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Table 5. Average error rate obtained by IMPSO using ring topology with Ry», As mention above, the tow other basic and important parameters of island models are migration rate a1 migration frequency, that indicate how frequently migrations occur, here we used the iterations number and ho many particles migrate. The value of iterations number p =500. T the impact of the migration rate on convergence and diversity be values of R,, are studied (R,, = 10%, 20% and 30%), using three he last set of experiments is designed to measu haviours of IMPSO algorithm. Three alternati topologies migration (chain, ring and torus) wi islands number equals to 4. The value of R,,;= 20% means the number of migrants are I, X 20% = IMPSO/I, 20% = 40/4 * 20% = 2. The table 5 shows t cases of migration rate that the smaller value migration, which suggest that a single particle i of R,, tends to have an effect on diversity simp he results produced of R,, indicates an According to the comparison between the d s able to impact as a for the 25 IEEE-CEC2005 functions for the thr increase in diversity in generations following seed for changes in a stagnated island. Big val y due to replacing a ifferent kind of topologies and the use of many cases of the islan lager number of particles.

Table 5 Average error rate obtained by IMPSO using ring topology with Ry», As mention above, the tow other basic and important parameters of island models are migration rate a1 migration frequency, that indicate how frequently migrations occur, here we used the iterations number and ho many particles migrate. The value of iterations number p =500. T the impact of the migration rate on convergence and diversity be values of R,, are studied (R,, = 10%, 20% and 30%), using three he last set of experiments is designed to measu haviours of IMPSO algorithm. Three alternati topologies migration (chain, ring and torus) wi islands number equals to 4. The value of R,,;= 20% means the number of migrants are I, X 20% = IMPSO/I, 20% = 40/4 * 20% = 2. The table 5 shows t cases of migration rate that the smaller value migration, which suggest that a single particle i of R,, tends to have an effect on diversity simp he results produced of R,, indicates an According to the comparison between the d s able to impact as a for the 25 IEEE-CEC2005 functions for the thr increase in diversity in generations following seed for changes in a stagnated island. Big val y due to replacing a ifferent kind of topologies and the use of many cases of the islan lager number of particles.

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In order to evaluate the proposed IMPSO, 25 test functions with different characteristics have been used (f, — f,,). They are selected from the set of test functions of IEEE-CEC2005. A brief summary of the test functions used in our experiments is provided in Tablel where each test function is abbreviated and its variables value range are recorded as appears in the original source’*. The dimension D of each solution vector used in the experiments is also recorded together with the fitness value of the optimal solution f(x* ). Ww. OP TIRMM MMMANNEF,. 41. Cf... at OU em ®% ..-. @.- £2... a en. a | cee: (a, ee a aS er... 2 we Mme
In order to evaluate the proposed IMPSO, 25 test functions with different characteristics have been used (f, — f,,). They are selected from the set of test functions of IEEE-CEC2005. A brief summary of the test functions used in our experiments is provided in Tablel where each test function is abbreviated and its variables value range are recorded as appears in the original source’*. The dimension D of each solution vector used in the experiments is also recorded together with the fitness value of the optimal solution f(x* ). Ww. OP TIRMM MMMANNEF,. 41. Cf... at OU em ®% ..-. @.- £2... a en. a | cee: (a, ee a aS er... 2 we Mme
Table 2. Average error rate obtained by IMPSO using chain topology The results of the IMPSO for all 25 problems are reported in tables 3-5. It is clear that, for unimodal function (functions 1-5) using 10D, it is quite easy for the IMPSO to converge to the optimal points except for function 3 The proposed algorithm using the ring topology gives a better convergence rate for the function 3.
Table 2. Average error rate obtained by IMPSO using chain topology The results of the IMPSO for all 25 problems are reported in tables 3-5. It is clear that, for unimodal function (functions 1-5) using 10D, it is quite easy for the IMPSO to converge to the optimal points except for function 3 The proposed algorithm using the ring topology gives a better convergence rate for the function 3.
Table 4. Average error rate obtained by IMPSO using torus topology
Table 4. Average error rate obtained by IMPSO using torus topology
5. Conclusion value below 0.05) in the statistical tests. Successful tests are marked with "+" symbols in the last column in tables of iverage error and the unsuccessful tests are marked with "-" symbols means that no statistical confidence was found p-value > 0.05).
5. Conclusion value below 0.05) in the statistical tests. Successful tests are marked with "+" symbols in the last column in tables of iverage error and the unsuccessful tests are marked with "-" symbols means that no statistical confidence was found p-value > 0.05).
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Computer ScienceTechnologyEvolutionary AlgorithmMathematical Optimization
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