The Doctor Rostering Problem - Asser Fahrenholz

Chapter 4. Solving the DRP 25
• Reactive GRASP in which the RCL parameter is automatically tuned in each it-
eration of GRASP, produces better results than a static RCL parameter. Resende
and Ribeiro [20] restates a formulation including a set of RCL parameters coupled
with a probability to choose that exact parameter. The probability for each pa-
rameter is reevaluated each iteration, using the average value of solutions found
through the parameter and the incumbent.
• Cost pertubation is an idea of maintaining a list of prizes corresponding to the
value of adding each element to the solution in the construction phase. This list
is then maintained by two different schemes: Pertubation by elimination, where a
fraction of the element prizes are set to zero, and Pertubation by prize changes, in
which each prize is changed by a factor produced by a parameter.
• Bias functions are probability distributions used to bias the selection of the RCL
elements.
• Intelligent construction: memory and learning that covers long-term memory, such
as the one used in Tabu Search.
• POP in construction, where a Local Search is applied during the construction of
the initial solution.
• Path-relinking, where paths between elite solutions are constructed and explored
in hope of finding better solutions.
The time horizon on this project did not allow implementation of these improvements,
however, specific improvements to the current implementation has been suggested in
chapter 8.
4.3.4 The Simulated Annealing metaheuristic
The Simulated Annealing (SA) algorithm is an analogue to the real world process that
takes place during controlled cooling of solids. If a solid is melted, the particles in the
matter arranges themselves randomly, whereas in a solid state, the particles arranges
themselves in a structured lattice (Aarts et al. [1]). When cooling the melted solid, the
energy of the atoms decreases and the atoms then arrange themselves in the lattice. At
lower temperatures, a change of state in the solid is less likely to occur. The result of the
process, with a high enough maximum temperature and a slow enough cooling, being a
solid whose particles are arranged in the most stable way possible.
Analoguesly, in the appliance of SA to computational problems, the chance of accepting
a neighborhood leading to a worse objective function value (higher energy in the solid)