Why simple optimization doesn't help
Often, we cannot simply throw design criteria to an optimizer and use the optimum design that it suggest. In practice, design optimization is a decision making process that requires not only finding the best solution but also confidence in that solution. It is desirable if we can "see" the whole design space and see where the optimal design is, and make sure the optimal design is globally optimum. A simple optimization algorithm fall short of those practical requirements.
This is the way to go
A better way is to use DOE to generate enough probing points to build a surrogate representation of the design space, and then visualize, study and optimize quickly on the surrogate design space. The whole process is made easy with Maxflow and captured in the following YouTube video: