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In-Depth Information
Fig. 1.
Chromosome encoding and example
permutation. The procedure for the latter is as follows: one crossover point is
selected, the first part of the first parent is directly copied into the child and
then the remaining distinct values are copied in order from the second parent
into the remaining loci of the child.
Mutation by resetting a gene is performed to the split points part of the
chromosome. In order to keep the chromosome valid, the split points are sorted
in an ascending order. If two split points are equal, a new mutation is used to
make them different, because each agent must be allocated at least one task.
For the permutation part, the interchange mutation is used, i.e. two genes are
randomly selected and interchanged. In this way, a new valid permutation is
generated, because no duplicate values appear.
The chosen selection method is the tournament selection with two individuals,
because it is fast and uses only local information. Elitism is used, i.e. the best
individual is directly copied into the next generation, in order not to lose the
best solution of the current generation. However, it was considered that copying
more than one individual would decrease the genetic diversity needed to find a
global optimal solution.
2.3 Agent Adaptation: Learning and Forgetting
It is considered that the knowledge of the agents traverses a sigmoid learning
curve, defined by an equation inspired after a recent psychology study [8]:
1
1+e
−α·
(
x
+
β
)
L
(
x
)=
(3)
Here, parameter
α
controls the steepness of the sigmoid curve in its central part
while parameter
β
translates the learning curve on the abscise in order to fit the
domain of the task attributes.
The main feature of the proposed adaptation process is that it takes into
account the effort of reaching different competence levels, as defined by the
inverse of the sigmoid function from equation (3). Thus, the agents perform
equal small steps on the ordinate, and these reflect into unequal steps on the
abscise:
l
a
(
k
+1)=
L
−
1
(1
(
k
)) +
λ · L
(
c
j
)
,l
a
· L
(
l
a
− λ
)
(
k
)
≤ c
j
L
−
1
(1
(
k
)) +
ϕ · L
(
c
j
)
,l
a
(4)
· L
(
l
a
− ϕ
)
(
k
)
>c
j
When an agent receives a task above its competence level, it will learn using
learning rate
λ
. The basic idea of moving a small distance towards the target,
