The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 4. Solving the DRP 21 Figure 4.4: The rotation principle this neighborhood and it would then populate the shifts itself. This would then be similar to the random initial solution. Figure 4.5: The inversion principle For each of them, it applies that a random set of shifts are selected, upon which the function is carried out. One immediate advantage of these neighborhoods, is that they are simple and easy to implement. The implementation of these can be found in appendix A.1. Nielsen [17] also implements the inversion and rotation, which is similar to the insert, delete and replace moves in the neighborhoods chosen in Meisels and Schaerf [16]. Both rotation and inversion can be translated to a combination of replace moves. Other than these sources, very few authors in the literature describe their neighborhood functions in-depth. This may be due to how the structure and nature of problems often limits the choices in neighborhoods to a degree, where the choice seems obvious. It is important to recognise that the generation of neighbors is a factor in the running time of the entire search. As such, I have placed an upper limit on how many shifts are randomly selected and used in the neighborhood.
Chapter 4. Solving the DRP 22 Since the two neighborhoods described above are both based on a set of randomly chosen shifts and we are dealing with a relatively large problem, search exhaustion of the neighborhoods in any reasonable amount of time is impossible. As one of the goals of this project is to reach a relatively good solution within a relatively short amount of time, LS needs another stop-criterion. Two very common criteria are time and iterations (neighborhoods explored), which is implemented in this project. A less common criteria, also worth noting, is stopping LS after a certain amount of time has passed without any improvements to the incumbent solution. For a minimisation problem algorithm 4.2 lists the basic LS. Algorithm 4.2 Local Search - require: schedule S S ← S while ¬Stop do S ← choose S from N(S) if z( S) < z(S) then S ← S end if end while If the N(S) function selects random neighbors, then the LS in algorithm 4.2 is called a random improving search, moving to the first (randomly selected) solution that im- proves the value of the incumbent. Contrary to this approach, there is also the best improving search, where all members of the neighborhood is inspected and the best is chosen (Nielsen [17], Resende and Feo [19]) and first improving, where the neighbors are investigated systematically and the first one to improve the incumbent is chosen (Nielsen [17]). When LS is only accepting better solutions, it can suffer the fate of getting stuck in a local optimum. To get out of these, and hopefully move on to a global optimum, several techniques exist that allows Local Search to leave a better solution for a worse, in hope of eventually finding a new best solution. Three such techniques are GRASP, the Simulated Annealing (SA) algorithm and the Tabu Search (TS). The TS, originally presented in its final form by Glover [11], enables the search to accept non-improving solutions, while cycling back to previously explored solutions is prevented through the Tabu List containing the most recent solutions visited. While both TS and Simulated Annealing can require extensive parameter tuning for desired results to be reached, GRASP requires little to none. GRASP and Simulated Annealing was chosen and will be described in the following sections.
Page 1 and 2: TECHNICAL UNIVERSITY OF DENMARK The
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Page 5 and 6: Acknowledgements Foremost, I would
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Appendix B GAMS Model This chapter
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Appendix C. Tests 88 C.1.1 Instance
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Appendix C. Tests 94 JST PZH HP SDA
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Appendix C. Tests 100 Cons 12 Imps
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Appendix C. Tests 102 Test 3 RCL 1
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Appendix C. Tests 116 160 140 120 1
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Bibliography 118 [10] Michael R. Ga
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