Use of Constraint Programming for Design

Abstract

Three families of methods coexist for managing (i.e. representing and propagating) uncertainty of product data during the preliminary design, namely: fuzzy methods, probabilistic methods and Constraint Programming (CP) methods. CP methods over reals are, up to now, the less frequently used approaches, but they are worth further study for use in design engineering thanks to a number of good properties and 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, 3B-weak, 3B}-consistency methods in the context of the preliminary design of mechanical products where large variable domains are considered and a representation of the remaining consistent design space turns out to be of practical interest to support the designers’ understanding and decision making. A measure for comparing the level of consistency of the methods is then proposed in the context of engineering design. It consists of a pairwise comparison of the overlapping part of the remaining design spaces for a given splitting grain size. Numerical results are established for an example of a combustion chamber design with 6 variables and 12 constraints. Next, a sensitivity analysis of the consistency of the previous methods is performed in regards to a variable splitting grain size. Experiments have been performed on a research platform including up-to-date NCSP methods. The paper concludes that NCSP methods are not easy-to-use and that the designer must be aware of a number of concepts so as to select the best choices in the resolution strategies.