Estimating the Parameters in a Mathematical Product Design Model

Abstract

Mathematical approaches for solving product designs problem can be used by not only elder designers who have implicit/ambiguous knowledge of design experienced, but also younger designers even they have not so much experience, because such mathematical methods lead designers to obtain an optimal design automatically. However, there is a very serious lake to use such optimal methods in practice where the optimal solution has been obtained by a set of given coefficient parameters, which are so hard to be fixed accurately by even those most-experienced designers. In this paper,a set of simultaneous equations is built to represent the relations between product designs and correlative category labels. Parameter estimation is to fix the parameters that making all of relations to be feasible. A Boltzmann machine algorithm with belief propagation is used to perform the parameter estimation, where the number of simultaneous equations may be less than the number of parameters, to be solved possibly. Numerical experiments are provided to show the efficiency and utility of the algorithm. As a result, the value of training error is approaching to 0 slowly and stably, so it can be foresaw that parameters are estimated.