Dynamic Constraint Propagation with Continuous Variables

which connict with them are activated. Thus, in example a) of Figure 5, new values for feasible and preferred intervals of Pier-width are found by propagating the constraint from Beam-depth. Preferences represent optimal values, and the closer the value is to the preference the better the criterion is adhered to. When preferences are in connict, they are therefore not dropped, but weakened so that the preferred value becomes the feasible value closest to the interval deened by the preference constraint. Thus, in example b) of Figure 5, the preferred interval of Pier-width is now set to 2.4..2.4], an interval representing the value which is closest to the interval de-ned by the preference constraint. In a later propagation step, this single preferred value may propagate to also x a single value for Beam-depth, as shown in the gure. In both examples of Figure 4 and Figure 5, the label of Beam-depth stays intact even after connict resolution. This assumes that it does not depend on the values for Pier-height and Pier-width. If there is such a dependency, our system follows the truth maintenance algorithm of Doyle (DOY79]) and withdraws the support of all consequences of the revised variables. In the example, the resulting contexts would then be identical to the ones shown, but lack all assertions about the variable Beam-depth which would have to be rededuced. 5 Conclusions We have presented an algorithm for dynamic constraint satisfaction with continous variables, an important problem which has not been addressed in the literature. We have shown that the nature of the problem in continous domains is diierent from discrete domains. In particular, the unbounded nature requires an incremental construction and solution of the constraint network. Contrary to common belief, few published techniques for constraint propagation are applicable to continous domains, and we hope that the topic will receive more attention by the research community in the future. The incremental solution means that the nal results depends essentially on the order in which solutions are generated. Our algorithm provides defaults and preferences as a means to specify heuristics for controlling this ordering. This control is important in view of the fact that realistic design problems are too complex to model domain constraints completely and accurately, and heuristics are necessary to ensure that the result is actually useful. The algorithm we have developed has been implemented as a central element in an intelligent CAD system …