Ar#ficial Intelligence

Transcription

1 Ar#ficial Intelligence Advanced Searching Prof Alexiei Dingli

2 Gene#c Algorithms Charles Darwin

3 Genetic Algorithms are good at taking large, potentially huge search spaces and navigating them, looking for optimal combinations of things, solutions you might not otherwise find in a lifetime. - Salvatore Mangano Computer Design, May 1995

4 The Gene#c Algorithm Directed search algorithms based on the mechanics of biological evolu#on Developed by John Holland, University of Michigan (1970 s) To understand the adap#ve processes of natural systems To design ar#ficial systems sokware that retains the robustness of natural systems

5 The Gene#c Algorithm Provide efficient, effec#ve techniques for op#miza#on and machine learning applica#ons Widely- used today in business, scien#fic and engineering circles

6 Evolu#onary Compu#ng A collec'on of computa'onal methods inspired by biological evolu'on: A popula#on of candidate solu#ons evolves over #me, with the fiuest at each genera#on contribu#ng the most offspring to the next genera#on Offspring are produced via crossover between parents, along with random muta#ons and other gene#c opera#ons

7 Components of a GA A problem to solve, and... Encoding technique (gene, chromosome) Ini#aliza#on procedure (crea'on) Evalua#on/fitness func#on (environment) Selec#on of parents (reproduc'on) Gene#c operators (muta'on, recombina'on) Parameter se[ngs (prac'ce and art)

8 Simple Gene#c Algorithm { } ini#alize popula#on; evaluate popula#on; while Termina#onCriteriaNotSa#sfied { } select parents for reproduc#on; perform recombina#on and muta#on; evaluate popula#on;

9 The GA Cycle of Reproduc#on Reproduc)on Children Modifica)on Parents Modified Children Popula)on Deleted Members Evaluated Children Evalua)on Discard

10 Popula#on Chromosomes could be: Bit strings ( ) Real numbers ( ) Permuta#ons of element (E11 E3 E7... E1 E15) Lists of rules (R1 R2 R3... R22 R23) Program elements (gene#c programming) Any data structure...

11 Reproduc#on Reproduc)on Children Parents Parents are selected at random with selec#on chances biased in rela#on to chromosome evalua#ons

12 Chromosome Modifica#on Children Modifica)on Modified Children Modifica#ons are randomly triggered Operator types are: Muta#on Crossover (recombina#on)

13 Muta#on: Local Modifica#on Before: ( ) AKer: ( ) Before: ( ) AKer: ( ) Causes movement in the search space (local or global) Restores lost informa#on to the popula#on

14 Crossover: Recombina#on P1 ( ) P2 ( ) ( ) C1 ( ) C2 Crossover is a cri#cal feature of gene#c algorithms: It greatly accelerates search early in evolu#on of a popula#on It leads to effec#ve combina#on of schemata (sub solu#ons on different chromosomes)

15 More Crossover

16 Evalua#on Modified Children Evaluated Children Evalua)on The evaluator decodes a chromosome and assigns it a fitness measure The evaluator is the only link between a classical GA and the problem it is solving

17 Dele#on Popula)on Deleted Members Discard Genera'onal GA: en#re popula#ons replaced with each itera#on Steady- state GA: a few members replaced each genera#on

18 An Abstract Example Distribu#on of Individuals in Genera#on 0 Distribu#on of Individuals in Genera#on N

19 A Simple Example The Traveling Salesman Problem: Find a tour of a given set of ci#es so that each city is visited only once the total distance traveled is minimized

20 Representa#on Representa#on is an ordered list of city numbers known as an order- based GA 1) London 3) ValleUa 5) Beijing 7) Tokyo 2) Venice 4) Singapore 6) Rome 8) Prague CityList1 ( ) CityList2 ( )

21 Crossover Crossover combines inversion and recombina#on: Parent1 ( ) Parent2 ( ) Child ( ) Adjustment Child ( )

22 Muta#on Muta#on involves reordering of the list: Before: ( ) AKer: ( )

23 TSP Example: 30 Ci#es

24 Solu#on i (Distance = 941)

25 Solu#on j (Distance = 800)

26 Solu#on k (Distance = 652)

27 Best Solu#on (Distance = 420)

28 Overview of Performance

29 Issues for GA Prac##oners Choosing basic implementa#on issues: representa#on popula#on size, muta#on rate,... selec#on, dele#on policies crossover, muta#on operators Termina#on Criteria Performance, scalability Solu#on is only as good as the evalua#on func#on (oken hardest part)

30 Benefits of Gene#c Algorithms Concept is easy to understand Modular, separate from applica#on Supports mul#- objec#ve op#miza#on Good for noisy environments Always an answer; answer gets beuer with #me Inherently parallel; easily distributed

31 Benefits of Gene#c Algorithms (cont.) Many ways to speed up and improve a GA- based applica#on as knowledge about problem domain is gained Easy to exploit previous or alternate solu#ons Flexible building blocks for hybrid applica#ons Substan#al history and range of use

32 When to Use a GA Alternate solu#ons are too slow or overly complicated Need an exploratory tool to examine new approaches Problem is similar to one that has already been successfully solved by using a GA Want to hybridize with an exis#ng solu#on Benefits of the GA technology meet key problem requirements

33 Exercise How would you implement GA s in Super Mario? Fitness Func#on Muta#on Crossover Survival rate

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35 Simulated Annealing 1970 s Op#misa#on of Integrated Circuits Annealing Metallurgical process of hea#ng up a solid and then cooling slowly un#l it crystallizes Atoms have high energies at very high temperatures Allow them to restructure themselves and as the temperature is reduced the energy of these atoms decreases If this cooling process is carried out too quickly (rapid quenching) many irregulari#es and defects will be seen in the crystal structure

36 The Process Begins at a very high temperature Input values are allowed to assume a great range of random values As the training progresses the temperature is allowed to fall Restricts the degree to which the inputs are allowed to vary.

37 The Approach Itera#ve Improvement Local Random Search Explora#on Greed

38 Itera#ve Improvement

39 Local Random Search C = Current candidate P = Poten#al candidate P P P C

40 Explora#on (1) C = Current candidate P = Poten#al candidate Time Hill Climbing P P C

41 Explora#on (2) C = Current candidate P = Poten#al candidate Time C P P

42 Explora#on (2) C = Current candidate P = Poten#al candidate P Time C P

43 Greed C = Current candidate P = Poten#al candidate P C

44 The Algorithm Generate Random Solu#ons Calculate Energy (E) Set Ini#al Temperature While Temperature > Cutoff Temperature Test Solu#on = Best Solu#on For n Itera#ons Adjust Test Solu#on Calculate Energy of Test Solu#on Delta = Energy Test Solu#on Energy Best Solu#on If Delta < 0 Best Solu#on = Test Solu#on Else If Random(0,1) < e Best Solu#on = Test Solu#on ( Delta / Temperature )

45 Ball on terrain example The ball is ini#ally placed at a random posi#on on the terrain. From the current posi#on, the ball should be fired such that it can only move one step lek or right. What algorithm should we follow for the ball to finally seule at the lowest point on the terrain?

46 Ball on terrain example Initial position of the ball Simulated Annealing explores more. Chooses this move with a small probability (Hill Climbing) Greedy Algorithm gets stuck here! Locally Optimum Solution. Upon a large no. of iterations, SA converges to this solution.

47 Applica#ons Circuit par##oning and placement Water distribu#on system Umpire scheduling in US Open Tennis tournament!

48 Conclusion Simulated Annealing algorithms are usually beuer than other greedy algorithms, when it comes to problems that have numerous locally op#mum solu#ons Might not always be the best or fastest solu#on Simulated Annealing guarantees a convergence upon running sufficiently large number of itera#ons

49 Exercise What is the probability of accep#ng the following moves? Assume the problem is trying to maximize the objec#ve func#on Best Solu)on Test Solu)on Temperature

50 Answer What is the probability of accep#ng the following moves? Assume the problem is trying to maximize the objec#ve func#on Best Solu)on Test Solu)on Temperature Answer % % % %

51 Ques#ons?