Current service and installation activities for offshore wind turbines are carried out by jack-up vessels, which eliminate wave disturbances to a large extent. The use of these vessels imposes several disadvantages, including high operational costs and the limitation of operating in restricted water depths. An alternative is a crane mounted on a floating vessel (monohull), which is quicker in operation and multi-deployable. With these vessels, however, a motion compensator is needed to eliminate most of the hydrodynamic disturbances. The purpose of this graduation assignment is to develop a concept design for a passive motion compensator (PMC) to isolate the vessel motion from the payload. This goal is achieved by the implementation of a multi-objective optimization algorithm based on genetic programming (GP) that constructs a two-dimensional PMC based on the principle of quasi-zero stiffness. The GP employs a set of genetic operators to explore the design space in terms of topology and design variables, which effectively mimics Darwin’s Theory of Evolution. The better a mechanism performs, the higher the fitness, and thus the higher the chance this design appear in future generations. Each design is a composition of cylinders and nodes that are assembled into a mechanism. During the fitness evaluation, all mechanisms are examined by a nonlinear finite element method to extract the force-displacement relations. The arc-length control method is used due to the large displacements and rotations of the members in the mechanism, whereby both the nodal displacement vector and external load vector are varied to follow an equilibrium path in an incremental-iterative way. To provide sufficient support to the payload, the mechanism is prestressed, which is applied by using the arc-length procedure as well. Static and dynamic results show that the GP is suitable for constructing a high-level planar QZS mechanism for the intended application in various sea states. From multiple runs, it can be concluded that the optimizer generally produces designs with the same topology. Dynamic analyses in the time domain show that motions are effectively mitigated in the horizontal and vertical directions for the chosen designs. In addition, analysis in the frequency domain shows that the mechanisms effectively attenuate motions in the frequencies of interest.