Arc-elasticity and hierarchical exploration of the neighborhood of solutions in mechanical design

In most industrial design processes, the approaches used to obtain a design solution that best fits the specification requirements result in many iterations of the ''trial-and-error'' type, starting from an initial solution. In this paper, a method is proposed to formalize the decision process in order to automate it, and to provide optimal design solutions. Two types of knowledge are formalized. The first expresses the satisfaction of design objectives, relating to physical behaviors of candidate design solutions. This formalization uses three models, an observation one, an interpretation one and an aggregation one; every design solution is qualified through a single performance variable (a single objective function). The second model is related to modifications that may or may not be applicable to the pre-existing solution. The Designer is often able to define preferences concerning design variables. Some modifications related to this pre-existing solution, can be preferred to other ones. A hierarchy of design variables is proposed to formalize these preferences. The concept of arc-elasticity is introduced as a post-processing indicator to qualify candidate solutions through a trade-off between the performance improvement and their relative distances to the initial solution. The proposed method is used and applied to a riveted assembly, and a genetic algorithm is used to identify optimal solutions.