The Doctor Rostering Problem - Asser Fahrenholz

Chapter 4. Solving the DRP 20
Given a schedule, a need to improve upon this schedule arises. This is where neighbor-
hoods comes in.
4.3.2 Neighborhoods and Local Search
To guide the search in finding better solutions, I introduce the well known term Neigh-
borhoods. A neighborhood is defined as:
N(S) = { solutions obtained by applying a single local transformation to S }
A neighbor is a potential replacement for a solution and need only vary from the solution
at hand by a single element. The whole set of replacements produced by some change
or function on the solution is called a neighborhood. The process of moving from one
solution to another in its basic form, is called Local Search (LS) and is, if exhaustive,
able to find a local optimum. Figure 4.3 shows how moving through the solution space
may increase and decrease the heuristic value of the solution. Only accepting solutions
with higher Z(S) is called hill climbing (and analogously hill descending).
Figure 4.3: Local and global optima
For any given problem, several possible neighborhoods often exist. The neighborhoods
identified in this thesis are, thanks to the nature of this problem, two very simple
functions:
Rotation is moving the doctor of all shifts to another shift in the set, such that all
doctors are moved in rotation. The principle is depicted in figure 4.4 on the next
page
Inversion is for all selected shifts, to populate the shifts with another doctor than the
one that is originally assigned to it. Figure 4.5 on the following page illustrates the
principle. One could pass an empty schedule to a Local Search algorithm using