Information Technology Reference
In-Depth Information
The equation for the utility of an individual attribute is adapted after the shape
of a fuzzy triangular number with centre
l
a
,leftwidth
μ
a
and right width
ν
a
.
Thus, agents have non-monotonic utility functions. Although the shape of all
utility functions is the same, the actual functions are different depending on
parameters
l
a
,
μ
a
and
ν
a
which are unique for each agent.
If the task is too easy, the agent can solve it with no problems, but it has no
“challenge” associated with it. If the task is too complex, the agent will have
diculty achieving it, although it can improve its own competence level.
This adapting behaviour of the agents is rooted in the classic psychological
theory of
cognitive dissonance
[6], meaning that an agent working in a low-
preference (or unpleasant) situation gradually improves its attitude toward it,
in order to reduce the discrepancy (or dissonance) between the reality and its
own “painful” perspective about it.
2.2 Evolutionary Approach to Determine Negotiation Outcomes
A negotiation problem is one where multiple agents try to come to an agreement
or deal. Each agent is assumed to have a preference over all possible deals. Agents
want to maximize their own utility but they also face the risk of a breakdown
in negotiation [12]. A qualitative criterion to identify system states that are
optimal from a social point of view is the identification of the Pareto optimal
states, i.e. states where it is not possible to increase the utility of some agents
without reducing that of any of the others. Commonly encountered quantitative
solutions for the bargaining problem are, among others, the Nash solution (the
deal that maximizes the product of the utilities) and the utilitarian solution (the
deal that maximizes the sum of the utilities).
Let
X
be a finite set of potential agreements. In our case,
X
contains combi-
nations of disjunct sets of tasks such that all the tasks are allocated, and each
task is allocated to exactly one agent:
X
=
{S
1
× ... × S
n
|S
i
⊂ S, S
i
∩ S
j
=
φ, ∀i
=
j, i, j ∈ A, S
1
∪ ... ∪ S
n
=
S} ,
(2)
where
S
=
℘
(
T
)and
n
=
|A|
.
An evolutionary approach is considered for finding the negotiation outcomes
that are usually believed to be fair or desirable: the Nash solution and the
utilitarian solution. The encoding takes into account the specificity of the prob-
lem, i.e. each task must appear only once in a possible allocation. Therefore, a
permutation-based encoding is used. The partition of the permutation between
different agents is defined by
n −
1.
Therefore, a hybrid representation is used: the first genes of the chromosome are
the split points and the rest contains the actual permutation of tasks, as shown
in Fig. 1.
The fitness function is the product or the sum of agent utilities for a given
deal, i.e. a chromosome. The crossover and mutation operations are different for
the first and the second part of the chromosome. A normal one-point crossover
is applied to the split point section, while a modified crossover is applied to the
1 integer genes, with values from 1 to
m −
