Conference Paper

Minimal Perturbance in Dynamic Scheduling.

Source: DBLP

ABSTRACT This paper describes an algorithm, unimodular probing, conceived to optimally reconfigure schedules in response to a changing environ- ment. In the problems studied, resources may become unavailable, and scheduled activities may change. The total shift in the start and end times of activities should be kept to a minimum. This require- ment is captured in terms of a linear optimization function over lin- ear constraints. However, the disjunctive nature of many scheduling problems impedes traditional mathematical programming approaches. The unimodular probing algorithm interleaves constraint program- ming and linear programming. The linear programming solver is ap- plied to a dynamically controlled subset of the problem constraints, to guarantee that the values returned are discrete. Using a r epair strat- egy, these values are naturally integrated into the constra int program- ming search. We explore why the algorithm is effective and discuss its applicability to a wider class of problems. It appears th at other problems comprising disjunctive constraints and a linear o ptimiza- tion function may be suited to the algorithm. Unimodular probing outperforms alternative algorithms on randomly generated bench- marks, and on a major airline application.

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    ABSTRACT: Acknowledgments I would like to express my deep thanks to doc. Lud,ek Matyska and dr. Hana Rudov,a for supporting me in my work and motivating me. I would also like to thank to all fellows from the Laboratory of Advances Networking Technologies at the Faculty of Informatics, Masaryk University, for their help. My work was also continuously supported by the Ministry of Education, Youth and Sports of the Czech Republic under the research intent No. 0021622419, and by the Grant Agency of the Czech Republic with grant No. 201/07/0205 which I highly appreciate. Dalibor Klus,a,cek Contents
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    ABSTRACT: Constraint programming (CP) methods exhibit several parallels with branch-and-cut methods for mixed integer programming (MIP). Both generate a branching tree. Both use inference methods that take advantage of problem structure: cutting planes in the case of MIP, and filtering algorithms in the case of CP. A major difference, however, is that CP associates each constraint with an algorithm that operates on the solution space so as to remove infeasible solutions. This allows CP to exploit substructure in the problem in a way that MIP cannot, while MIP benefits from strong continuous relaxations that are unavailable in CP. This chapter outlines the basic concepts of CP, including consistency, global constraints, constraint propagation, filtering, finite domain modeling, and search techniques. It concludes by indicating how CP may be integrated with MIP to combine their complementary strengths.
    Handbook of Discrete Optimization, Edited by K. Aardal, G. Nemhauser, R. Weismantel, 01/2005: chapter Constraint programming: pages 559-600;