Logic-based Multi-Objective Optimization for Restoration Planning

After a disruption in an interconnected set of systems, it is necessary to restore service. This requires the determination of the tasks that need to be undertaken to restore service, and then scheduling those tasks using the available resources. This paper discusses combining mathematical programming and constraint programming into multiple objective restoration planning in order to schedule the tasks that need to be performed. There are three classical objectives involved in scheduling problems: the cost, the tardiness, and the makespan. Efficient solutions for the multiple objective function problem are determined using convex combinations of the classical objectives. For each combination, a mixed integer program is solved using a Benders decomposition approach. The Master Problem assigns tasks to workgroups, and then subproblems schedule the tasks assigned to each workgroup. Hooker has proposed using integer programming to solve the master problem and constraint programming to solve the subproblems, when using one of the classical objective functions. We show that this approach can be successfully generalized to the multiple objective problem. The speed at which a useful set of points on the efficient frontier can be determined should allow the integration of the determination of the tasks to be performed with the evaluation of the various costs of performing those tasks.