Page 40 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2017 4th Student Computer Science Research Conference. Koper: University of Primorska Press, 2017
P. 40
le 2: Overall performance by total population sizes and number of agents
NP MAS 1 5 8 N
10 16 20 25
50 56.7574 58.6826 n/a 25.6366 n/a n/a n/a
100 55.4424 66.2785 n/a 60.6823 n/a 21.5483 15.5059
200 53.1856 64.7585 67.1079 70.1968 n/a 55.2277 33.7031
400 41.2382 52.2476 55.8367 58.0758 59.2057 60.2217 56.6458
Avg 51.6559 60.4918 61.4723 53.6478 59.2057 45.6659 35.2849
Table 3: Algorithm MAS-jDE overall performance for the best solution (NP MAS = 200 and N = 10)
F1(10) F1(50) F2 F3 F4 F5 F6
T1 0.0149787 0.0148135 0.0183885 0.0152204 0.0190092 0.0220642 0.0152638
T2 0.0141223 0.0137885 0.00997478 0.00335469 0.0108478 0.0227195 0.0156269
T3 0.0137606 0.0129679 0.0145688 0.0065958 0.013584 0.02233 0.0170243
T4 0.0149597 0.0149308 0.0142835 0.0112827 0.0178799 0.0229582 0.0135977
T5 0.0141646 0.0146022 0.0115689 0.00435399 0.0114108 0.0225239 0.0177137
T6 0.0136714 0.01301 0.0165458 0.0106462 0.0171642 0.0231245 0.0150692
T7 0.0088615 0.00938833 0.0109534 0.00691136 0.0112994 0.0148324 0.0132556
Mark 0.0945188 0.09350123 0.09628368 0.05836514 0.10119530 0.1505527 0.1075512
Performance (summed the mark obtained for each case and multiplied by 100): 70.1968
algorithms outperformed it. Similar, but better results were achieved against jDE* and
CDDE Ar. Similarity between MAS-jDE and JDE* results
Table 4: Overall performance comparison can be contributed to the fact that both algorithms use the
same self-adaptive algorithm to search for a global optimum.
Algorithm Performance Our algorithm was outperformed by MLSDO and mSQDE-i.
MAS-jDE 70.1968 Future plan is to study the results of diversity measurements
and consequences of migrations of individuals more closely,
DOP DE 45.4996 and add mechanisms like k-means clustering algorithm to
spread initial population more equally over search-space.
DOP jDE 55.4424 Initial tests show promising results.
jDE* 69.7269 6. REFERENCES
CDDE Ar 69.4700 [1] J. Brest, S. Greiner, B. Boˇskovi´c, M. Mernik, and
V. Zˇumer. Self-adapting control parameters in
MLSDO 81.2760 differential evolution: A comparative study on
numerical benchmark problems. IEEE Transactions
mSQDE-i 77.1458 on Evolutionary Computation, 10(6):646–657, 2006.
5. CONCLUSIONS [2] J. Brest, A. Zamuda, B. Boˇskovi´c, M. S. Mauˇcec, and
V. Zˇumer. Dynamic optimization using self-adaptive
In this paper we proposed MAS-jDE algorithm that is a differential evolution. In Evolutionary Computation,
MAS, where agents independently of each other explore the 2009. CEC’09. IEEE Congress on., pages 415–422.
search space using the jDE. To prevent stagnation of the IEEE, May 2009.
agent’s populations, theirs population diversity is measured.
If diversity falls bellow threshold, migration mechanism be- [3] A. Eiben and J. E. Smith. Introduction to
tween agents takes place. Evolutionary Computing. Natural Computing Series.
Springer-Verlag Berlin Heidelberg, 1 edition, 2003.
Algorithm was tested on CEC’09 benchmark functions for
DOP. In line with this, two experiments were conducted. [4] H. Fu, P. R. Lewis, B. Sendhoff, K. Tang, and X. Yao.
In the first, we compared multi-agent systems with different What are dynamic optimization problems? In
configurations, where the population sizes and the number Evolutionary Computation (CEC), 2014 IEEE
of agents were varied. The results were compared according Congress on, 2014.
to the benchmark’s overall performance measure. The best
solution was found when the total population size was 200 [5] U. Halder, S. Das, and D. Maity. A cluster-based
and the number of agents was 10. From the results of the differential evolution algorithm with external archive
experiments we can observe, that although we used diver- for optimization in dynamic environments. IEEE
sity measurements and migration of individuals, stagnation transactions on cybernetics, 43(3):881–897, June 2013.
of population appears in combinations, where agent’s had
smaller population sizes. [6] J. Lepagnot, A. Nakib, H. Oulhadj, and P. Siarry. A
multiple local search algorithm for continuous
The results of the MAS-jDE with the best parameter set- dynamic optimization. Journal of Heuristics,
ting from the first experiment were also compared with other 19(1):35–76, Feb. 2013.
state-of-the-art optimization algorithms. The MAS-jDE
showed much better results then DOP DE and DOP jDE.
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference 40
Ljubljana, Slovenia, 11 October
NP MAS 1 5 8 N
10 16 20 25
50 56.7574 58.6826 n/a 25.6366 n/a n/a n/a
100 55.4424 66.2785 n/a 60.6823 n/a 21.5483 15.5059
200 53.1856 64.7585 67.1079 70.1968 n/a 55.2277 33.7031
400 41.2382 52.2476 55.8367 58.0758 59.2057 60.2217 56.6458
Avg 51.6559 60.4918 61.4723 53.6478 59.2057 45.6659 35.2849
Table 3: Algorithm MAS-jDE overall performance for the best solution (NP MAS = 200 and N = 10)
F1(10) F1(50) F2 F3 F4 F5 F6
T1 0.0149787 0.0148135 0.0183885 0.0152204 0.0190092 0.0220642 0.0152638
T2 0.0141223 0.0137885 0.00997478 0.00335469 0.0108478 0.0227195 0.0156269
T3 0.0137606 0.0129679 0.0145688 0.0065958 0.013584 0.02233 0.0170243
T4 0.0149597 0.0149308 0.0142835 0.0112827 0.0178799 0.0229582 0.0135977
T5 0.0141646 0.0146022 0.0115689 0.00435399 0.0114108 0.0225239 0.0177137
T6 0.0136714 0.01301 0.0165458 0.0106462 0.0171642 0.0231245 0.0150692
T7 0.0088615 0.00938833 0.0109534 0.00691136 0.0112994 0.0148324 0.0132556
Mark 0.0945188 0.09350123 0.09628368 0.05836514 0.10119530 0.1505527 0.1075512
Performance (summed the mark obtained for each case and multiplied by 100): 70.1968
algorithms outperformed it. Similar, but better results were achieved against jDE* and
CDDE Ar. Similarity between MAS-jDE and JDE* results
Table 4: Overall performance comparison can be contributed to the fact that both algorithms use the
same self-adaptive algorithm to search for a global optimum.
Algorithm Performance Our algorithm was outperformed by MLSDO and mSQDE-i.
MAS-jDE 70.1968 Future plan is to study the results of diversity measurements
and consequences of migrations of individuals more closely,
DOP DE 45.4996 and add mechanisms like k-means clustering algorithm to
spread initial population more equally over search-space.
DOP jDE 55.4424 Initial tests show promising results.
jDE* 69.7269 6. REFERENCES
CDDE Ar 69.4700 [1] J. Brest, S. Greiner, B. Boˇskovi´c, M. Mernik, and
V. Zˇumer. Self-adapting control parameters in
MLSDO 81.2760 differential evolution: A comparative study on
numerical benchmark problems. IEEE Transactions
mSQDE-i 77.1458 on Evolutionary Computation, 10(6):646–657, 2006.
5. CONCLUSIONS [2] J. Brest, A. Zamuda, B. Boˇskovi´c, M. S. Mauˇcec, and
V. Zˇumer. Dynamic optimization using self-adaptive
In this paper we proposed MAS-jDE algorithm that is a differential evolution. In Evolutionary Computation,
MAS, where agents independently of each other explore the 2009. CEC’09. IEEE Congress on., pages 415–422.
search space using the jDE. To prevent stagnation of the IEEE, May 2009.
agent’s populations, theirs population diversity is measured.
If diversity falls bellow threshold, migration mechanism be- [3] A. Eiben and J. E. Smith. Introduction to
tween agents takes place. Evolutionary Computing. Natural Computing Series.
Springer-Verlag Berlin Heidelberg, 1 edition, 2003.
Algorithm was tested on CEC’09 benchmark functions for
DOP. In line with this, two experiments were conducted. [4] H. Fu, P. R. Lewis, B. Sendhoff, K. Tang, and X. Yao.
In the first, we compared multi-agent systems with different What are dynamic optimization problems? In
configurations, where the population sizes and the number Evolutionary Computation (CEC), 2014 IEEE
of agents were varied. The results were compared according Congress on, 2014.
to the benchmark’s overall performance measure. The best
solution was found when the total population size was 200 [5] U. Halder, S. Das, and D. Maity. A cluster-based
and the number of agents was 10. From the results of the differential evolution algorithm with external archive
experiments we can observe, that although we used diver- for optimization in dynamic environments. IEEE
sity measurements and migration of individuals, stagnation transactions on cybernetics, 43(3):881–897, June 2013.
of population appears in combinations, where agent’s had
smaller population sizes. [6] J. Lepagnot, A. Nakib, H. Oulhadj, and P. Siarry. A
multiple local search algorithm for continuous
The results of the MAS-jDE with the best parameter set- dynamic optimization. Journal of Heuristics,
ting from the first experiment were also compared with other 19(1):35–76, Feb. 2013.
state-of-the-art optimization algorithms. The MAS-jDE
showed much better results then DOP DE and DOP jDE.
StuCoSReC Proceedings of the 2017 4th Student Computer Science Research Conference 40
Ljubljana, Slovenia, 11 October
