The Doctor Rostering Problem - Asser Fahrenholz

Chapter 7. Tests, results and discussion 49
Table 7.15: Iterations effect: All tests
Iterations Z(S) V(S)
GRASP 156 105,1354 27,78333
3276 143,3542 19,64583
SA 500 257,9729 12,31146
2500 270,3089 3,597446
Focusing on the real world problem once again, figures 7.1 and 7.2 on the following
page shows the performance of a GRASP and SA taking over from the GRASP. It is
clear that GRASP with enumeration finds near optimal values (using a higher number
of iterations results in actual optimal solutions, see figure C.1 in appendix C.2.5 on
page 115) and compared to that of GRASP without enumeration is greatly superior.
Figure 7.2(b) on the following page shows how SA is able to optimize the output from
GRASP without enumeration, but in minimising V(S), it also increases Z(S). The same
observation applies to figure 7.2(a) on the next page.
20
15
10
5
0
GRASP-Day-1-10-R2-13%
0 25 50 75 100 125 150
Iterations
GRASP-Day-1-10-R2-13%-vio GRASP-Day-1-10-R2-13%-value
Working vio Working score
(a) GRASP, enumeration, R2, RCL 1
100
80
60
40
20
0
GRASP-Shift-1-2-R2-13%
0 25 50 75 100 125 150
Iterations
GRASP-Shift-1-2-R2-13%-vio GRASP-Shift-1-2-R2-13%-value
Working vio Working score
Figure 7.1: GRASP performance: Test 0
(b) GRASP, no enumeration, R2, RCL 1
One observation to be made from figure 7.1(b), is that GRASP without enumeration
restarts too soon. It restarts while it is still able to find improving neighborhoods in LS,
and ends up not being able to improve the incumbent solution again.
Emphasising the effect of the enumeration I refer to figures 7.3 on the next page and 7.4
on page 51.
The effect of the enumeration is so strong, that in most cases, there isn’t anything for SA
to optimise. The following will show that SA is in fact able to optimise poor solutions
produced by GRASP.