3.2. Optimization Problems
An optimization problem is a problem in which certain parameters (design variables) need to be determined to achieve the best measurable performance (objective function) under given constraints. In Section 3.1, we introduced the basic idea of design optimization using a very simple beer can example. The design problem is straightforward to formulate, analytical expressions are available for the objective and constraint functions, and the optimal solution is obtained graphically. Although the simple problem illustrates the basic concepts of design optimization, in reality, design problems are much more involved in many aspects, including problem formulation, solutions, and results interpretation.