It is generally admitted that several models differing along various dimensions are needed for executing complex engineering tasks such as diagnosis and monitoring. A key problem is thus to decide what model to use in a particular situation in front of a specified problem-solving task and reasoning objectives. We address this problem within the Multimodeling framework for reasoning about physical systems that we proposed in a previous work. After having characterized the space of possible models in the Multimodeling approach, we formulate the selection problem using the conceptual tools offered by the economic theory of rationality. In this frame we illustrate a preference-based model selection method that is used to navigate in the universe of available models of a system searching for the model that best matches a given task and reasoning objectives. The method exploits the use of a model map that is a metalevel concept representing the ontology and teleology of each model and the transformational relations (abstractions and approximations) connecting each model to other models. The model map is used to compare models on the basis of their content and to understand what can be gained or lost when switching from one model to another. Finally, some implications of the foregoing selection method in developing action-based diagnostic systems are discussed.