Developing and comparing alternative design optimization formulations for a vibration absorber example

In some cases, the level of effort required to formulate and solve an engineering design problem as a mathematical optimization problem is significant, and the potential improved design performance may not be worth the excessive effort. In this article we address the tradeoffs associated with formulation and modeling effort. Here we define three core elements (dimensions) of design formulations: design representation, comparison metrics, and predictive model. Each formulation dimension offers opportunities for the design engineer to balance the expected quality of the solution with the level of effort and time required to reach that solution. This paper demonstrates how using guidelines can be used to help create alternative formulations for the same underlying design problem, and then how the resulting solutions can be evaluated and compared. Using a vibration absorber design example, the guidelines are enumerated, explained, and used to compose six alternative optimization formulations, featuring different objective functions, decision variables, and constraints. The six alternative optimization formulations are subsequently solved, and their scores reflecting their complexity, computational time, and solution quality are quantified and compared. The results illustrate the unavoidable tradeoffs among these three attributes. The best formulation depends on the set of tradeoffs that are best in that situation.