Logic-based Multi-Objective Optimization for Restoration
Planning
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Authors:
Jing Gong
DSES
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
gongj at rpi.edu
E. Lee
DSES
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
elee at udel.edu
John E. Mitchell
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
mitchj at rpi.edu
W. A.
Wallace
DSES
Rensselaer Polytechnic Institute
Troy, NY 12180 USA
wallaw at rpi.edu
Citation details:
Chapter 11,
Optimization
and Logistics Challenges in the Enterprise,
Springer, New York, 2009, edited by
W. Chaovalitwongse, K.C. Furman, and P.M. Pardalos.
Abstract:
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.
Keywords:
Constraint programming, Mixed integer programming,
Multi-Objective, Scheduling and planning
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