Applying Genetic
Programming to
Stratego
Ryan Albarelli
Overview
Problem definition & Motivation
Stratego
Minimax Algorithm
Problem Representation
GP Implementation
Tournament
Future Work
Problem Definition
• Devise a minimax heuristic for Stratego
using Genetic Programming
• Devise a method for evaluating heurstic
against non-GP generated intelligence
Motivation
• Develop generic minimax heuristic
generator for new game solutions
• Add another level to the man vs.
machine debate
• Auction X-Box prize on eBay for gas
money home
Solution Viability
• Determine heuristic’s playability against
other types of intelligence
– “by hand” heuristics
– human opponents
– AI tournament
Stratego
• Turn based strategy board game
• Pieces of increasing rank and
decreasing frequency
• Hidden information
• Initial piece layout determined by each
player
• Objective is to capture enemy flag
Board Layout
Minimax Algorithm
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Tree representation
Branch represents possible move
Leafs values generated by heuristic
Depth first search of all possible moves
Simple minimization/maximization at each level
Alpha-Beta pruning
Partial Information
Minimax Tree (depth=2)
6
Turn of
Player 1
Maximize
6
1
5
Turn of
Player 2
Minimize
6
9
1
2
Each leaf contains a value
generated by the game heuristic
5
8
Arrows represent
move candidates
Problem Representation
• Heuristic as Expression Tree
• Binary operations
– Standard arithmetic
– Custom relationships
• Terminals
– Piece values
– formulas
401 is my Evil Organization!
Experiment Methodology
• Each heuristic expression tree is an
individual in the population
• Competition among individuals in the
form of a full game to determine fitness.
• Apply genetic operations to survivors.
• Rinse, Repeat
Binary Operations
• Standard arithmetic operations: + - * /
Terminals
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Number of pieces in hand (of Rank X)
“Center of gravity” of your/opponents pieces
Position/rank of pieces on board
Constants (numbers)
Number of adjacent friendly/enemy pieces
Distance of key pieces to enemy key pieces
Expression Tree
+
/
*
500
Flag count
4
CGrav
Fitness Evaluation
• Victory against other GP individuals in
the pool.
• Age bonus
• Number of moves required to win
• Final piece count
Selection / Competition
• Rank based
• Drop lowest candidates from the pool
• Candidates with only one loss given
slight waiver
Genetic Operations
• Expression Trees
• Crossover
– Similar sized subtree swapping
– Subtree shrinking
• Mutation
– Mutate terminals and operations
– Adding a operation/terminal
Tournament
• Best solution to be competing in the CS
AI tournament in December
Future Work
• Generalize GP for any board game
• Develop method to automatically
compile expression trees for faster
evaluation
Questions?