Many mesh optimization applications are based on vertex repositioning algorithms (VrPA). The execution times of these numerical algorithms vary widely, usually with a trade-off between different parameters. In this work, we analyze the impacts of six parameters of sequential VrPA on runtime. Our analysis is used to propose a new workload measure called number of mesh element evaluations. Since the execution time required for VrPA programs may be too large and there is concurrency in processing mesh elements, parallelism has been used to improve performance efficiently. The performance model is extended to parallel VrPA algorithms that are implemented in MPI. This model has been validated using two Open MPI versions on two distributed-memory computers and is the basis for the quantitative analysis of performance scalability, load balancing and synchronization and communication overheads. Finally, a new approach to mesh partitioning that improves load balancing is proposed.