Determining Optimal Model Complexity in an Iterative Design Process

In design, trade-offs are made between quality, cost and schedule. As the versatility of design tools has increased, so has the difficulty of making these trade-offs. This is especially true when choosing appropriate complexities for analytical and computational models. A fact known to designers and analysts is that more complex models yield more accurate results, but take longer to create and analyze. This paper shows that in an iterative design process there exists an optimal model complexity for each iteration, and alternatively, one optimal for the process as a whole. Quantitative methods for determining these complexities are developed, and three strategies for controlling the design modelling process are contrasted. Dependent on the stopping criteria, the best strategy will either minimize resource expenditure subject to quality requirements, or conversely, will maximize quality subject to resource constraints. These concepts are formalized with a view towards the design theory and methodology research community providing a first step in quantifying model trade-offs. An illustrative shape-optimal design example is shown wherein cost savings up to 84% were achieved. These savings were seen using several standard optimization algorithms. A customized optimization algorithm that incorporates this work should produce even better results.