In multiobjective design optimization problems, the designer may know that some objectives are harder to extremize than others or that some regions of the objective space are more desirable/important. Such useful information can be incorporated into the genetic algorithm optimization procedure by treating the more challenging/important objectives as constraints whose ideal values are adaptively improved/tightened during the procedure to guide the search. Employing this adaptive constraint strategy and a morphological representation of geometric variables, a genetic algorithm was developed and evaluated through special 'Target Matching' test problems which are simulated topology/shape optimization problems with multiple objectives and constraints.