The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 8. Future considerations 55 in the solution, a value of the contribution to the objective function is stored (both violations of hard constraints, but also the objective function value contribution). Algorithm 8.1 outlines a possible implementation of a delta function for equation H0. Algorithm 8.1 Delta function H0 - require: schedule S ∆H0 = 0 Set ← Select random shifts from S for all Shifti in Set do Shift2 ← S.getNextShift(Shifti) if Shifti.getDoctor()= Shift2.getDoctor() then ∆H0 = ∆H0 + 1 end if end for Return ∆H0 ∆H0 is then the amount of shifts in the new neighborhood that are violating constraint H0. Similar rules could be devised for the rest of the constraints, keeping hard constraints violations separated from soft constraints objective function value contribution. The total ∆ (over all constraints) could then be compared to that of the contribution made by the shifts affected by the neighborhood. 8.3 GRASP learning A simple way to improve the GRASP algorithm used in this project would be to incor- porate one or more of the learning mechanisms described in section 4.3.3. One way to do this would be to track the (shift,doctor)-assignment that violates one or more rules and bias that specific assignment such that GRASP would be more inclined not to perform the same assignment in the next iteration. Expanding on this, could be more biasing towards (shift,doctor)-assignments that violate more or less rules than other (shift,doctor)-assignments. The bias-function could then be introduced through a ranking, where a higher rank means less violations and higher priority, or a probability distribution, with a probability for each assignment based on the average number of rules it violated in the previous iterations of GRASP (and perhaps how many violations it produces in the current). 8.3.1 GRASP stop criterion An improvement, other than those presented in section 4.3.3, to the GRASP implementation is that of another stop criterion. As concluded in chapter 7, the GRASP
Chapter 8. Future considerations 56 algorithm may end an iteration even though it has improved the incumbent solution in the last LS-iteration. As such it could lead to faster convergence if the stop- and restart criterias was to be changed from time/iterations to ’time/iterations since improvement’. 8.4 SA extensions The core property of Simulated Annealing is the opportunity to escape local optima, in search for global optima, done through the Metropolis criteria (see the Metropolis criterion on page 26). The current implementation of the Update(T )-function, makes sure that T converges towards a defined end-temperature, as time progresses. But, as the main feature of the temperature is to allow escape of local optima, it could make sense to actually increase the temperature if no improvements to the incumbent had been found in a certain amount of time. This would allow for much more inferior solutions to be accepted, if such are needed to escape the local optima, in which SA finds itself. Following this, an update to the α is also needed, seeing as temperature must converge towards the end-temperature near the end of Simulated Annealing. As such, some quick math could be done to decrease α by a certain amount, in order to ensure this convergence.
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TECHNICAL UNIVERSITY OF DENMARK The
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TECHNICAL UNIVERSITY OF DENMARK Abs
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Acknowledgements Foremost, I would
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Contents vi 4.3.1 A construction he
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List of Figures 4.1 The transformat
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List of Algorithms 4.1 Adaptive gre
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Chapter 1. Introduction and problem
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Page 41 and 42: Chapter 4. Solving the DRP 30 Simul
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Page 45 and 46: Chapter 6 The DRP Program Through t
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Page 69 and 70: Chapter 9. Conclusion 58 The three
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Appendix C. Tests 106 Test 1 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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The Doctor Rostering Problem - Asser Fahrenholz

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