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Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.

Reverse engineering is the process of extracting information about a product from the product itself. An estimate of the barrier and time to extract information from any product is useful for the original designer and those reverse engineering, as both are affected by reverse engineering activities. The authors have previously presented a set of metrics and parameters to estimate the barrier and time to reverse engineer a product once. This work has laid the foundation for the developments of the current paper, which address the issue of characterizing the reverse engineering time and barrier when multiple samples of the same product are reverse engineered. Frequently in practice, several samples of the same product are reverse engineered to increase accuracy, extract tolerances, or to gather additional information from the product. In this paper, we introduce metrics that (i) characterize learning in the reverse engineering process as additional product samples are evaluated and (ii) estimate the total time to reverse engineer multiple samples of the same product. Additionally, an example of reverse engineering parts from a control valve is introduced to illustrate how to use the newly developed metrics and to serve as empirical validation.

Reverse engineering is a common design strategy in industry. It is a term that has come to encompass a large array of engineering and design activities in the literature; however, in its basic form, reverse engineering is simply the process of extracting information about a product from the product itself. Depending on its use, it may or may not be advantageous to utilize a reverse engineering strategy. As with any rational decision, reverse engineering is only favorable when the benefits from its use outweigh the investment. Therefore, a general understanding of the principles that increase the difficulty or investment required to reverse engineer mechanical products would be helpful for everyone affected by reverse engineering activities. In this paper, we articulate and explore these fundamental principles by reviewing several examples from the literature and from our own experience. We then use the principles as a basis for the development of a methodology to build barriers to reverse engineering into new products, and provide a simple example to illustrate its use.