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.

Engineering systems require considering technical, social, economic, and environmental issues on a large and interconnected scale. Addressing engineering systems problems challenges the limits of analytic methods; this paper focuses on optimization as the method. Traditional normative optimization addresses objective trade‐off issues by quantifying the relationships among decision‐maker choices and system performance. Engineering systems can present options and trade‐offs that are outside traditional analysis boundaries and often require different domain expertise. The usual response is to expand the frame of analysis, relying on expert heuristic rules of thumb to make the task manageable. However, these heuristics can create irrelevant constraints, lead to cognitive biases, or result in unnecessarily suboptimal solutions. This paper presents an initial framework to encourage explicit examination of decisions made when framing and formulating an engineering systems‐relevant optimization problem. This includes consciously determining when to keep heuristics for efficiency and when to replace them with a more normative approach. The paper provides two examples that use optimization in two different roles. The first uses an optimization problem in a simulation tool that predicts future CO2 emissions from commercial aviation for scenarios with different technology and economic inputs. The second example is based on an actively controlled wind turbine and demonstrates how a reasonable‐seeming heuristic for defining the objective can lead to a result that is suboptimal in terms of the true system performance objective. These examples demonstrate the explicit examination of the framing and formulation to achieve a good combination of normative and heuristic approaches.

Procedure-based design is well-established, supporting engineers via expert knowledge codified in resources such as handbooks, tables, and heuristic if-then rules of thumb. These procedures enable even inexperienced designers to benefit from the knowledge obtained by more experienced counterparts through years of practice and discovery. While procedural approaches have many advantages, they do have limitations. They tend to produce only satisficing, rather than optimal, solutions. In addition, they are based on historical designs, so offer little assistance for new system types, and are often descriptive rather than normative in nature. In contrast, normative methods — such as constrained optimization — can resolve many of these issues, but at the cost of significant development effort. Here we present a synergistic hybrid strategy with the objective of capitalizing on established procedure-based design methods for a subset of design problem elements, while incorporating normative strategies for the remaining elements. A design procedure is analyzed to identify steps that involve specification of design variables, and a subset of rule-based steps that could be replaced with optimization algorithms. A single-stage spur gear train design example is used to illustrate this process, and for comparing alternative hybrid solution strategies. Initial results indicate that solution quality can be improved significantly over purely procedure-based design when incorporating limited optimization elements, while maintaining a reasonable level of additional modeling effort.