Optimizing a Chess Heuristic Using Evolutionary Algorithms

1. Benjamin Rhew 11-29-04 Optimizing a Chess Heuristic Using Evolutionary Algorithms

2. Chess and AI in History • Hoaxes • The Automaton Chess-Player • Ajeeb automaton • Endgame Machine (1890) • 1950s – True Chess Playing • 1988 – Deep Thought • 1997 – Deep Blue (vs Kasparov)

3. Why Optimize (aka Motivation)? • Current evaluation method is becoming obsolete • Evaluate against optimized heuristic instead • Apply to other similar, more difficult problems • Other games • Optimization problems • etc

4. The Problem • Take a previously existing heuristic and evolve it so that it becomes more effective • More generally, development of a heuristic to be used in a game-tree search algorithm

5. Representing an Individual • An individual has several genes, with most genes represented by a 64 by 64 array. • Genes that are not arrays are single integers. • Each of these genes corresponds to a heuristic for one piece, sometimes distinguished by color. {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10}

6. Evolutionary Operators • Crossover • Uniform based on genes (no sub-gene crossing) {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10} {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10} {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10} {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10} {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10} {-10,-5,-5,-5,-5,-5,-5, -10, -5 , 0, 0, 3, 3, 0, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5,10,10, 5, 0, -5, -5 , 0, 5, 5, 5, 5, 0, -5, -5 , 0, 0, 3, 3, 0, 0, -5, -10,-5,-5,-5, -5, -5,-5,-10}

7. Evolutionary Operators • Mutation • 1/n chance of mutating, where n is the number of genes. • Once a gene is picked, every value in it is mutated by a gaussian random value.

8. Other Evolutionary Parameters • Uses the Parallel Framework to speed up calculation • Split into 10 islands of 10 individuals each • Passes 1 individual every 10 generations • Individual is random

9. The Fitness Function • Fitness is based on win/lose/stalemate • Win=1, lose=-1, stalemate=0 • Initialized at 10 fitness, which is then modified by playing original heuristic • Each side has 30 minutes total • Fitness is then based on playing a random solution – and both fitnesses will be updated

10. Cassandre • Chess engine compatible with winboard and xboard • Already has moves and board representation in place • Only need to provide heuristic

11. Questions?