Logic Aided Lamarckian Evolution

1
Logic Aided Lamarckian Evolution

• Evelina Lamma(1), Fabrizio Riguzzi(2),
• Luís Moniz Pereira(3)
• (1) DEIS, University of Bologna, Italy
• (2) DI, University of Ferrara, Italy
• (3) CENTRIA, Departamento de Informática
• Universidade Nova de Lisboa, Portugal

2
Summary

• Genetic algorithms
• Lamarckian operator
• Multi-agent genetic algorithms
• Genes and Memes
• Multi-agent Crossover
• Belief revision
• Evolutionary approach to belief revision
• Example
• Experiments
• Conclusions

3
Genetic Algorithms

• Darwinian operators
• selection
• mutation
• crossover

4
Lamarckian operator

• Given a chromosome
• express it as a phenotype
• modify the phenotype in order to improve its
  fitness
• translate back the phenotype into a genotype
• Model of cultural evolution
• Concept of meme

5
GA in Multi Agent Systems

• MAS communication of knowledge by means of
  explicit messages
• add communication of knowledge by exchange of
  genes and memes
• If the number of agents is fixed, each has a pool
  of chromosomes of its own or each agent is a
  single chromosome and there is a single pool of
  agents

6
Genetic Operators

• Crossover used in order to exchange genes and
  memes among agents
• a chromosome in an agent is crossed with
  chromosomes from other agents
• Lamarckian operator used to locally improve the
  fitness by experience directed self-mutation

7
Genes and Memes

• Genes are modified only by Darwinian operators
• individual physical features are fixed
• inherited irrespective of parental learning
• Memes are modified by Darwinian and Lamarckian
  operators
• individual cultural features are changeable
• inherited via parental learning

8
Asymmetrical flow of memes

• Memes only go from teacher to learner
• In crossover
• genes are copied from both parents
• memes are copied from another agent only if that
  agent has accessed and tagged them
• accessed confirmed or modified after an
  application of the Lamarckian operator
• tagged an extra bit is associated to each meme
  in order to code whether the meme has been
  accessed.

9
Multi-agent crossover

• A new agent offspring is produced from two parent
  chromosomes
• one parent comes from the pool of another agent
• bits from each parent are copied according to a
  mask
• The mask is such that
• genes are selected randomly, half from each
  parent
• memes are selected randomly, half from memes in
  the other agent, but only if they have been
  accessed

10
Multiagent crossover
genes
memes
Ag1
child in Ag1 pool

Ag2
Mask
11
Genetic algorithm

• GA(max_gen, p, r ,m, l, Fitness)
• max_gen maximum number of generations before
  termination
• p number of individuals in the population
• r fraction of population to be replaced by
  Crossover at each step
• m fraction of population to be mutated
• l fraction of population that evolves
  Lamarckianly
• Fitness fitness function F(hi)

12
Genetic algorithm

• GA(max_gen, p, r ,m, l, Fitness)
• Initialize population P set of p hypotheses
  randomly generated
• gen 0
• while gen lt max_gen
• Generate PS by applying the following operators
  to P
• selection
• crossover
• mutation
• Lamarck
• update P PS
• return the hypothesis from PS with the highest
  fitness

13
Genetic operators

• select select (1- r) p hypotheses from P with a
  probability Pb proportional to their fitness and
  add them to PS
• crossover for i1 to r p
• select h1 from P with probability Pb
• select h2 from another agent chosen at random
• crossover h1 with h2 obtaining h1, add h1 to
  PS
• mutate choose m percent of the members of PS
  with uniform probability
• and, for each, invert randomly one bit
• Lamarck choose l p hypotheses from PS with
  uniform probability
• and apply to them the Lamarckian operator

14
Belief Revision

• Important functionality of agents.
• Problem definition. Given
• an extended logic program containing integrity
  constraints, i.e.
• ? ? B1,,Bn, not C1,,not Cm
• a set of revisable literals, i.e., literals for
  which the revision is allowed.
• They must not have any definition

15
Belief Revision

• Find
• a truth value for the revisable literals so that
  the program is not contradictory, i.e., ? does
  not belong to the model of the program

16
GAs for Belief Revision

• Genetic Algorithms can be used for Belief
  Revision
• each revisable is encoded with a meme
• the meme has value 1 if the revisable is true and
  0 if it is false
• each set of assumptions about the values of
  revisables is coded as a chromosome

17
Fitness function

• ni number of integrity constraints satisfied by
  hypothesis hi
• n total number of integrity constraints

18
Example

• Digital circuit diagnosis
• Revisable literals indicate the assumed behaviour
  mode of each gate
• not ab(gate) gate behaves normally
• ab(gate) gate behaves abnormally

19
Example circuit c17
obs
obs
g1
0
1
1
g10
g3
g22
0
0
1
g11
g6
0
0
g16
g2
1
1
1
g23
1
g19
g7
0
20
Example circuit c17

• val( in(Type,Name,Nr), V ) -
• conn( in(Type,Name,Nr),
• out(Type2,Name2) ),
• val( out(Type2,Name2), V ).
• val( out(nand,Name), V ) -
• not ab(Name),
• val( in(nand,Name,1), W1),
• val( in(nand,Name,2), W2),
• nand_table(W1,W2,V).
• nand_table(0,0,1).
• ...

val( out(nand,Name), V ) - ab(Name),
val( in(nand,Name,1), W1), val(
in(nand,Name,2), W2), and_table(W1,W2,V).
val( out(inpt0, Name), V ) - obs(
out(inpt0, Name), V ).

21
Topology
conn(in(nand, g19, 1), out(nand,
g11)). conn(in(nand, g19, 2), out(inpt0,
g7)). conn(in(nand, g22, 1), out(nand,
g10)). conn(in(nand, g22, 2), out(nand,
g16)). conn(in(nand, g23, 1), out(nand,
g16)). conn(in(nand, g23, 2), out(nand, g19)).

• conn(in(nand, g10, 1), out(inpt0, g1)).
• conn(in(nand, g10, 2), out(inpt0, g3)).
• conn(in(nand, g11, 1), out(inpt0, g3)).
• conn(in(nand, g11, 2), out(inpt0, g6)).
• conn(in(nand, g16, 1), out(inpt0, g2)).
• conn(in(nand, g16, 2), out(nand, g11)).

22
Observations and constraints

• ? - obs(out(nand, g22), 0), val(out(nand, g22),
  1).
• ? - obs(out(nand, g22), 1), val(out(nand, g22),
  0).
• ? - obs(out(nand, g23), 0), val(out(nand, g23),
  1).
• ? - obs(out(nand, g23), 1), val(out(nand, g23),
  0).
• obs(out(inpt0, g1), 0).
• obs(out(inpt0, g2), 1).
• obs(out(inpt0, g3), 0).
• obs(out(inpt0, g6), 0).
• obs(out(inpt0, g7), 0).
• obs(out(nand, g22), 0).
• obs(out(nand, g23), 1).

23
Diagnosis

• One of the integrity constraints is violated
• the observed output for g22 is different from the
  computed output.
• Contradiction is removed by assuming
• ab(g22)
• which is a diagnosis for the circuit.

24
Belief Revision

• Support Set a support set of a literal L of a
  program P, denoted by SS(L), is a set of
  revisables sufficient to support a derivation of
  L in P

25
Belief Revision

• Hitting set a hitting set of for a collection of
  SS(L) is the union of one non-empty subset from
  each SS(L). It is minimal iff no proper subset
  is a hitting set.
• A contradiction removal set is a hitting set for
  the SS(?).

26
Lamarckian operator

• The Lamarckian operator uses techniques similar
  to BR ones.
• It differs from BR because it starts from an
  arbitrary chromosome C
• The Lamarckian support sets are all the support
  sets that are subsets of the current chromosome C

27
Lamarckian operator

• find all the Lamarckian support sets for ? with
  respect to C
• find a hitting set HS(?) for them
• change in C all its literals which are in HS(?).

28
Example circuit c17

• Suppose, initially
• Cab(g10), not ab(g11), ab(g16), not ab(g19),
  not ab(g22), not ab(g23)
• In this case, two constraints are violated
  because out(g22)1 and out(g23)0

29
Example circuit c17

• A BR operator would return as changes to C
• not ab(g10), not ab(g11), not ab(g16), not
  ab(g19), ab(g22), not ab(g23)
• these are consistent with both ICs

30
Example circuit c17

• Lamarckian support sets of ?
• not ab(g11),not ab(g19),not ab(g11),ab(g16),not
  ab(g23)
• not ab(g11),ab(g16),ab(g10),not ab(g22)
• Lamarck returns these changes to C, one for each
  hitting set
• Cab(g10), ab(g11), ab(g16), not ab(g19), not
  ab(g22), not ab(g23)
• Cab(g10), not ab(g11), not ab(g16), not
  ab(g19), not ab(g22), not ab(g23)
• one constraint in either case is still violated

31
Experiments

• ISCAS85 collection of benchmark digital circuits
• Four algorithms considered
• S-L single agent GA without the Lamarckian
  operator
• M-L as S-L but multi agent
• ML-A as M-L plus Lamarck, without asymmetry
• MLA as ML-A plus asymmetry

32
Results

• alu4_flat circuit
• 100 gates (100 revisables)
• 8 outputs (16 constraints)
• 4 agents, with same observations and constraints
• 10 chromosomes each, l0.6
• 5 experiments
• Average fitness

33
Conclusions

• Framework for solving problems represented with
  logic
• belief revision
• dynamic world, control of observable outputs
• Performance improvement by
• distributed agents
• Lamarckian operator
• asymmetric crossover on memes

34
Future work

• Situations where
• agents do not have the same observations,
  constraints or revisables
• observations change over time
• Three-valued memes for expressing irrelevancy
• Integrating Lamarckism with other agent features

35

• ab(c11gat),ab(c19gat),ab(c11gat),ab(c16gat),ab(c2
  3gat),
• not ab(c11gat),ab(c19gat),ab(c11gat),ab(c16gat),a
  b(c23gat),
• ab(c11gat),not ab(c19gat),ab(c11gat),ab(c16gat),a
  b(c23gat),
• not ab(c11gat),not ab(c19gat),ab(c11gat),ab(c16ga
  t),ab(c23gat),
• ab(c11gat),ab(c19gat),not ab(c11gat),ab(c16gat),a
  b(c23gat),
• not ab(c11gat),ab(c19gat),not ab(c11gat),ab(c16ga
  t),ab(c23gat),
• ab(c11gat),ab(c19gat),ab(c11gat),not
  ab(c16gat),ab(c23gat),
• not ab(c11gat),ab(c19gat),ab(c11gat),not
  ab(c16gat),ab(c23gat),
• ab(c11gat),ab(c19gat),not ab(c11gat),not
  ab(c16gat),ab(c23gat),
• not ab(c11gat),ab(c19gat),not ab(c11gat),not
  ab(c16gat),ab(c23gat),
• ab(c11gat),not ab(c19gat),not ab(c11gat),not
  ab(c16gat),ab(c23gat),
• not ab(c11gat),not ab(c19gat),not ab(c11gat),not
  ab(c16gat),ab(c23gat),
• ab(c11gat),not ab(c19gat),not ab(c11gat),ab(c16ga
  t),not ab(c23gat),
• not ab(c11gat),not ab(c19gat),not
  ab(c11gat),ab(c16gat),not ab(c23gat),
• ab(c11gat),not ab(c19gat),ab(c11gat),not
  ab(c16gat),not ab(c23gat),
• not ab(c11gat),not ab(c19gat),ab(c11gat),not
  ab(c16gat),not ab(c23gat),
• not ab(c11gat),ab(c16gat),not ab(c10gat),ab(c22ga
  t),
• ab(c11gat),not ab(c16gat),not ab(c10gat),ab(c22ga
  t),
• ab(c11gat),ab(c16gat),ab(c10gat),not
  ab(c22gat),

36
Belief Revision

• Support Set a support set of a literal L of a
  program P, denoted by SS(L), is obtained as
  follows
• if L is not a revisable literal, then, for each
  rule L ?B in P, there is one SS(L) given by the
  union of SS(Bi) for each Bi ? B. If B is empty
  then SS(L)
• if L is a revisable literal then SS(L)L

37
Lamarckian operator
Lamarckian support set given an hypothesis C, a
Lamarckian support set of a literal L of a
program P, denoted by SS(L), is obtained as
follows if L is not a revisable literal, then,
for each rule L ? B in P there is one SS(L) given
by the union of SS(Bi) for each Bi ? B. If B is
empty then SS(L) if L is a revisable literal
then if L belongs to C, then SS(L)L if L is
not in C or the default complement belongs to C
then the SS(L) under construction is not a
support set
38
Results, single agent

• Single agent, with and without the Lamarckian
  operator
• Fitness function
• fi number of revisables of hi that are false