The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 4. Solving the DRP 23 4.3.3 The GRASP metaheuristic When heuristics come up short in the search for an acceptable solution, perhaps getting stuck in local optima, several improvements can be implemented. The improvement can be as simple as implementing a restart mechanism into the algorithm. The framework consisting of such ’outer’ mechanisms that guide heuristics are called metaheuristics. Burke and Kendall [4] defines a metaheuristics, referring to Glover and Laguna [12], as: . . . a master strategy that guides and modifies other heuristics to produce solutions beyond those that are normally generated in a quest for local op- timality. which is also implied in the name, derived from the prefix meta (beyond) and heuristic (to find). A metaheuristic is a general framework used when knowledge of the problem, that can be exploited, is sparse or if implementation of a problem-specific algorithm is impractical. It requires little to no information and as such, acts similar to a black box, taking a problem as input and if it can find one, gives a solution as output. The fact that metaheuristics are general search algorithms brings up the issue of whether there exists a better algorithm for the purpose of solving the problem. Whitley and Watson [25] concludes from Wolpert and Macready [26] that: For all possible performance measures, no search algorithm is better than another when its performance is averaged over all possible discrete functions. Which is the conclusion of applying the No Free Lunch theorem to search. Whitley and Watson [25] notes, much as Wolpert and Macready [27] concludes, that search algorithms need to be tailored to the problem, exploiting problem specific information as much as possible. The search algorithms in this project does not, as the above suggests, exploit problem specific information in the search for better solutions. The two neighborhood functions described in section 4.3.2 on page 20 can be enhanced to cater for the problem specific constraints, which is also suggested in section 8.2. The Greedy Randomized Adaptive Search Procedure (GRASP) is a metaheuristic. GRASP has very few parameters, namely a RCL parameter and a stop-criterion (commonly time or iterations) and as such is easy to implement. This allows the developer to put focus on implementing optimal data structures. GRASP is an iterative process, in which each iteration consists of two phases:
Chapter 4. Solving the DRP 24 1. Construction of an initial solution, using a given construction heuristic. In this project, the construction heuristic used in GRASP is the same as the adaptive greedy algorithm described above. The RCL parameter is used during the construction phase in the same manner, though, in more sophisticated versions of GRASP, the probabilistic when choosing the random element from the RCL can be influenced by a learning mechanism (more on this later). Resende and Ribeiro [20] defines the re-evaluation of the RCL list as the adaptive part of the algorithm. In this project, re-evaluation of the RCL does not occur as the RCL list is only created once per shift. 2. Local Search for a better solution. Over all iterations, the best incumbent solution is kept and at the end returned by the algorithm. The basic GRASP algorithm, for a minimisation problem, is listed in algorithm 4.3. Algorithm 4.3 GRASP - require: RCL parameter p S ← new empty schedule S ← ∅ while ¬ Stop do S ← Greedy(p, S) S ← Local Search( S) if z( S) < z(S) then S ← S end if end while One key point, as noted in Resende and Feo [19] and Resende and Ribeiro [20], of GRASP is that many initial solutions can be generated in the same amount of time that one LS takes to finish. The best of these random initial solutions are often better than the one found by LS. Resende and Feo [19] also notes that while a fully greedy RCL parameter (one that leaves only the best element in the RCL) may produce a good mean solution value, it is also often suboptimal. When relaxing the RCL parameter, the mean value degrades but the variance of the solutions found increases and thus leaves room for finding a solution that outperforms the mean of the fully greedy RCL parameter. While being a simple algorithm, GRASP still allows for a number of hybridisations. These enhancements are meant to remove or improve upon the shortcomings of the framework. One obvious flaw in the GRASP framework is the lack of memory usage. In the basic GRASP, all information is discarded between each iteration. Resende and Feo [19] identifies several enhancements that could well be classified as learning mechanisms. These include:
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Bibliography 118 [10] Michael R. Ga
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