Multicore

Pure R implementation, works on multicore machines.

Take advantage of the function mclapply (package multicore) to partition the job across multiple cores.

Generalizable

Mixed implementation, uses independent modular scripts to

1. Launch optimization
2. Perform optimization
   (# Collect results) [can be part of the launcher]

The advantage of this approach is that it can be used on a multicore machine or on iPlant's Condor cluster with minimal modifications. The core of this approach is on the script that performs the optimization. It should have externalized parameters: range for the lower bound, range for the upper bound, algorithm(s) and starting value.
The launcher script will partition the entire range into chunks that will be sent to different cores (via fork calls) and the output will be collected. Alternatively, the optimization script can write its output to files that can be then parsed and concatenated. The collect script should also produce the required graphical output.