Simulated annealing is an attractive, but expensive, heuristic method for approximating the solution to combinatorial optimization problems. Attempts to parallel simulated annealing, particularly on distributed memory multicomputers, are hampered by the algorithm's requirement of a globally consistent system state. In a multicomputer, maintaining the global state S involves explicit message traffic and is a critical performance bottleneck. To mitigate this bottleneck, it becomes necessary to amortize the overhead of these state updates over as many parallel state changes as possible. By using this technique, errors in the actual cost C(S) of a particular state S will be introduced into the annealing process. This paper places analytically derived bounds on this error in order to assure convergence to the correct optimal result. The resulting parallel simulated annealing algorithm dynamically changes the frequency of global updates as a function of the annealing control parameter, i.e. temperature. Implementation results on an Intel iPSC/2 are reported.