In general, design optimization is a process that iterates through a range of design variables (plate thickness, beam cross section) to obtain an optimum result based on a set of objectives. A design optimization analysis will create a new model with the design variables set to the optimum values; it also produces the results for the optimized model, so the same type of results available in a normal analysis will be available for the optimized design.
A Design study is similar to an optimization analysis in that the design variables and objectives are specified. A design study will create charts that show how the objectives are affected by changing each of the design variables.
For details, refer to the page Setting Up and Performing the Analysis: Performing Design Optimization. For a step-by-step example, click the link below to the example that you want to see.