Qualitative Model Evolution

A genetic algorithm is used for learning qualitative model* baaed on the QSIM formalism. Hierarchical representation enables formation of "submodels" relevant for induction of domain explanation. Daring the search for better coding of the candidates, in parallel with the search for better solutions, the sise and shape of candidate solutions are dynamically created. Optimisation is based on the maximisation of the number of examples covered by a candidate solution combined with the minimisation of the number of constraints used in the solution. The result of learning is a set of models of different specificity that explain all given examples. An experiment in learning a qualitative model of the connected container system (U-TUBE) is described in detail. Several solutions, equivalent to the original model, were discovered. 1 Introduction Qualitative models successfully provide domain knowledge for many qualitative reasoning tasks. It is also recognized [Feigenbaum, 1977] that it is very difficult for a domain expert to articulate his "know-how" into "say-how". Often, a domain model is not even known. One way to avoid this knowledge acquisition bottleneck is to provide a number of examples, from which a qualitative model of the domain can be automatically induced by means of machine learning techniques. A method for learning qualitative models of dynamic systems from examples using genetic algorithms is presented. This approach has been named Qualitative Model Evolution (QME). The problem, also known as system identification, is defined as follows: GIVEN examples and counterexamples of the system behavior, FIND a model that explains these examples. In this paper quantitative (i.e. numerical or differential equation) models are not considered. We are interested in qualitative models, where quantities are typically represented by a small set of qualitative values. Among several alternatives the QSIM formalism [Kuipers, 1986] was chosen for the representation of qualitative models because of its firm mathematical basis. Learning is considered to be an instance of a combinatorial optimization problem [Papadimitriou and Steiglitz, 1982], i.e. a pair (F, c), where F is a finite or countably infinite set of feasible solutions and is a cost function. The task is to find an , such that In our case, F is the set of all possible QSIM models in the given problem domain and c(f) is the number of examples correctly classified by the model / plus a bonus that decreases with the size of /. Genetic algorithms provide a robust framework for performing such …