Although the case-based reasoning (CBR) process is domain dependent, certain aspects of it can readily be captured into a generic framework which in turn can be applied to various engineering domains. One such exercise that has been carried out is described here. In this paper, we present the notion that CBR can be formalized and applied in a specialized framework in an integrated knowledge-based environment. We first analyze the CBR process to abstract the steps involved in the development of a CBR system. We then propose a framework in which most of these steps are formalized so that they can be applied in a domain-independent manner. The salient features of this framework, called CASETOOL (CASE-based reasoning TOOL-kit), are then described. The highlight of this approach is the use of a concept called design criticism in the CBR process. The versatility of the tool is demonstrated through an application from the bridge engineering domain.

Interval arithmetic has been extensively applied to systems of linear equations by the interval matrix arithmetic community. This paper demonstrates through simple examples that some of this work can be viewed as particular instantiations of an abstract “design operation,” the RANGE operation of the Labeled Interval Calculus formalism for inference about sets of possibilities in design. These particular operations promise to solve a variety of design problems that lay beyond the reach of the original Labeled Interval Calculus. However, the abstract view also leads to a new operation, apparently overlooked by the matrix mathematics community, that should also be useful in design; the paper provides an algorithm for computing it.

This paper defines, develops algorithms for, and illustrates the utility in design of a class of mathematical operations. These accept as inputs a system of linear constraint equations, Ax = b, an interval matrix of values for the coefficients, A, and an interval vector of values for either x or b. They return a set of values for the “domain” of the other vector, in the sense that all combinations of the output vector values set and values for A, when inserted into the constraint equation, correspond to values for the input vector that lie within the input interval. These operations have been mostly overlooked by the interval matrix arithmetic community, but are mathematically interesting and useful in the design, for example, of structures.

This paper defines, develops algorithms for, and illustrates the design use of a class of mathematical operations. These operations accept as inputs a system of linear constraint equations, Ax = b, an interval matrix of values for the coefficients A, and an interval vector of values for either x or b. They return a set of values for the other variable that is “sufficient” in this sense. Suppose that ◯ is an interval of input vectors, and  an interval matrix. Then, one Sufficient-Points operation returns a set of vectors ~ such that for each b in ~, the set of x values that can be produced by inserting all the values of  into Ax = b is a superset of the input vector x. These operations have been partly overlooked by the interval matrix mathematics community, but are mathematically interesting and useful in the design, for example, of circuits.

Current design practices mandate that engineering designs be evaluated based on multiple attributes, e.g., cost, power, and area. For multiattribute design problems, generation and evaluation of the Pareto optimal set guarantees the optimal design will be found, but is not practical for a large class of problems. Iterative techniques can be applied to most problems, but sacrifice optimality. In this paper, we introduce a new technique that extends the set of design problems that can be solved optimally. By first constructing an imprecise value function, the number of nondominated alternatives that must be generated is reduced. We describe an implementation based on combinatorial optimization and constraint satisfaction which achieves additional performance gains by decomposing the value function to identify dominated design-variable assignments. Test results indicate that our approach extends the set of problems that can be solved optimally.

This paper extends previously developed generalized set propagation operations to work over relationships among an arbitrary number of variables, thereby expanding the domain of engineering design problems the theory can address. It then narrows its scope to a class of functions and sets useful to designers solving engineering problems: monotonic algebraic functions and closed intervals of real numbers, proving formulas for computing the operations under these conditions. The work is aimed at the automated optimal design of electro-mechanical systems from catalogs of parts; an electronic example illustrates.