Optimizing a Chess Heuristic Using Evolutionary Algorithms

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,
5,10,10, 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
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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
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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.

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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

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The Fitness Function

• Fitness is based on win/lose/stalemate
• Win1, lose-1, stalemate0
• 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

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Questions?