The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 7. Tests, results and discussion 47 The enumeration Table 7.8: RCL Effect: All tests RCL Z(S) V(S) GRASP 1 4,125 28,53125 50 5,5 21,98125 100 356,1875 20,34375 The enumeration changes the way the construction heuristic builds the initial solution. Thus, in the following, we shall, as in the previous section, only focus on how GRASP performs with and without the enumeration mechanism. Table 7.9: Enumeration effect: All tests Z(S) V(S) Test Day Shift Day Shift 0 112,6667 155,2917 5,625 38,625 1 112,625 137,25 9,458333 48,79167 2 73,125 103,3333 7,916667 32,08333 3 131 186,3333 8,291667 44,45833 4 205,375 288,3333 9 82,54167 5 133,2917 188,75 10,75 47,75 6 52,45833 73,91667 3,125 18,25 7 141,2917 204,7917 7,208333 61,125 8 52,66667 77,08333 2,291667 26,75 9 2,416667 6,75 0 8,333333 From table 7.9, I conclude that the enumeration improves the performance of grasp considerably. For all instances, it is the case that the average solution of GRASP with enumeration is superior to the average solutions of GRASP without enumeration. To highlight the effect, see table 7.10 and 7.11 respectively. These two tables, for RCL 1 and RCL 50 respectively, shows the effect of the enumeration to a great extend. Espe- cially, table 7.11, where 50% randomisation has been implemented in the construction mechanism, the enumeration still ensures low average values of V(S). RCL 1 GRASP Z(S) V(S) Day 3 0,125 Shift 5,75 110 4,375 55,0625 Table 7.10: Enumeration effect: Test 4, RCL 1 RCL 50 GRASP Z(S) V(S) Day 7,875 5,375 Shift 5,625 53,375 6,75 29,375 Table 7.11: Enumeration effect: Test 7, RCL 50
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.
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TECHNICAL UNIVERSITY OF DENMARK The
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Acknowledgements Foremost, I would
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Appendix C. Tests 98 C.1.8 Instance
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Appendix C. Tests 100 Cons 12 Imps
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Appendix C. Tests 102 Test 3 RCL 1
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Bibliography 118 [10] Michael R. Ga
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