Sequential drug decision problems in long-term medical conditions: a case Study of Primary Hypertension Eunju Kim ba, ma, msc
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7.5Genetic algorithmInitial tests of GA were undertaken to determine the best setup of the number of generations and the population size. The population size in GA means the number of policies evaluated at the same time in each generation. A total of nine sets of experiments with different combinations of generations (25, 50 and 100) and population sizes (10, 30, 50 and 100) were implemented. In each generation, 90% of the fittest parents were assumed to remain in the future generation. The initial population was selected randomly. In the base-case, crossover rate was assumed to be 0.7, and mutation rate was 0.1. Each test was repeated 20 times to evaluate the percentage of the separate GA simulation runs to find the global optimum and the average penalty rate using Equation 7.1. Table 7. summarises the computational results of the GA experiments. The evaluation of the objective function (each evaluation includes 100 Monte Carlo simulation replications) was repeated from a minimum 235 times to a maximum 2,730 times, compared to 4,128 times using enumeration. Overall computational time increased as the number of iterations increased. Population size had a greater impact on computational time. Average computation time was approximately 10.97 seconds per run. All GA experiments found the optimal solution or the statistically equivalent solutions. The potential reason that the point estimate of the total net benefits of the same policy numbers were slightly different is due to the noise from the random drug allocation after the use of fourth-line drug and for the patients who have a CVD or DM. Search rates increased as the number of iterations increased; however, the objective function value was not always increased proportionally to the increment in iterations or computational time. The maximum total net benefit was obtained when the number of generations was 100 and the size of population was 10. However, premature convergence may happen when the population size was small (i.e., 10) (see Table 7. and Figure 7.). The performance of GA also depends on the crossover and mutation rates. The following eight combinations of crossover rates (0.7 and 0.8) and mutation rates (0.01, 0.05, 0.1 and 0.2) were implemented where the population size was 30 and the number of generation was 100. Table 7. and Table 7. shows that the decrease in the crossover and mutation rates has a potential risk of premature convergence due to a lack of population diversity. On the contrary, the trade-off between population diversity and the quality of solution may also exist, depending on the choice of the crossover and mutation rates, although this was not clear in this study. Table 7.. Computational results by the number of generations and population size from GA
1) Iteration number means the evaluation of the objective function including 100 Monte Carlo simulations. 2) The solution numbers with * are included in the top eight policies identified from the enumeration in Table 7.. 3) Crossover rate was set to 0.7 and mutation rate was set to 0.1. 4) The base-case is in grey. Table 7.. The average performance of GA from 20 repeated runs, depending on the generation number and the population size
1) G represents the generation number and P represents the population size.
1) G represents the generation number and P represents the population size. Figure 7.. Convergence of GA depending on the number of generation and population Table 7.. Computational results by crossover and mutation rates from GA
1) Iteration number means the evaluation of the objective function including 100 Monte Carlo simulations. 2) The solution numbers with * are included in the top eight policies identified from enumeration in Table 7.. 3) The population size was set to 30 and the number of generation was set to 100. 4) The base-case is in grey. Table 7.. The average performance of GA from 20 repeated runs, depending on the crossover rate and the mutation rate
1) C represents the cooling rate and M represents the mutation rate.
1) X-axis represents the policy numbers; Y-axis represents the frequency of evaluation; C represents the cooling rate; and M represents the mutation rate. Figure 7.. Search rate of GA depending on the crossover and mutation rates Yüklə 10,52 Mb. Dostları ilə paylaş:
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