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.
[Show abstract][Hide abstract] ABSTRACT: Solving real-life planning, scheduling, and timetabling problems is usually an iterative process in which, after seeing the generated solution, users may change the problem constraints. This change requires producing a new solution which satisfies these constraints but not being too far from the original solution. This type of problem is called a minimal perturbation problem. The paper formally describes a minimal perturbation problem in the context of constraint satisfaction and it proposes a new depth-first search algorithm for solving a particular instance of the minimal perturbation problem.
[Show abstract][Hide abstract] 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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