The Doctor Rostering Problem - Asser Fahrenholz

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Chapter 7. Tests, results and discussion 43 Table 7.1 displays the test instances and the problem factors that can affect the solution. For every instance, Cons notes how constrained the problem is. I expect that adding more night shifts, evening shifts and wishes (raising the Cons) also make the problem harder to solve and likewise when decreasing the number of doctors. Table 7.1: Test instances Test Length (months) Cons (%) Doctors 0 4 13 6 1 4 17 6 2 4 12 7 3 4 13 5 4 8 13 6 5 4 18 6 6 2 17 7 7 6 13 8 8 4 5 6 9 4 0 6 The test instances can then be partitioned into the groups shown in table 7.2. This shows the test instances that have equal values in what categories and will be used for comparing results across groups in the next section. Table 7.2: Test instance groups Length Constrained Doctors {0,1,2,3,5,8,9}, {4}, {6}, {7} {0,3,4,7}, {1,6}, {2}, {5}, {8}, {9} {0,1,4,5,8,9}, {2,6}, {3}, {7} The problem factors will be the starting point for evaluating test results. From there, I move on to discuss effects of the metaheuristic factors, such as the RCL parameter, the enumeration and the weight of the constraints. The test instances have all been tested with the following parameters: RCL parameter {1 (Leaving only the best element in the list), 50 (cutting the list in half), 100 (leave the list as it is)} Enumeration Day, Shift Constraint weights δi = 1, δi = 2 In the following, I denote the value of the objective function value Z(S) and the number of invalid hard constraints by V (S). Together they will be noted in the form of (Z(S), V (S)).
Chapter 7. Tests, results and discussion 44 7.2 Results and discussion There are two types of test results documented by the tests. The first documents, by a graph, the performance of the metaheuristic on a given test instance, with given parameters, which I leave for the last part of this chapter. The second is the metaheuristic results, given all combinations of the above parameters, on a given instance. I will then, in the next section, try to perform a well founded instance and parameter evaluation by comparing each test instance and metaheuristic result to these derived values. I will not cross-compare every parameter result, as the number of comparisons, given the parameters of these tests, are simply too many to be covered in this project. I shall, though, highlight the cases where a clear observation can be made even if the results are across parameters. 7.2.1 Instance parameter effects In this section I will highlight the effects of the problem parameters and on that basis conclude, if possible, which parameters have what effects. Table 7.3: Test instance results Test Cons (%) Z(S) V(S) Doctors Test 0 13 196,099 14,38281 6 Test 1 17 222,9297 19,58594 6 Test 2 12 164,1276 12,68229 7 Test 3 13 258,3281 18,03646 5 Test 4 13 349,0755 32,41927 6 Test 5 18 251,0703 20,03125 6 Test 6 17 109,6927 6,403646 7 Test 7 13 246,9219 22,96354 8 Test 8 7 127,4193 9,070313 6 Test 9 0 4,364583 2,289063 6 The data in table 7.3 summarises the test results and are averages over all parameters. It is brought to the readers attention, to underline the effects of varying these parameters, which will be described in the next sections. Note that the average value of the solutions generated is not representative of average values of searches for optimal values. They are averages over all results, including the test runs where weights of the constraints has been set to 1 and those for which it was set to 2. The comparisons are meant to highlight numbers relative to each other, not their absolute value.
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TECHNICAL UNIVERSITY OF DENMARK The
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Bibliography 118 [10] Michael R. Ga
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The Doctor Rostering Problem - Asser Fahrenholz

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