ADTs (Abstract Data Types) have been known as a promising feature for extending the database applications to CAD/CAM and other engineering areas. This extension has brought a new dimension to query optimization. Conventional query optimization methods, which considers only joins as the dominant cost factor, are based on the belief that the executions of selections and projections basically take no time. However, in databases that support ADTs, this may not be true since the execution of a selection involving ADT functions may be very time-cosuming. Thus selections with ADT functions should not be considered as inexpensive operations in queries, and the conventional optimization heuristics should be enhanced to correspond to the appearance of the queries of this kind. In this paper, we show the possibility that semijoins can be used as an effective means to reduce the number of evaluations of an ADT function and consequently optimize queries containing expensive ADT selections. We suggest the enhancement of an conventional optimization heuristics by adding a semijoins pre-stage which is an additional component corresponding to expensive ADT selections. By this way, the applicable range of the conventional heuristics are extended to hold the ability of handling queries with ADT functions. Several optimization algorithms are given and some simulation results show the effectiveness of our methods.