Commercial floating offshore wind projects are expected to emerge in the U.S. by the end of this decade. Currently, however, high costs for the technology limit its commercial viability, and a lack of data regarding system reliability heightens project risk. This work presents an optimization algorithm to examine the tradeoffs between cost and reliability for a floating offshore wind array that uses shared anchoring. Combining a multivariable genetic algorithm with elements of Bayesian optimization, the optimization algorithm selectively increases anchor strengths to minimize the added costs of failure for a large floating wind farm in the Gulf of Maine under survival load conditions. The algorithm uses an evaluation function that computes the probability of mooring system failure, then calculates the expected maintenance costs of a failure via a Monte Carlo method. A cost sensitivity analysis is also performed to compare results for a range of maintenance cost profiles. The results indicate that virtually all of the farm's anchors are strengthened in the minimum cost solution. Anchor strength is increased between 5 and 35% depending on farm location, with anchor strength nearest the export cable being increased the most. The optimal solutions maintain a failure probability of 1.25%, demonstrating the tradeoff point between cost and reliability. System reliability was found to be particularly sensitive to changes in turbine costs and downtime, suggesting further research into floating offshore wind turbine failure modes in extreme loading conditions could be particularly impactful in reducing project uncertainty.