This paper describes the integration of topology optimization with sizing, shape, and other types of optimization. Engineers and designers who use multiple types of optimization, have typically used topology optimization for preliminary designs and then used sizing and/or shape optimization to further refine their designs. Considering that usage, we originally implemented topology as a separate type of optimization. In the last decade we have implemented more advanced types of sizing and shape optimization. These types are topometry, topography, and freeform which like topology optimization have also been used for preliminary designs. Some of the users of these types of optimizations have found the need for a merged solution where topology and the other types of optimization can be used simultaneously. In response to this need, we have integrated topology with the other types of optimization. This paper describes the use of the approximation concepts approach to efficiently solve the mixed topology, shape, sizing, topometry, topography, and freeform optimization problem. This work has already been implemented in the structural optimization program GENESIS. Several examples, that show the benefits of the integration, are presented. One example will demonstrate the integration of topology and size optimization. Another example will demonstrate the integration of topology and shape optimization. Finally, an example that shows the integration of topology and freeform is presented.