Optimization problem formulation framework with application to engineering systems

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.