System Optimization

During the design of a technical system, one of the basic tasks is to choose between different options, such that an optimal behavior is achieved as closely as possible. Optimization is the problem of finding specific parameter values for a given system such that an optimal behavior is reached. It is a key issue in the design of complex technical systems because even comparably small performance improvements can lead to huge savings. This chapter presents an efficient optimization technique based on stochastic Petri net models.

Parameters (or decision variables) are values in the model, such as a machine speed, a buffer capacity, or the number of pallets, that have some degree of freedom in the design and need to be decided. We denote the number of those parameters for a specific optimization problem by D in the following. Each parameter set x thus consists of D elements x1 … xD, which are assumed to be real values for simplicity x ? RD. Actual parameters may be integers, real values, or enumerations, all of which can be mapped to a real number. The search space X of possible solutions thus has D dimensions, and is constrained by the restrictions of the parameters xmin and xmax such that