The Doctor Rostering Problem - Asser Fahrenholz

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 con-
struction 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: