An improved system and method is provided for searching a collection of objects that may be located in hierarchies of auxiliary information for retrieval of response objects. A framework to perform a generalization search in hierarchies may be used to generalize a search by moving up to a higher level in a hierarchy of taxonomies or to specialize a search by moving down to a lower level in the hierarchy of taxonomies. Once the system may decide to enumerate response objects at a particular level of generalization, a budgeted generalization search may be used for enumerating a set of response objects within a budgeted cost.