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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. Automata based programming. Proposed in Russia in 1991 - PowerPoint PPT Presentation
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
2
ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
Control System
Controlled Object
E, X2
Z X1
States Events and input variables Output events Finite state machine System of finite state
machines
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Method advantages
Effective for systems with complicated behavior
Formal and understandable behavior description
Automatic code generation from transition diagrams
Possibility of program verificationProject documentation
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
“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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Finite state machine – method of ant description
Automaton with transition’s action (Mealy). Automaton with transition’s 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
2
3
45
1
F / M
!F / R
F / M
!F / R
!F / R
!F / R
!F / M
F / MF / M
F / M
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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 stringAutomaton with 13 states which solves this
problem
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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. 88–91. (in Russian)
Genetic programming
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Mealy automaton with 7 states
Two automata with 7 seven were created after exploring over 160 and 230 millions of automata 0
6
!F / R !F / M
F / M
F / M
!F / R
!F / R
F / M
!F / M
!F / M
F / M
F / M
F / M
F / M
!F / L
2
4
3
1
5
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Problem
Only Mealy automata are discussed in all papers
Goal of this work – creating Moore automata and systems of interacting Mealy automata
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Approach proposed – 1
Island genetic algorithmAutomaton = start state + description of
states + internal automatonState = two transitions + action in state (only
for Moore automata)Transitions = number of state to which this
transition leads + action (only for Mealy automaton)
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Approach proposed – 2
class Automaton {
Transition[][] transitions;
int initialState;
Automaton nestedAutomaton;
char[] stateAction; // for Moore automata
}
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Initial generation creation
A predefined number of automata (systems of automata) is randomly generated
All automata consists of the same number of states
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Next generation creation – 1
ElitismFixed 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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Next generation creation – 2
Evolution on island is independent from other islands
After fixed number of generation islands exchange fixed part of elite individuals
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Moore automaton mutation
Change start stateChange one of state actionsChange the state to which one of the
transitions leadsChange transition condition
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Mealy automata system mutation
Change start stateDelete (insert) transition (only for external
automaton)Change the state to which one of transitions
leadsChange transition action Internal automaton mutation
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Moore automata crossover
Input: two individualsOutput: two individualsParents – P1 and P2Child – S1 and S2Start state: S1.is = P1.is and S2.is = P2.is, or
S1.is = P2.is and S2.is = P1.is
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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)
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Four variants
i
i
i
i
i
i
i
i
i
i
P1
P2
S1
S2
S1
S1 S1
S2
S2
S2
ИЛИ
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Systems of Mealy automata crossover
External automata – the same way as for Moore automata
Internal automaton – crossover is done with some probability
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Fitness function for Moore automata
F – number of units of food which ant eats in
200 stepsT – number of step when ant eats last unit of
food
200
TF
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
ZCT
F *200
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
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
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Adjustable parameters of genetic algorithm – 2
Number of exchangeable individualsParameters of small mutationParameters of crossoverRatio of “mutants”, randomly generated
individuals and “children”С – external automaton influence coefficient
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Moore automaton
This automaton allows ant to eat all food in 198 steps
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
System of pair nested automata
This automata system allows ant to eat 87 units of food in 198 steps
A. Davydov, D. Sokolov, F. TsarevApplication of Genetic Algorithms for Construction of Moore Automaton and Systems of Interacting Mealy Automata in “Artificial Ant” Problem
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ГОСУДАРСТВЕННЫЙУНИВЕРСИТЕТ
Thank you!
Thank you!