Comparing the performance of a nested to a continuous evolution strategy with covariance matrix adaption for optimization of drilling EDM

Abstract

Electrical discharge machining (EDM) is a complex manufacturing process where the correlation of the individual process parameters is not fully known. When introducing new materials or complex, individual geometries in EDM, a satisfactory vector of parameters for the process must be found. This challenge is often encountered in the aerospace industry as well as in mold and tool making. One previously successful method to tackle this challenge is the stochastic optimization procedure Evolutionary Strategy (ES). Utilizing an appropriately chosen objective function, the search for a suitable vector of input parameters may be formulated as a mathematical minimization problem over the parameter space. The ES with a covariance matrix adaption (CMA) was utilized to sample from this parameter space in a stochastic manner. Examining the impact of the CMA within an ES is a promising way to gain better insight into the performance of ES. For this purpose, a vector of input parameters was optimized for a drilling EDM process with a comma and a nested comma ES with CMA. It was found that the comma ES led to a reduction in erosion duration tero of 38 % compared to the initially chosen parameters and the nested comma ES led to a reduction in erosion duration tero of 27 % compared to the same initial parameters. The additional information stored in the covariance matrix enables the ES to find a local optimum of the parameter vector faster and more consistently. This fact is verified by use of visualizations of the covariance matrix on a two-dimensional subspace. From these findings it can be concluded, that for the application of the ES to the optimization of EDM processes the CMA should be performed continuously over all generations as opposed to resetting this matrix after a number of generations.