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G5BAIM Artificial Intelligence Methods Graham Kendall History G5BAIM History Predictions • “Within 10 years a computer will be a chess champion” – Herbert Simon, 1958 • Conversion from Russian to English, when presented with – “The spirit is willing but the flesh is weak” produced – “The vodka is good but the meat is rotten” • National Research Council, 1957 G5BAIM History The Travelling Salesman Problem • A salesperson has to visit a number of cities • (S)He can start at any city and must finish at that same city • The salesperson must visit each city only once • The number of possible routes is (n!)/2 G5BAIM History Combinatorial Explosion Travelling Salesman Problem Routes 2000000 1500000 1000000 500000 0 1 2 3 4 5 6 Cities 7 8 9 10 G5BAIM History Combinatorial Explosion Cities Routes 1 1 2 1 3 3 4 12 5 60 6 360 7 2520 8 20160 9 181440 10 1814400 11 19958400 G5BAIM History Combinatorial Explosion A 10 city TSP has 181,000 possible solutions A 20 city TSP has 10,000,000,000,000,000 possible solutions A 50 City TSP has 100,000,000,000,000,000,000,000,000,000,00 0,000,000,000,000,000,000,000,000,000,000 possible solutions There are 1,000,000,000,000,000,000,000 litres of water on the planet Mchalewicz, Z, Evolutionary Algorithms for Constrained Optimization Problems, CEC 2000 (Tutorial) G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi G5BAIM History Combinatorial Explosion - Towers of Hanoi • How many moves does it take to move four rings? • You might like to try writing a towers of hanoi program (and you may well have to in one of your courses!) G5BAIM History Combinatorial Explosion - Towers of Hanoi • If you are interested in an algorithm here is a very simple one • Assume the pegs are arranged in a circle • 1. Do the following until 1.2 cannot be done – 1.1 Move the smallest ring to the peg residing next to it, in clockwise order – 1.2 Make the only legal move that does not involve the smallest ring • 2. Stop • P. Buneman and L.Levy (1980). The Towers of Hanoi Problem, Information Processing Letters, 10, 243-4 G5BAIM History Combinatorial Explosion - Towers of Hanoi • A time analysis of the problem shows that the lower bound for the number of moves is 2N-1 • Since N appears as the exponent we have an exponential function G5BAIM History Combinatorial Explosion - Towers of Hanoi N Pegs 2 -1 3 4 5 6 … 10 7 15 32 63 … 1023 G5BAIM History Combinatorial Explosion - Towers of Hanoi • The original problem was stated that a group of tibetan monks had to move 64 gold rings which were placed on diamond pegs. • When they finished this task the world would end. • Assume they could move one ring every second (or more realistically every five seconds). • How long till the end of the world? G5BAIM History Combinatorial Explosion - Towers of Hanoi • > 500,000 years!!!!! Or 3 Trillion years • Using a computer we could do many more moves than one second so go and try implementing the 64 rings towers of hanoi problem. • If you are still alive at the end, try 1,000 rings!!!! G5BAIM History Combinatorial Explosion - Optimization • • • • Optimize f(x1, x2,…, x100) where f is complex and xi is 0 or 1 The size of the search space is 2100 1030 An exhaustive search is not an option – At 1000 evaluations per second – Start the algorithm at the time the universe was created – As of now we would have considered 1% of all possible solutions G5BAIM History Combinatorial Explosion 1E+280 1E+266 1E+252 1E+238 1E+224 1E+210 1E+196 1E+182 1E+168 1E+154 1E+140 1E+126 1E+112 1E+98 1E+84 1E+70 1E+56 1E+42 1E+28 1E+14 1 5N N^3 N^5 N^10 1.2^N 2^N N^N 2 4 8 16 Microseconds in a Day 32 64 128 256 512 1024 2048 Microseconds since Big Bang G5BAIM History Combinatorial Explosion Running on a computer capable of 1 million instructions/second N2 N5 10 1/10,000 second 20 1/2500 second 50 1/400 second 100 1/100 second 200 1/25 second 1/10 second 3.2 seconds 5.2 minutes 2.8 hours 3.7 days > 400 trillion centuries 45 digit no. of centuries 2N 1/1000 second 1 second 35.7 years NN 2.8 hours 3.3 trillion years 70 digit no. of centuries 185 digit no. of centuries Ref : Harel, D. 2000. Computer Ltd. : What they really can’t do, Oxford University Press 445 digit no. of centuries G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top Left = Cognitive Science G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top Left Bottom Left = = Cognitive Science The Turing Test G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top Left Bottom Left Top Right = = = Cognitive Science The Turing Test Logical Approach G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top Left Bottom Left Top Right Bottom Right = = = = Cognitive Science The Turing Test Logical Approach Acting to achieve one’s goals G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top = Thought Processes and Reasoning G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top = Bottom = Thought Processes and Reasoning Behaviour G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top = Bottom = Left = Thought Processes and Reasoning Behaviour Measure success against ourselves G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally Top Bottom Left Right = = = = Thought Processes and Reasoning Behaviour Measure success against ourselves Measure against rationality G5BAIM History Definition of AI Systems that think like humans Systems that think rationally Systems that act like Systems that act humans rationally G5BAIM History Not Examinable - but in notes • Turing Test • Chinese Room • Physical Symbol System Hypothesis • ELIZA • MYCIN • Forward/Backward Chaining • Means End Analysis G5BAIM Artificial Intelligence Methods Graham Kendall End of History