The Doctor Rostering Problem - Asser Fahrenholz

Chapter 7. Tests, results and discussion 48
The constraint weights
Table 7.12 shows the overall effect of solving problems with weights δR1 = 1 and δR2 = 2
respectively. The V(S), as expected, is not affected by varying weights, but for Z(S) we
see a small increase in objective function value. Note, however, that the Z(S) for R2 is
not double of Z(S) for R1, this means, on average, fewer soft constraints invalidated.
Table 7.12: Weights effect: All tests
Z(S) V(S)
GRASP R1 106,075 23,99167
R2 137,8 23,24583
SA R1 234,8229 8,035417
R2 293,4839 7,877352
Highlighting a few, more in-depth, examples, tables 7.13 and 7.14 shows how Simulated
Annealing ends up with just about equal numbers of soft constraints broken, for both
R1 and R2.
SA Z(S) V(S)
R1 73,875 6,84375
R2 148,5938 7,40625
Ave 111,2344 7,125
Table 7.13: Weights effect: Test
0, RCL 1
The number of iterations
SA Z(S) V(S)
R1 85,65625 20,5625
R2 162,875 20,375
Ave 124,2656 20,46875
Table 7.14: Weights effect: Test
4, RCL 1
Not surprisingly, the number of iterations also has great effect on the quality of the
produced solution. Table 7.15 on the following page shows the average solution values
over all tests, grouped by the number of iterations for each of the metaheuristics. As
expected, Z(S) is also higher on average, for lower values of V(S).
7.2.3 Metaheuristic performance
The performances of the metaheuristics has so far been investigated in the light of
the parameters that guide them and the problems they solve. How the metaheuristics
converge and how they compare to each other, are some of the aspects that will be
discussed in this section.