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the main purpose of the system, defines the necessary
agents to accomplish it, then introduces the various
failures of agents and ends by introducing the commu-
nication model and error recovery mechanisms. The
refinement process ensures a set of properties, mainly
1) reachability of the main purpose of the system, 2)
the integrity between agents’ local information and
global information and 3) efficiency of cooperative
activities for error recovery. The aim of the works
presented above is to ensure that the designed indi-
vidual behavior will give rise to the desired global
properties. Some of them make use of simulation,
while others employ formal techniques. The major-
ity of these works utilize a bottom-up approach (ex-
cept (Brambilla et al., 2012) and (Pereverzeva et al.,
2012)) which is ideally suited to self-organizing sys-
tems. The use of Event-B in (Pereverzeva et al., 2012)
is extremely important because of the use of the re-
finement principle that permits a progressive, guided
and correct construction of the desired system, which
is not allowed in the other works. In our proposition,
we combine a bottom-up approach with the use of re-
finement and design patterns in order to give more
guidance to the designer when designing the individ-
ual behavior (AGP
0
pattern) and when doing proofs
(GBP
0
and SOP
0
patterns).
6 CONCLUSIONS
We have presented in this paper a formal approach for
the design of SO-MAS based on design patterns, re-
finement and Event-B. Three patterns were proposed;
AGP
0
gives refinement steps for modeling the local
behavior of the agents and guarantees deadlock free-
ness of any agent, GBP
0
allowing to prove that the
modeled local behavior will converge towards the de-
sired global behavior and finally SOP
0
letting the eval-
uation of the ability of self-organizing mechanisms to
encounter the environment perturbations.
The main challenges for future work can be summa-
rized in the three following points:
- Proving the convergence of the events when apply-
ing the patterns GBP
0
and SOP
0
which is not trivial
task because of the non determinism in SO-MAS. One
possible solution for this is to prove the convergence
under fairness assumption like in (M
´
ery and Popple-
ton, 2013).
- Automation of the refinement process and the gen-
eration of machines according to the design patterns.
- Formal reasoning about the improvement of the sys-
tem performance. A probabilistic approach coupled
with Event-B can be useful in this case.
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