Part-selection triptych: A representation, problem properties and problem definition, and problem-solving method TIMOTHY P. DARR 1 and WILLIAM P. BIRMINGHAM 2 Artificial Intelligence Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, 1101 Beal Avenue, Ann Arbor, MI 48109 (Received September 1, 1998; Accepted September 8, 1999! Abstract In part-selection problems, parts are selected from catalogs and connected to meet the following problem require- ments: functionality, specifications, and constraints. This paper formally defines the part-selection problem, enumer- ates a set of design properties that are useful during a search for a design solution, and provides an algorithm for solving part-selection problems based on a novel set of operators for manipulating portions of the design space. Keywords: Part selection; Constraint-satisfaction; Design; Optimization; Configuration 1. INTRODUCTION Many products today are designed using “components off the shelf” ~COTS!. These products can range from sophis- ticated computer systems, to aircraft subsystems, to soft- ware systems, to integrated circuits ~e.g., “intellectual property” modules!, and even to buildings. With the prolif- eration of “electronic” catalogs, we expect that increasingly more products will be designed with COTS. In general, designing with COTS is an example of a com- monly occurring, fundamental class of engineering-design problems called the part-selection problem. In these prob- lems, parts are selected from catalogs and connected to meet the following problem requirements: functionality, specifi- cations, and constraints. Functionality defines what the ar- tifact is supposed to do; specifications define optimality conditions; and, constraints define the feasibility relation- ships that must be satisfied for the artifact to operate cor- rectly. An artifact that satisfies these requirements is a solution to the design problem. In contrast with configuration ~ Darr & Dym, 1997!, the part-selection problem does not include part arrangement. As such, part selection is a subset of the more general con- figuration problem. Even though, as we show in this paper, part selection is a very difficult modeling and computa- tional problem. The results given in this paper apply di- rectly to configuration problems, since configuration requires part selection. In this paper, we aim to do the following things: • Provide a new and comprehensive formal representa- tion for part-selection problems that extends previous ~related! problem representations, yet is compact with well-defined semantics. • Describe several important properties about part- selection problems and solutions. These properties, combined with our representation, help to uncover struc- ture in the problem that can be exploited to create heu- ristics. An example of this is the “boundary” part, defined later in this paper, which eliminates search dur- ing problem solving. Further, the representation pro- vides a basis to rigorously compare various problem- solving approaches to the part-selection problem. • Provide a new solution method that effectively ex- ploits our novel “attribute-space” representation. This solution method suggests a family of efficient problem solvers. Reprint requests to: Timothy P. Darr. 1 Now at Trilogy Development Group, 6034 West Courtyard Drive, Aus- tin, TX, 78730. 2 All editorial decisions regarding this paper were made by the Editor Emeritus, Clive Dym. Artificial Intelligence for Engineering Design, Analysis and Manufacturing ~2000!, 14, 39–51. Printed in the USA. Copyright © 2000 Cambridge University Press 0890-0604000 $12.50 39