.0 7.8 Crossover 13 5.9 6.2 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  22. P30 P2 78 7 9 5 9 8 11 8 1 10 16 81 7 27 76 7 36 2 24 … 4 … 44 … 24 … … … 19 79 P1 Genetic Algorithm Example II Next generation 5.9 6.2 … 6.0 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  23. Genetic Algorithm Example II • Traveling Salesman Problem • No. of cities: 100 • Population size: 30 Cost: 6.37 Generation: 88 Cost: 6.34 Generation: 1100 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  24. Genetic Algorithm Example III Applying Genetic Algorithms to Personnel Scheduling Personnel scheduling in healthcare is usually a very complex operation which has a profound effect upon the efficient usage of expensive resources. E.K. Burke, T. Curtois, R. Qu and G. Vanden Berghe. "A Time Predefined Variable Depth Search for Nurse Rostering". INFORMS Journal on Computing, 2012. doi: 10.1287/ijoc.1120.0510 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  25. Genetic Algorithm Example III • shift coverage • one shift per day • resting time • workload per month • consecutive shifts • working weekends • … A number of nurses A number of shifts each day A set of constraints

  26. Genetic Algorithm Example III • Genetic Algorithm • Initial population • construct rosters • repair infeasible ones Dr. R Qu G54SAI – Evolutionary Algorithms

  27. Genetic Algorithm Example III • Genetic Algorithm • Select parents • Recombine rows in the two rosters • repair infeasible ones +

  28. Genetic Algorithm Example III • Genetic Algorithm • Mutation • Local optimiser Dr. R Qu G54SAI – Evolutionary Algorithms

  29. Genetic Algorithm Example III Population Size Crossover Probability Mutation Probability Local Optimiser 50 0.7 0.001 ON Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  30. GA - performance • There are a number of factors which affect the performance of a genetic algorithm • The size of the population • The initial population • Selection pressure (elitism, tournament) • The cross-over probability • The mutation probability • Defining convergence • Local optimisation Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  31. GA - Conclusions • Survival of the fittest, the most fit of a particular generation (the best possible answer) are used as parents for the next generation. • GAs are a very powerful tool, allowing searching for solutions when there are no other feasible means to do so. • More advanced evolutionary algorithms emerged in the last two decades. Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  32. Evolutionary Algorithms • Evaluation is responsible for evaluating the fitness of individuals in the population • It is the only part of the GA that has any knowledge about the specific problem. The rest of the GA modules are simply operating on chromosomes with no information about the problem. • A different evaluation module is needed for each problem. Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  33. Evolutionary Algorithms • Conceivable solutions are represented, the 'fittest' will have the greatest chance of reproducing. • Successful properties will therefore be favourably represented within the population of solutions. • The population is successively 'optimised' after a number of generations. Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  34. Evolutionary Algorithms • Representation • Population • Objective function • Selection • Replacement • Stopping Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  35. Estimation of Distribution Algorithms (EDA) Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  36. Initial Population Generation n = 1 Build probability model Final Population n = n + 1 EDA Flowchart (20 generations) Selection of better individuals Sample model to generate new individuals New Population n<20? Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  37. EDA • A recent class of population based metaheuristics • Uses probability distribution of the population • Statistical information extracted from the population used to generate the next population • Probability model (vector) • Replaces the genetic operators to evolve the population Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  38. Template of an EDA Adapted from Metaheuristics – From Design to Implementation pp. 223 (Talbi, 2009) Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  39. Template of a PBIL Adapted from Metaheuristics – From Design to Implementation pp. 224 (Talbi, 2009) Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  40. PBIL Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 x represented using 5 binary digits Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  41. PBIL Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Generating initial population based on Evaluate the population Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  42. PBIL Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Update the PV based on Xbest D = (1-α)D + αXbest Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  43. PBIL Example I Maximise f(x) = x^3 - 60 * x^2 + 900 * x +100 0 <= x <= 31 Generating new population based on D = (1-α)D + αXbest Mutation in GA vs. Randomness in PBIL Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  44. PBIL Example II • Portfolio Selection Problem • Given a set of assets (stocks, etc.) and their associated return and risk • What’s the best investmentplan (i.e. which assets tochoose to achieve the highestreturn and lowest risk)? Mathworks

  45. PBIL Example II • Portfolio Selection Problem • Modern Portfolio Theory • Nobel memorial prize winner Harry Markowitz • Diversification: “don’tput all your eggs intoone basket” • Which assets to choose? • How much to invest toeach asset? • Real world constraints Asset Allocation and Portfolio Optimization, Mathworks

  46. PBIL Example II • Portfolio Selection Problem • Which assets to choose? • A binary vector of size nn: number of assets • How much to invest to each asset? • A real vector of size n, n: number of assets • Additional constraints • Cardinality: a limited number of assets • Boundary: a lower and upper bound of investment to the assets K. Lwin, R. Qu. "Hybrid Algorithm for Constrained Portfolio Selection Problem". Applied Intelligence, 39(2): 251-266, 2013. doi: 10.1007/s10489-012-0411-7 Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  47. PBIL Example II • Portfolio Selection Problem • Evaluation function • Return: combined return based on historical data • Risk: combined risk (variance of return) of all chosen assets • Constraint handling • Cardinality • Boundaries Dr. R Qu G54STA/G54SDA – Evolutionary Computing

  48. Evolutionary Algorithm Applications Combinatorial optimisation problems • bin packing problems • vehicle routing problems • job shop scheduling

  49. Evolutionary Algorithm Applications Combinatorial optimisation problems • portfolio optimization • multimedia multicast routing • knapsack problem

  50. appendix Other Evolutionary Algorithms Dr. R Qu G54STA/G54SDA – Evolutionary Computing

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