Seminar: An integrated methodology to solve optimization problems with Petri nets as disjunctive constraints
Thu, 18/02/2010 - 12:00 - 13:00
Title: An integrated methodology to solve optimization problems with Petri nets as disjunctive constraints
Speaker: Juan Ignacio Latorre
Abstract: This work is focused on the transformation of a
decision problem based on a DES into an optimization problem based on a Petri
net (PN) model. The optimisation model has some parameters that model the
undefined characteristics of the original system, and in this case there are at
least one undefined parameter in the incidence matrices. From the undefined
structural parameters of a PN it is possible to define what have been called
Alternatives Petri nets (APN). Some of their properties are demonstrated. In
particular, it has been proven the equivalence between different types of sets
of APN to describe the disjunctive constraint to the optimisation problem.
Several techniques are provided to afford the transformation of the disjunctive
constraint of the Petri net in order to allow the application of classical
methodologies to solve problems of combinatorial optimization in a single
process. The developed techniques are based in Alternative Aggregation Petri
nets (AAPN). Several methodologies based on AAPN are detailed according to
different representations of the PN disjunctive constraint (compound Petri net,
mixed compound and simple alternative PN, and simple alternative PN). As an
additional step in the theoretical results, the relationship between coloured
Petri nets (CPN) and AAPN is analysed, proving that it is possible to obtain an
equivalent CPN from any AAPN. Therefore, it is demonstrated the possibility of
applying the optimization methodologies based on AAPN by means of CPN. It is
also analysed how to use a simulator of CPN to apply these techniques.
Location:
Seminario del Departamento
Edificio Ada Byron, María de Luna 1 Zaragoza
Spain
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