Processing time estimations by variable structure TSK rules learned through genetic programming

Accuracy in processing time estimation of different manufacturing operations is fundamental to get more competitive prices and higher profits in an industry. The manufacturing times of a machine depend on several input variables and, for each class or type of product, a regression function for that machine can be defined. Time estimations are used for implementing production plans. These plans are usually supervised and modified by an expert, so information about the dependencies of processing time with the input variables is also very important. Taking into account both premises (accuracy and simplicity in information extraction), a model based on TSK (Takagi–Sugeno–Kang) fuzzy rules has been used. TSK rules fulfill both requisites: the system has a high accuracy, and the knowledge structure makes explicit the dependencies between time estimations and the input variables. We propose a TSK fuzzy rule model in which the rules have a variable structure in the consequent, as the regression functions can be completely distinct for different machines or, even, for different classes of inputs to the same machine. The methodology to learn the TSK knowledge base is based on genetic programming together with a context-free grammar to restrict the valid structures of the regression functions. The system has been tested with real data coming from five different machines of a wood furniture industry.