The paper describes results of a sensitivity study on an optimum mooring cost as a function of safety factor and allowable maximum offset of the offshore floating structure by finding the anchor leg component size and the declination angle. A harmony search (HS) based mooring optimization program was developed to conduct the study. This mooring optimization model was integrated with a frequency-domain global motion analysis program to assess both cost and design constraints of the mooring system. To find a trend of anchor leg system cost for the proposed sensitivity study, optimum costs after a certain number of improvisation were found and compared. For a case study a turret-moored FPSO with 3 ${ imes}$ 3 anchor leg system was considered. To better guide search for the optimum cost, three different penalty functions were applied. The results show that the presented HS-based cost-optimum offshore mooring design tool can be used to find optimum mooring design values such as declination angle and horizontal end point separation as well as a cost-optimum mooring system in case either the allowable maximum offset or factor of safety varies.