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

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, 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, 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, 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, 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, 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, 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, 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?