Automating the Construction of Patchers That Satisfy Global Constraints

Generate-and-test algorithms to solve con­ straint satisfaction problems are often ineffi­ cient , but can be constructed fairly easily by knowledge compilation techniques that con­ vert declarative problem knowledge and do­ main knowledge into a procedural format [Liew and Tong, 1987]. Current research is focus­ ing on methods to improve the efficiency of generate-and-test algorithms by completely in­ corporating local constraints into generators of parts of composite solutions [Braudaway, 1988]. More global constraints on multiple parts can­ not necessarily be incorporated into the part generators. Their satisfaction must be ensured in a different way. We describe an (unimplemented) method for transforming a generate-and-test algorithm into a generate-test-and-patch algorithm that efficiently hillclimbs toward a solution satisfy­ ing a particular global constraint. Our method is based on constructing an evaluation function from the global constraint, that reflects the "de­ gree" to which the constraint has been satisfied. Some of the steps in this method rely on categorizing the global constraint into a generic class. In this paper, the constraint classes on which we focus are quota-meeting and covering constraints. We illustrate the general approach by apply­ ing it to a simple generate-and-test algorithm for house floorplanning. We provide empirical results that corroborate our claim that the ef­ ficiency of the algorithm has been significantly improved. provided The opinions expressed in this paper are those of the authors and do not reflect any policies, either expressed or implied, of any granting agency. Room lengths must be at least minValue. Room widths must be at least minValue. Rooms have to be inside the house. Rooms must be adjacent to the house boundary. Rooms must not overlap. The rooms must completely fill the house space. 1 Introduction In this paper, we address part of the problem of compiling a declarative representation of a class of problems and knowledge relevant to solving it into an efficient problem-solving system. Example domain. We will use the domain of house floorplanning to illustrate several domain-independent ideas for addressing this research problem. Floorplans are arrangements of rectangular rooms in a rectangu­ lar house space. Rooms and houses are aligned with an integer-valued grid of points in a plane. The con­ straints in Figure 1 define a particular class of floorplan­ ning problems. The number of rooms, the dimensions of the house space, and minimum values for room lengths and widths are problem-specific parameters. [Liew and Tong, 1987] h as shown …