Logic-based MultiObjective 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 chapter 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 classic objectives involved in scheduling problems: the cost, the tardiness, and the make span. Efficient solutions for the multiple objective function problem are determined using convex combinations of the classic objectives. For each combination, a mixed integer program is solved using a Benders decomposition approach. The master problem assigns tasks to work groups, and then subproblems schedule the tasks assigned to each work group. Hooker has proposed using integer programming to solve the master problem and constraint programming to solve the subproblems when using one of the classic 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.
KeywordsSchedule Problem Constraint Programming Master Problem Bender Decomposition Restoration Planning
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This research is supported by NSF grant CMS 0301661, Decision Technologies for Managing Critical Infrastructure Interdependencies
- 2.E.E. Lee. Assessing vulnerability and managing disruptions to interdependent infrastructure systems: A network flows approach. Ph.D. Thesis, Rensselaer Polytechnic Institute, 2006.Google Scholar
- 3.I.J. Lustig, J.F. Puget. Program does not equal program: Constraint programming and its relationship to mathematical programming. Interfaces, 31:29-53, 2001.Google Scholar
- 4.P.V. Hentenryck, L. Perron, J.F. Puget. Search and strategies in OPL. ACM Transactions on Computational Logic, 1:282-315, 2000.Google Scholar
- 7.J.N. Hooker. A search-infer-and-relax framework for integrating solution methods. In Roman Bartàk and Michela Milano, editors, Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR), pages 243-257. Springer, 2005.Google Scholar
- 8.J.N. Hooker. Logic-based Methods for Optimization: Combining Optimization and Constraint Satisfaction. John Wiley, 2000.Google Scholar
- 9.M. Pinedo. Scheduling: Theory, Algorithms and Systems. Prentice Hall, 2002.Google Scholar
- 15.J.N. Hooker. Integrated Methods for Optimization. Springer, 2007.Google Scholar
- 17.ILOG Inc. ILOG OPL Studio 3.7.1 Language Manual. ILOG Inc. Mountain View, 2002.Google Scholar
- 18.ILOG Inc. ILOG OPL Studio 3.7.1 User’s Manual. ILOG Inc. Mountain View, 2002.Google Scholar
- 19.ILOG Inc. ILOG CPLEX 8.0 User’s Manual. ILOG Inc. Mountain View, 2002.Google Scholar