Estimation of a suitable window shape and appropriate weights in weighted median filters is one of important problems. In this study, we formulate the design of weighted median filter as an optimization problem, and estimate optimal filters directly from degraded images. In our previous work, we estimated optimal window shapes and weights by using a Genetic Algorithm (GA) with a fixed size of window as a constraint in optimization. To determine an appropriate window size is difficult but essential since it depends on both a type of texture and a noise rate. Here, we optimize weighted median filters without the constraint in the size of filters. Numerical experiments show that our method design a filter with a suitable size to both a size of pattern in textures and the noise rates. In addition, we compare the designed filters with the filters obtained by conventional supervised design and another unsupervised design methods.