COLLABORATIVELY SOLVING AN OPTIMIZATION PROBLEM USING FIRST AND SECOND OPTIMIZATION SOFTWARE EACH HAVING AT LEAST PARTIAL INFORMATION CONCERNING THE OPTIMIZATION PROBLEM

In one embodiment, a method is provided for collaboratively solving an optimization problem using at least first optimization software and second optimization software each having at least partial information concerning the optimization problem. The method includes: (1) determining a solution to a first sub-problem of the optimization problem using the first optimization software based on the at least partial information concerning the optimization problem known to the first optimization software; (2) communicating from the first optimization software to the second optimization software the solution to the first sub-problem and information concerning one or more penalties for deviating from the solution to the first sub-problem; and (3) determining a solution to a second sub-problem using the second optimization software based on the at least partial information concerning the optimization problem known to the second optimization software, the communicated solution to the first sub-problem, and the communicated information concerning one or more penalties for deviating from the solution to the first sub-problem.