Logic-based MultiObjective Optimization for Restoration Planning

  • Jing Gong
  • Earl E. Lee
  • John E. Mitchell
  • William A. Wallace
Part of the Springer Optimization and Its Applications book series (SOIA, volume 30)


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.


Schedule Problem Constraint Programming Master Problem Bender Decomposition Restoration Planning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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This research is supported by NSF grant CMS 0301661, Decision Technologies for Managing Critical Infrastructure Interdependencies


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Copyright information

© Springer-Verlag US 2009

Authors and Affiliations

  • Jing Gong
    • 1
  • Earl E. Lee
    • 2
  • John E. Mitchell
    • 3
  • William A. Wallace
    • 1
  1. 1.Department of Decision Sciences and Engineering SystemsRensselaer Polytechnic InstituteTroy
  2. 2.Department of Civil and Environmental EngineeringUniversity of DelawareNewark
  3. 3.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroy

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