A Comparative Study of Constraint Programming Techniques Over Intervals in Preliminary Design

Abstract

Three families of methods coexist for managing uncertainty (i.e. representing and propagating) of the product data during the preliminary design stages, namely: fuzzy methods, probabilistic methods and Constraint Programming (CP) methods. CP methods over reals are, up to now, the least frequently used approaches but they are worth being studied further for a use in design engineering thanks to a number of satisfactory properties and to recent significant advances. They may be roughly considered as a collection of methods that are sophisticated evolutions of interval analysis. The objective of this paper is to assess four of these major methods (namely the {hull, box, weak-3B, 3B} filtering or consistency methods) in the context of the preliminary design of mechanical products where large variable domains are considered and a precise (consistent) representation of the remaining design space turns out to be of practical interest to support the designers’ understanding and decision making. A measure for comparing the degree of consistency of the methods is then proposed in the context of engineering design. It consists in pairwise comparing the overlapping part of the remaining design spaces, for a given splitting grain size. Numerical results are established in an example of the design of a combustion chamber (6 variables and 12 constraints). Next a sensitivity analysis of the consistency of the previous methods is performed with regards to a variable splitting grain size. Experiments have been performed on a research platform including up-to-date filtering methods. The paper concludes that the weak-3B filtering technique is a good trade off in design engineering since it provides a sufficiently consistent representation of the remaining design space for an acceptable computation time.