This work proposes, implements and evaluates the FP-QIEA-R model as a new quantum inspired evolutionary algorithm based on the concept of quantum superposition that allows the optimization process to be carried on with a smaller number of evaluations. This model is based on a QIEA-R, but instead of just using quantum individuals based on uniform probability density functions, where the update consists on change the width and mean of each pdf; this proposal uses a combined mechanism inspired in particle filter and multilinear regression, re-sampling and relative frequency with the QIEA-R to estimate the probability density functions in a better way. To evaluate this proposal, some experiments under benchmark functions are presented. The obtained statistics from the outcomes show the improved performance of this proposal optimizing numerical problems.