The efficiency of difference mapping in space mapping-based optimization

In space mapping, a time-consuming but accurate fine model is used along with a less accurate but fast coarse model to reduce the overall computational effort. In this work, techniques using the difference mapping concept will be introduced. These techniques are efficient in reducing the computational effort while improving convergence. Difference mapping is constructed similarly to the mechanism used in space mapping, but, unlike space mapping, it facilitates the use of terminating conditions based on the simultaneous use of input and output values. Rigorous mathematical expressions related to difference mapping techniques will be given, and the improvement provided by these techniques will be discussed. Furthermore, to expose the efficiency of using the difference in input and output, simulation results obtained for high-dimensional applications will be given.