In engineering design, many design problems have multiple constraints and objectives, which may be nondifferentiable. For this problem type, only zero-order solution methods are applicable. In this paper, we present a relaxed lexicographic pattern search method for solving this design problem type, where the objectives are preferenced in either an Archimedean or preemptive formulation. The Hooke-Jeeves (HJ) pattern search method is the basis of this method, which is implemented as the MORPS (Multi-Objective Randomized Pattern Search) algorithm. The HJ pattern search method is used because it requires only function values and has an intuitive graphical interpretation through which to gain insight into the nature of complex design spaces. A relatively new class of simultaneous product/process design problem utilizing virtual prototypes to support design for disassembly is introduced to motivate the need for the MORPS algorithm. An example, based on the design of an automotive center console for disassembly, illustrates the application of the MORPS algorithm.