Towards a conceptual design explorer using metamodeling approaches and constraint programming

Constraint Programming (CP) is a promising technique for managing uncertainty in conceptual design. It provides efficient algorithms for reducing, as quickly as possible, the domains of the design and performance variables while complying to the engineering and performance constraints linking them. In addition, CP techniques are suitable to graphically represent 3D projections of the complete design space. This is a useful capability for a better understanding of the product concept's degrees of freedom and a valuable alternative to optimization based upon the construction of an arbitrary preference aggregation function. Unfortunately, one of the main impediments for using Constraint Programming on industrial problems of practical interest is that constraints must be represented by analytical equations, which is not the case of hard mechanical performances - such as meshing and finite element computations - that are usually obtained after lengthy simulations. We propose to use metamodeling techniques (MM) to generate approximated mathematical models of these analyses which can be employed directly within a CP environment, expanding the scope of CP to applications that previously could not be solved by CP due to the unavailability of analytical equations. We show that there is a tradeoff between the metamodel fidelity and the resulting CP constraint tractability. A strategy to find this compromise is presented. The case study of a combustion chamber design shows amazingly that the compromise is to favor the simplest and the coarsest first-order response surface model.