## An Optimization Method for Petri Net Models of Manufacturing Systems

### Vortrag im Rahmen der Ringvorlesung des Graduiertenkollegs

### Dr. Armin Zimmermann

**Zusammenfassung**

The search for near-optimal setup and parameter choices is a key issue in
the design of manufacturing systems. The detailed behavior of such a system is usually
too complex to be analyzed with efficient optimization methods like linear programming.
Stochastic Petri nets are an adequate modeling formalism to express structures and complex
processes that are typical in a manufacturing system. However, the cost function value for a
certain parameter set can then only be derived using a performance evaluation algorithm, e.g.
by simulation or numerical analysis. Heuristic methods as simulated annealing can be used
to guide the search for a near-optimal solution. However, as there are a lot of
evaluations necessary, which each take a considerable amount of computing time, this approach is
often infeasable.

The talk presents a two-phase approach for the optimization of
manufacturing systems, which are expressed as stochastic Petri net models. Structural properties of the
Petri net are used to approximate the cost function during the first phase in an efficient
way. The result is taken as the starting point for the second phase, which can be significantly
accelerated.

The method has been implemented as a prototype tool. A speedup of about two
orders of magnitude was reached for the studied application examples.