Page 34 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2015 2nd Student Computer Science Research Conference. Koper: University of Primorska Press, 2015
P. 34
Table 1: Summary of the benchmark functions. Domain
Tag Function Definition
[−10, 10]
f1 Ackley’s f (x) = −20 exp(−0.2 1 n xi2) − exp( 1 n cos(2πxi )) + 20 + e [−10, 10]
n i=1 n i=1 [−10, 10]
[−10, 10]
f2 Griewank f (x) = 1 + 1 n x2i − n cos( √xi )
4000 i=1 i=1 i [−10, 10]
n
f3 Rastrigin f (x) = 10n + i=1 (xi2 − 10 cos(2πxi))
f4 Sphere f (x) = n xi2
i=1
(100(xi2−xj )2+(1−xj )2)2
f5 Whitley f (x) = n n 4000 − cos(100(x2i − xj )2 + (1 − xj )2) + 1
i=1 j=1
Table 2: Experimental results.
Alg. Np f1 f2 f3 f4 f5
1.11e+01±8.66e-01 2.76e-01±2.70e-01 1.70e+02±3.92e+01 7.79e+01±2.53e+01 3.21e+04±1.95e+04
BA 40 1.15e+01±8.91e-01 3.96e-01±2.68e-01 2.18e+02±4.61e+01 9.65e+01±3.33e+01 4.87e+04±2.47e+04
PL-1 10 1.13e+01±1.15e+00 3.63e-01±2.94e-01 1.72e+02±5.09e+01 7.80e+01±2.82e+01 4.65e+04±2.65e+04
PL-2 20 1.06e+01±7.11e-01 2.52e-01±2.59e-01 1.46e+02±4.47e+01 6.56e+01±2.00e+01 3.03e+04±1.27e+04
PL-3 40 1.01e+01±7.59e-01 1.79e-01±1.64e-01 1.27e+02±3.58e+01 5.49e+01±1.88e+01 1.90e+04±1.26e+04
PL-4 80 9.68e+00±8.44e-01 1.07e-01±3.24e-02 1.24e+02±3.59e+01 4.58e+01±1.58e+01 1.63e+04±7.32e+03
PL-5 160 9.42e+00±7.32e-01 1.16e-01±3.82e-02 1.01e+02±2.25e+01 3.67e+01±1.17e+01 1.16e+04±3.95e+03
PL-6 320 8.76e+00±9.29e-01 1.02e-01±2.45e-02 9.28e+01±2.45e+01 3.16e+01±1.38e+01 9.08e+03±3.49e+03
PL-7 640 8.57e+00±8.62e-01 1.02e-01±2.08e-02 9.22e+01±2.63e+01 3.23e+01±1.07e+01 1.08e+04±4.40e+03
PL-8 1280
the proposed PLBA can achieve comparable results as those IEEE International Conference on, volume 4, pages
obtained by the original BA. Such findings encourage us to 1942–1948. IEEE, 1995.
continue with this work in the future. As the first goal,
we would like to develop also a variant of a parameterless [10] S Kirkpatrick, CD Gelatt Jr, and MP Vecchi.
cuckoo search algorithm. We will also investigate the effect Optimization by simulated annealing. Science,
of the population size further in various applications. 220(4598), 1983.
6. REFERENCES [11] John Koza. Genetic Programming 2 - Automatic
Discovery of Reusable Programs. MIT Press,
[1] Thomas Ba¨ck. Evolutionary Algorithms in Theory and Cambridge, USA:, 1994.
Practice: Evolution Strategies, Evolutionary
Programming, Genetic Algorithms. Oxford University [12] Fernando G. Lobo and David E. Goldberg. An
Press, Oxford, UK:, 1996. overview of the parameter-less genetic algorithm. In
Proceedings of the 7th Joint Conference on
[2] Janez Demˇsar. Statistical comparisons of classifiers Information Sciences. (Invited paper), pages 20–23,
over multiple data sets. J. Mach. Learn. Res., 7:1–30, 2003.
December 2006.
[13] Navaneethakrishna Makaram and Ramakrishnan
[3] Iztok Fister Jr., Simon Fong, Janez Brest, and Iztok Swaminathan. A binary bat approach for
Fister. A novel hybrid self-adaptive bat algorithm. identification of fatigue condition from semg signals.
The Scientific World Journal, 2014, 2014. In Swarm, Evolutionary, and Memetic Computing,
pages 480–489. Springer, 2014.
[4] Iztok Fister Jr, Xin-She Yang, Iztok Fister, Janez
Brest, and Duˇsan Fister. A brief review of [14] Rainer Storn and Kenneth Price. Differential
nature-inspired algorithms for optimization. evolution–a simple and efficient heuristic for global
Elektrotehniˇski vestnik, 80(3):116–122, 2013. optimization over continuous spaces. Journal of global
optimization, 11(4):341–359, 1997.
[5] Lawrence Jerome Fogel, Alvin J. Owens, and
Michael John Walsh. Artificial Intelligence through [15] Anass Taha, Mohamed Hachimi, and Ali Moudden.
Simulated Evolution. John Willey & Sons, Inc., New Adapted bat algorithm for capacitated vehicle routing
York, USA:, 1966. problem. International Review on Computers and
Software (IRECOS), 10(6):610–619, 2015.
[6] Milton Friedman. A comparison of alternative tests of
significance for the problem of m rankings. Ann. [16] TP Talafuse and EA Pohl. A bat algorithm for the
Math. Statist., 11(1):86–92, 03 1940. redundancy allocation problem. Engineering
Optimization, (ahead-of-print):1–11, 2015.
[7] David E. Goldberg. Genetic Algorithms in Search,
Optimization and Machine Learning. Addison-Wesley [17] Jinfeng Wang, Xiaoliang Fan, Ailin Zhao, and
Longman Publishing Co., Inc., Boston, USA:, 1989. Mingqiang Yang. A hybrid bat algorithm for process
planning problem. IFAC-PapersOnLine,
[8] Andr´es Iglesias, Akemi G´alvez, and Marta Collantes. 48(3):1708–1713, 2015.
Global-support rational curve method for data
approximation with bat algorithm. In Artificial [18] Xin-She Yang. Firefly algorithm. In Nature-Inspired
Intelligence Applications and Innovations: 11th IFIP Metaheuristic Algorithms, pages 79–90. Luniver Press,
WG 12.5 International Conference, AIAI 2015, London, UK:, 2008.
Bayonne, France, September 14-17, 2015, Proceedings,
volume 458, page 191. Springer, 2015. [19] Xin-She Yang. A new metaheuristic bat-inspired
algorithm. In Nature inspired cooperative strategies for
[9] James Kennedy and Russell Eberhart. Particle swarm optimization (NICSO 2010), pages 65–74. Springer,
optimization. In Neural Networks, 1995. Proceedings., 2010.
StuCoSReC Proceedings of the 2015 2nd Student Computer Science Research Conference 34
Ljubljana, Slovenia, 6 October
Tag Function Definition
[−10, 10]
f1 Ackley’s f (x) = −20 exp(−0.2 1 n xi2) − exp( 1 n cos(2πxi )) + 20 + e [−10, 10]
n i=1 n i=1 [−10, 10]
[−10, 10]
f2 Griewank f (x) = 1 + 1 n x2i − n cos( √xi )
4000 i=1 i=1 i [−10, 10]
n
f3 Rastrigin f (x) = 10n + i=1 (xi2 − 10 cos(2πxi))
f4 Sphere f (x) = n xi2
i=1
(100(xi2−xj )2+(1−xj )2)2
f5 Whitley f (x) = n n 4000 − cos(100(x2i − xj )2 + (1 − xj )2) + 1
i=1 j=1
Table 2: Experimental results.
Alg. Np f1 f2 f3 f4 f5
1.11e+01±8.66e-01 2.76e-01±2.70e-01 1.70e+02±3.92e+01 7.79e+01±2.53e+01 3.21e+04±1.95e+04
BA 40 1.15e+01±8.91e-01 3.96e-01±2.68e-01 2.18e+02±4.61e+01 9.65e+01±3.33e+01 4.87e+04±2.47e+04
PL-1 10 1.13e+01±1.15e+00 3.63e-01±2.94e-01 1.72e+02±5.09e+01 7.80e+01±2.82e+01 4.65e+04±2.65e+04
PL-2 20 1.06e+01±7.11e-01 2.52e-01±2.59e-01 1.46e+02±4.47e+01 6.56e+01±2.00e+01 3.03e+04±1.27e+04
PL-3 40 1.01e+01±7.59e-01 1.79e-01±1.64e-01 1.27e+02±3.58e+01 5.49e+01±1.88e+01 1.90e+04±1.26e+04
PL-4 80 9.68e+00±8.44e-01 1.07e-01±3.24e-02 1.24e+02±3.59e+01 4.58e+01±1.58e+01 1.63e+04±7.32e+03
PL-5 160 9.42e+00±7.32e-01 1.16e-01±3.82e-02 1.01e+02±2.25e+01 3.67e+01±1.17e+01 1.16e+04±3.95e+03
PL-6 320 8.76e+00±9.29e-01 1.02e-01±2.45e-02 9.28e+01±2.45e+01 3.16e+01±1.38e+01 9.08e+03±3.49e+03
PL-7 640 8.57e+00±8.62e-01 1.02e-01±2.08e-02 9.22e+01±2.63e+01 3.23e+01±1.07e+01 1.08e+04±4.40e+03
PL-8 1280
the proposed PLBA can achieve comparable results as those IEEE International Conference on, volume 4, pages
obtained by the original BA. Such findings encourage us to 1942–1948. IEEE, 1995.
continue with this work in the future. As the first goal,
we would like to develop also a variant of a parameterless [10] S Kirkpatrick, CD Gelatt Jr, and MP Vecchi.
cuckoo search algorithm. We will also investigate the effect Optimization by simulated annealing. Science,
of the population size further in various applications. 220(4598), 1983.
6. REFERENCES [11] John Koza. Genetic Programming 2 - Automatic
Discovery of Reusable Programs. MIT Press,
[1] Thomas Ba¨ck. Evolutionary Algorithms in Theory and Cambridge, USA:, 1994.
Practice: Evolution Strategies, Evolutionary
Programming, Genetic Algorithms. Oxford University [12] Fernando G. Lobo and David E. Goldberg. An
Press, Oxford, UK:, 1996. overview of the parameter-less genetic algorithm. In
Proceedings of the 7th Joint Conference on
[2] Janez Demˇsar. Statistical comparisons of classifiers Information Sciences. (Invited paper), pages 20–23,
over multiple data sets. J. Mach. Learn. Res., 7:1–30, 2003.
December 2006.
[13] Navaneethakrishna Makaram and Ramakrishnan
[3] Iztok Fister Jr., Simon Fong, Janez Brest, and Iztok Swaminathan. A binary bat approach for
Fister. A novel hybrid self-adaptive bat algorithm. identification of fatigue condition from semg signals.
The Scientific World Journal, 2014, 2014. In Swarm, Evolutionary, and Memetic Computing,
pages 480–489. Springer, 2014.
[4] Iztok Fister Jr, Xin-She Yang, Iztok Fister, Janez
Brest, and Duˇsan Fister. A brief review of [14] Rainer Storn and Kenneth Price. Differential
nature-inspired algorithms for optimization. evolution–a simple and efficient heuristic for global
Elektrotehniˇski vestnik, 80(3):116–122, 2013. optimization over continuous spaces. Journal of global
optimization, 11(4):341–359, 1997.
[5] Lawrence Jerome Fogel, Alvin J. Owens, and
Michael John Walsh. Artificial Intelligence through [15] Anass Taha, Mohamed Hachimi, and Ali Moudden.
Simulated Evolution. John Willey & Sons, Inc., New Adapted bat algorithm for capacitated vehicle routing
York, USA:, 1966. problem. International Review on Computers and
Software (IRECOS), 10(6):610–619, 2015.
[6] Milton Friedman. A comparison of alternative tests of
significance for the problem of m rankings. Ann. [16] TP Talafuse and EA Pohl. A bat algorithm for the
Math. Statist., 11(1):86–92, 03 1940. redundancy allocation problem. Engineering
Optimization, (ahead-of-print):1–11, 2015.
[7] David E. Goldberg. Genetic Algorithms in Search,
Optimization and Machine Learning. Addison-Wesley [17] Jinfeng Wang, Xiaoliang Fan, Ailin Zhao, and
Longman Publishing Co., Inc., Boston, USA:, 1989. Mingqiang Yang. A hybrid bat algorithm for process
planning problem. IFAC-PapersOnLine,
[8] Andr´es Iglesias, Akemi G´alvez, and Marta Collantes. 48(3):1708–1713, 2015.
Global-support rational curve method for data
approximation with bat algorithm. In Artificial [18] Xin-She Yang. Firefly algorithm. In Nature-Inspired
Intelligence Applications and Innovations: 11th IFIP Metaheuristic Algorithms, pages 79–90. Luniver Press,
WG 12.5 International Conference, AIAI 2015, London, UK:, 2008.
Bayonne, France, September 14-17, 2015, Proceedings,
volume 458, page 191. Springer, 2015. [19] Xin-She Yang. A new metaheuristic bat-inspired
algorithm. In Nature inspired cooperative strategies for
[9] James Kennedy and Russell Eberhart. Particle swarm optimization (NICSO 2010), pages 65–74. Springer,
optimization. In Neural Networks, 1995. Proceedings., 2010.
StuCoSReC Proceedings of the 2015 2nd Student Computer Science Research Conference 34
Ljubljana, Slovenia, 6 October
