Application of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in

1
Application of Genetic Algorithms for
Construction of Moore Automaton and Systems of
Interacting Mealy Automata in Artificial Ant
Problem

• A. Davydov, D. Sokolov, F. Tsarev
• Scientific advisor prof. A. Shalyto
• 2008

2
Automata based programming

• Proposed in Russia in 1991
• Software systems are developed as well as
  automation of engineering (and other) process
• Control system is a system of interacting finite
  state machines

• States
• Events and input variables
• Output events
• Finite state machine
• System of finite state machines

3
Method advantages

• Effective for systems with complicated behavior
• Formal and understandable behavior description
• Automatic code generation from transition
  diagrams
• Possibility of program verification
• Project documentation

4
Problem

• The general difficulty in automata based
  programming is automata construction
• In a majority of cases automata are designed
  manually
• Heuristic automata construction is often very
  hard and time-consuming
• The solution is to use genetic programming for
  automatic finite state machines generation

5
Artificial ant problem

• Torus 32x32
• 89 cells with food
• 200 steps
• The locations of food are fixed
• Goal is to create an ant which can eat all food
  in 200 steps

6
What ant can do?

• Determine is there food in front of it
• Do one of these actions in one step
• step forward and eat food if it is in the next
  cell
• turn left
• turn right
• nothing

7
Finite state machine method of ant description

• Automaton with transitions action (Mealy).
  Automaton with transitions action (Moore).
  System (couple) of automata which interact by
  nesting
• It is easy to create automata with many states
• There is Mealy automaton with 5 states which
  allow to eat 81 units of food

8
Genetic Algorithms 1

• Jefferson D., Collins R., Cooper C., Dyer M.,
  Flowers M., Korf R., Taylor C., Wang A. The
  Genesys System. 1992.
• Coding automata to bit string
• Automaton with 13 states which solves this problem

9
Genetic Algorithms 2

• Angeline P. J., Pollack J. Evolutionary Module
  Acquisition // Proceedings of the Second Annual
  Conference on Evolutionary Programming. 1993.
• Coding automata to bit string freezing
• Automaton with 11 states which solves this
  problem in 193 steps

10
Genetic Algorithms 3

• Chambers L. D. Practical Handbook of Genetic
  Algorithms, Volume 3, Chapter 26, 6 Algorithms
  to Improve the Convergence of a Genetic Algorithm
  with a Finite State Machine Genome. CRC Press,
  1999.
• Coding automata to bit string canonical
  representation
• Automaton with 8 states which solves this problem

11
Genetic Algorithms 4

• Tsarev F., Shalyto A. About construction of
  automata with minimal number of states for
  Artificial ant problem /Proceedings of X
  international conference of soft compitation and
  measurement. SPbETU LETI. Vol.2, 2007, pp.
  8891. (in Russian)
• Genetic programming

12
Mealy automaton with 7 states

• Two automata with 7 seven were created after
  exploring over 160 and 230 millions of automata

13
Problem

• Only Mealy automata are discussed in all papers
• Goal of this work creating Moore automata and
  systems of interacting Mealy automata

14
Approach proposed 1

• Island genetic algorithm
• Automaton start state description of states
  internal automaton
• State two transitions action in state (only
  for Moore automata)
• Transitions number of state to which this
  transition leads action (only for Mealy
  automaton)

15
Approach proposed 2

• class Automaton
• Transition transitions
• int initialState
• Automaton nestedAutomaton
• char stateAction // for Moore automata

16
Initial generation creation

• A predefined number of automata (systems of
  automata) is randomly generated
• All automata consists of the same number of states

17
Next generation creation 1

• Elitism
• Fixed part of individuals move to next generation
  
• For other individuals tournament strategy.
  Choose two pairs of individual, mutation or
  crossover with some probability is applied to
  best individuals of each pair

18
Next generation creation 2

• Evolution on island is independent from other
  islands
• After fixed number of generation islands exchange
  fixed part of elite individuals

19
Moore automaton mutation

• Change start state
• Change one of state actions
• Change the state to which one of the transitions
  leads
• Change transition condition

20
Mealy automata system mutation

• Change start state
• Delete (insert) transition (only for external
  automaton)
• Change the state to which one of transitions
  leads
• Change transition action
• Internal automaton mutation

21
Moore automata crossover

• Input two individuals
• Output two individuals
• Parents P1 and P2
• Child S1 and S2
• Start state S1.is  P1.is and S2.is  P2.is, or
  S1.is  P2.is and S2.is  P1.is

22
Transitions crossover

• State i
• There is food in front of ant ? P1(i, 0)
• There is no food in front of ant ? P1(i, 1)
• Similarly P2(i, 0), P2(i, 1), S1(i, 0), S1(i,1),
  S2(i, 0), S2(i, 1)
• There are 4 variants for S1(i, 0), S1(i,1), S2(i,
  0), S2(i, 1)

23
Four variants
24
Systems of Mealy automata crossover

• External automata the same way as for Moore
  automata
• Internal automaton crossover is done with some
  probability

25
Fitness function for Moore automata

• F  number of units of food which ant eats in 200
  steps
• T number of step when ant eats last unit of food

26
Fitness function for systems of Moore automata

• F  number of units of food which ant eats in 200
  steps
• T number of step when ant eats last unit of
  food
• Z number of visited states in external
  automaton
• C coefficient

27
Generation mutation

• After fixed number of generations there is big
  mutation
• Big mutation all individuals either change to
  mutants or change to randomly generated
  individuals

28
Adjustable parameters of genetic algorithm 1

• Number of islands
• Population size on an island
• Time between big mutations
• Part of islands which is destroyed in big
  mutation
• Part of individuals which moves to next
  generation
• Time to exchange of individual between islands

29
Adjustable parameters of genetic algorithm 2

• Number of exchangeable individuals
• Parameters of small mutation
• Parameters of crossover
• Ratio of mutants, randomly generated
  individuals and children
• ? external automaton influence coefficient

30
Moore automaton

• This automaton allows ant to eat all food in 198
  steps

31
System of pair nested automata

• This automata system allows ant to eat 87 units
  of food in 198 steps

32
Thank you!

• Thank you!