This paper describes our preliminary results in applying constraint satisfaction techniques in a system we call TRANS-FORM for designing automatic automobile power transmissions. The work is being conducted in collaboration with the Ford Motor Company Advanced Transmission Design Department in Livonia, Michigan. Our current focus is on the design of the mechanical subsystem, but we anticipate extending this later to the electrical and hydraulic subsystems also. For simplicity, in the initial work reported here we restrict ourselves to the relatively well-explored class of transmissions having four forward speeds and one reverse speed, built from two planetary gearsets, cross-connected by two permanent links. Moreover, we pursue design of such transmissions only at the ‘kinematic level’. These two restrictions correspond to limiting respectively the breadth (generality) and the depth (detail or granularity) of the search space employed. We find that, at least for the restricted version of the problem pursued here, transmission design is an application very naturally formulated as a constraint satisfaction problem. Our present problem requires only 10 variables, with an average of about seven values each, and 43 constraints—making it similar in difficulty to about the 10-queens problem. So far, two of the classic transmissions, known as Axod and HydraMatic, have been rediscovered (at the kinematic level) by our program. Preliminary results also indicate that the constraint satisfaction framework will continue to remain adequate and natural even when the search space is allowed to be much broader and deeper. We expect that searches of such expanded spaces will soon lead to the discovery of totally new transmissions.

The complexity of mechanical design is reflected in the complexity of the design constraints which relate functional requirements to design parameters. Reformulations of the design constraints can significantly reduce this complexity. This is accomplished by a transformation to alternative design parameters, such as a critical ratio, a non-dimensional parameter, or a simple difference; e.g. the ratio of surface area to volume for heat transfer loss, the Reynold's number in fluid mechanics, or the velocity difference across a fluid coupling. We have developed a method by which the alternative parameters are chosen for physical significance and for the ability to create a more direct correspondence to functional behavior as determined by measures of serial and block decomposability of the constraints. Rules have been developed for the creation of physically significant new parameters from the algebraic combination of the original parameters. The rules are based on engineering principles and rely on knowledge about what a parameter physically represents rather than other qualities such as dimensions. A computer based system, called EUDOXUS, has been developed to automate this procedure. The system operates on a set of design constraints to produce sets of transformed constraints in terms of alternative design parameters. The method and its implementation have demonstrated successful results for many highly nonlinear and highly coupled parameterized designs from many mechanical engineering domains.

In this paper we present an application of AI search techniques to a class of problems that arise in transportation systems analysis. Rather than adapting the time-space network formulation typically used in Operations Research, we propose a discrete dynamic network to represent a scheduled service network. In a discrete dynamic network, there are finite, discrete, predetermined possibilities for moving from one vertex to another. Visiting a vertex has a cost (possibly zero), which may depend both on how the vertex was reached and how it will be left.

We describe the DYNET search algorithm for finding optimal paths in discrete dynamic networks. DYNET has been implemented in a working system (TRAINS) which searches the entire Dutch railway services network. An optimal path in a discrete dynamic network makes us arrive at our destination as early as possible (given our planned earliest departure time), and given this earliest arrival time (eat), will allow us to leave as late as possible, thereby guaranteeing a shortest path relative to the eat. DYNET first conducts a forward search to find the earliest possible arrival time, then a backward search which uses results of the forward search, to find the latest departure to arrive at that eat. Various AI techniques (symmetries, abstraction spaces, distance estimates, etc.) improve the performance of DYNET.