• 沒有找到結果。

Solutions found by PSO-RDL for CEC’05 25 Real-Parameter

Functions

TableC.1:ThesolutionfoundbyPSO-RDLforeachfunctioninthebenchmark FunctionX1X2X3X4X5X6X7X8X9X10f(x) 1-39.31258.9-46.322-74.651-16.8-80.544-10.59424.96989.8389.1119-450 235.627-82.912-10.642-83.58283.15547.048-89.436-27.42276.145-39.06-450 3-32.201964.97619-38.3039-23.2536-54.009586.62329-6.29976-49.36085.34909252.24255-449.999619 435.6267-82.9123-10.6423-83.581583.155247.048-89.4359-27.421976.1448-39.0595-450 5-100-100-1008.38977.7182-8.3147100100100100-310 681.0232-48.39519.2316-2.523170.433847.1774-7.8358-86.669357.85319-9.95332390 7-276.268-11.911-578.788-287.649-84.3858-228.675-458.152-202.215-105.864-96.4898-180 8-19.960814.01622.693110.76284919.635252.95951316.626389.89564-1.99917-22.1767-139.999619 90.905541-1.5644-0.9788-2.25362.499-2.290340.9759-3.66610.0985-3.2465-330 102.684208-0.34563-1.18601-1.623442.684879-2.58328-0.29892-2.393230.146698-2.28207-330 110.100636-0.38906-0.374130.0743870.2931180.0145960.2386550.192788-0.245940.35138592.828684 12-1.48581-0.55785-1.48574-1.35094-0.361650.1478240.482965-1.529631.457278-4.00696-460 13-0.2376-1.58396-0.60608-1.03873-0.54839-1.1371-0.86921-0.17334-0.90296-0.81092-129.661766 14-13.543-2.63707-22.2218-31.7643.149738-17.083482.81796-4.177126.051408-46.8081-296.864114 154.329885-1.284421.898128-0.40647-1.902492.7621481.97788-2.80085-2.503222.734012220.6482 1650.8811792.1304280.425533-0.883782.4416272.055183-3.69536-2.52062.605947247.8216 174.9189160.1256561.973826-0.36212-0.195621.7280742.748412-3.3316-2.186523.307306238.6596 183.334302-0.8731.36354.2596982.5769010.8656-0.3686-3.97344.2912992.750802810 193.063854-1.64763-5-4.9465-3.71656-4.93662-4.98062-3.763694.7683760.558586705.264 203.334296-0.8731.3634984.2597042.5768970.865603-0.3686-3.97344.2913022.750797810 21-2.6639-2.1802-3.17922.02012.43221.5009-0.7393-0.2911-1.43122.7447660 22-2.56932-4.14768-4.934651.1652141.7170282.404797-2.217930.663713-2.003783.8832551110.2249 230.695732-4.02173-0.310464.4035780.0582893.1676273.032266-2.437073.6001580.84034785.1725 240.7973-2.64714.2808-3.18351.7367-2.3262-0.8345-2.91563.63083.8112460 2522.0228922.067772222.0046092.04254654.9999931997.223

Bibliography

[1] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of IEEE International Conference on Neural Networks, vol. 1942-1948, 1995.

[2] J. Kennedy and R. C. Eberhart, “A new optimizer using paritcle swarm theory,”

in Proceeding of the Sixth Int. Symposium on Micromachine and Human Science, Nagoya, Japan, 1995, pp. 39–43.

[3] J. H. Holland, Adaptation in natural and artificial systems. University of Michigan Press, 1975.

[4] D. E. Goldberg, Genetic algorithms in search, optimization, and machine learning.

Addison-Wesley, 1989.

[5] ——, The design of innovation: Lessons from and for competent genetic algorithms.

Kluwer Academic Publishers, 2002.

[6] D. E. Goldberg, B. Korb, and K. Deb, “Messy genetic algorithms: Motivation, analy-sis, and first result,” Complex Systems, vol. 3, pp. 493–530, 1989.

[7] D. E. Goldberg, K. Deb, and B. Korb, “Messy genetic algorithms revisited: Studies in mixed size and scale,” Complex Systems, vol. 4, pp. 415–444, 1990.

[8] R. C. Eberhart and Y. Shi, “Comparison between genetic algorithms and particle swarm optimization,” Evolutionary Programming of Lecture Notes in Computer Sci-ence, vol. 1447, pp. 611–616, 1998.

[9] P. Angeline, “Evolutionary optimization versus particle swarm optimization: Philos-ophy and performance differences,” Evolutonary Programming, vol. 1447 of Lecture Notes in Computer Science, pp. 601–610, 1998.

[10] M. Lvbjerg, T. K. Rasmussen, and T. Krink, “Hybrid particle swarm optimiser with breeding and subpopulations,” in Proceeding of Genetic and Evolutionary Computa-tion Conference, 2001.

[11] M. Settles and T. Soule, “Breeding swarms: A GA/PSO hybrid,” in Proceeding of Genetic and Evolutionary Computation Conference, Washington, DC, USA, 2005, pp. 161–168.

[12] D. Devicharan and C. K. Mohan, “Particle swarm optimization with adaptive linkage learning,” in Congress on Evolutionary Computation, Portland, Oregon, 2004, pp.

530–535.

[13] F. Heppner and U. Grenander, “A stochastic nonlinear model for coordinated bird flocks.” American Association for the Advancement of Science, 1990.

[14] C. W. Reynolds, “Flocks, herds and schools: a distributed behavioral model,” Com-puter Graphics, vol. 21, no. 4, pp. 25–34, 1987.

[15] E. O. Wilson, Sociobiology: The new synthesis. Belknap Press, Cambridge, MA, 1975.

[16] J. Kennedy, “The particle swarm: Social adaptation of knowledge,” in IEEE Inter-national Conference on Evolutionary Computation, 1997, pp. 303–308.

[17] Y. Shi and R. Eberhart, “A modified particle swarm optimization,” in IEEE In-ternational Conference on Evolutionary Computation, Anchorage, Alaska, 1998, pp.

69–73.

[18] Y. Shi and R. C. Eberhart, “Parameter selection in particle swarm optimization,”

Evolutionary Programming of Lecture Notes in Computer Science, vol. 1447, pp.

591–600, 1998.

[19] A. Carlisle and G. Dozier, “An off-the-shelf pso,” in The Particle Swarm Optimization Workshop, 2001, pp. 1–6.

[20] J. Kennedy, “Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance,” in IEEE Congress on Evolutionary Computation, 1999, pp. 1931–1938.

[21] R. C. Eberhart and X. Hu, “Multiobjective optimization using dynamic neighrbor-hood particle swarm optimization,” in IEEE Congress on Evolutionary Computation, Hawaii, 2002, pp. 1677–1681.

[22] J. J. Liang and P. N. Suganthan, “Dynamic multi-swarm particle optimizer,” in IEEE International Swarm Intelligence Symposium, 2005, pp. 124–129.

[23] J. J. Liang, A. K. Qin, P. N. Suganthan, and S. Baskar, “Particle swarm optimization algorithm with novel learning strategies,” in International Conference on Systems, Man and Cybernetics, The Netherlands, 2004.

[24] J. J. Liang, P. N. Suganthan, A. K. Qin, and S. Baskar, “Comprehensive learning particle swarm optimizer for global optimization of multimodal functions,” To appear in IEEE Transaction on Evolutionary Computation, 2006.

[25] J. Robinson, S. Sinton, and Y. Rahmat-Samii, “Particle swarm, genetic algorithm, and their hybrids: Optimization of a profiled corrugated horn antenna,” in IEEE An-tennas and Propagation Society International Symposium and URSI National Radio Science Meeting, San Antonio TX, 2002.

[26] X. H. Shi, Y. H. Lu, C. G. Zhou, H. P. Lee, W. Z. Lin, and Y. C. Liang, “Hybrid evolutionary algorithms based on PSO and GA,” in IEEE Congress on Evolutionary Computation, 2003, pp. 2393–2399.

[27] Y.-p. Chen, “Extending the scability of linkage learning genetic algorithms: Theory and practice,” Illinois Genetic Algorithms Laboratory (IlliGAL)Department of Gen-eral Engineering University of Illinois at Urbana-Champaign, Tech. Rep. 2004018, 2004.

[28] D. E. Goldberg, “Genetic algorithms and walsh functions: Part i, a gentle introduc-tion,” Complex Systems, vol. 3, no. 2, pp. 129–152, 1989.

[29] ——, “Genetic algorithms and walsh functions: Part ii, deception and its analysis,”

Complex Systems, vol. 3, no. 2, pp. 153–171, 1989.

[30] D. Thierens, “Analysis and design of genetic algorithms,” Ph.D. dissertation, Katholieke Universiteit Leuven, Leuven, Belgium, 1995.

[31] D. E. Goldberg, K. Deb, and D. Thierens, “Toward a better understanding of mixing in genetic algorithms,” Journal of the Society of Instrument and Control Engineers, vol. 32, no. 1, pp. 10–16, 1993.

[32] D. E. Goldberg, K. Deb, H. Kargupta, and G. Harik, “Rapid accurate optimization of difficult problems using fast messy genetic algorithms,” in Proc. of the Fifth Int.

Conf. on Genetic Algorithms, S. Forrest, Ed. San Mateo, CA: Morgan Kaufmann, 1993, pp. 56–64.

[33] H. Kargupta, “The gene expression messy genetic algorithm,” in International Con-ference on Evolutionary Computation, 1996, pp. 814–819.

[34] M. Munetomo and D. E. Goldberg, “Linkage identification by non-monotonicity de-tection for overlapping functions,” Evolutionary Computation, vol. 7, no. 4, pp. 377–

398, 1999.

[35] T.-L. Yu, D. E. Goldberg, Y. Ali, and Y.-p. Chen, “A genetic algorithm design inspired by organizational theory: Pilot study of a dependency structure matrix driven genetic algorithm,” in Artificial Neural Networks in Engineering, 2003, pp.

327–332.

[36] G. R. Harik and D. E. Goldberg, “Learning linkage,” in Foundations of Genetic Algorithms 4, R. K. Belew and M. D. Vose, Eds. San Francisco, CA: Morgan Kaufmann, 1997, pp. 247–262.

[37] Y.-p. Chen and D. E. Goldberg, “Introducing start expression genes to the linkage learning genetic algorithm,” 2002.

[38] S. Baluja, “Population-based incremental learning: A method of integrating genetic search based function optimization and competitive learning,” Carnegie Mellon Uni-versity, Tech. Rep. CMU-CS-94-163, 1994.

[39] M. Pelikan and H. M¨uhlenbein, “The bivariate marginal distribution algorithm,”

in Advances in Soft Computing - Engineering Design and Manufacturing, R. Roy, T. Furuhashi, and P. K. Chawdhry, Eds. London: Springer-Verlag, 1999, pp. 521–

535.

[40] G. Harik, “Linkage learning via probabilistic modeling in the ECGA,” 1999.

[41] P. Bosman and D. Thierens, “Linkage informatino processing in distribution estima-tion algorithms,” in Genetic and Evoluestima-tionary Computaestima-tion Conference, 1999, pp.

60–67.

[42] M. Pelikan and D. E. Goldberg, “Escaping hierarchical traps with competent genetic algorithms,” in Genetic and Evolutionary Computation Conference, 2001, pp. 511–

518.

[43] M. Pelikan, D. E. Goldberg, and E. Cant´u-Paz, “Linkage learning, estimation distrib-ution, and bayesian networks,” Evolutionary Computation, vol. 8, no. 3, pp. 314–341, 2000.

[44] K. Deb and D. E. Goldberg, “Analyzing deception in trap functions,” Foundations of Genetic Algorithms 2, pp. 93–108, 1994.

[45] M. Tezuka, M. Munetomo, and K. Akama, “Linkage identification by nonlinearity check for real-coded genetic algorithms,” in Genetic and Evolutionary Computation Conference, 2004, pp. 222–233.

[46] G. Syswerda, “Simulated crossover in genetic algorithms,” in Foundations of Genetic Algorithms 2, L. D. Whitley, Ed. Morgan Kaufmann, 1993, pp. 239–255.

[47] A. E. Eiben, P.-E. Rau´e, and Z. Ruttkay, “Genetic algorithms with multi-parent recombination,” in Parallel Problem Solving from Nature – PPSN III, Y. Davidor, H.-P. Schwefel, and R. M¨anner, Eds. Berlin: Springer, 1994, pp. 78–87.

[48] J. Smith and T. C. Fogarty, “An adaptive poly-parental recombination strategy,” in Proceedings of AISB-95 Workshop on Evolutionary computing, 1995, pp. 48–61.

[49] P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y.-p. Chen, A. Auger, and S. Ti-wari, “Problem definitions and evaluation criteria for the cec 2005 special session on real-parameter optimization,” Natural Computin Laboratory Department of Com-puter Science National Chiao Tung University, Tech. Rep. NCL-TR-2005001, May 2005.

[50] M. F. Tasgetiren, Y.-C. Liang, G. Gencyilmaz, and I. Eker, “Global optimization of continuous functions using particle swarm optimization,” 2005.

[51] J. J. Liang and P. N. Suganthan, “Dynamic multi-swarm particle swarm optimizer with local search,” in IEEE Congress on Evolutionary Computation, vol. 1, 2005, pp.

522–528.

[52] P. J. Ballester, J. Stephenson, J. N. Carter, and K. Gallagher, “Real-parameter optimization performance study on the cec-2005 benchmark with spc-pnx,” in IEEE Congress on Evolutionary Computation, 2005, pp. 498–505.

[53] J. Ronkkonen, S. Kukkonen, and K. V. Price, “Real-parameter optimization with differential evolution,” in IEEE Congress on Evolutionary Computation, 2005, pp.

506–513.

[54] A. K. Qin and P. N. Suganthan, “Self-adaptive differential evolution algorithm for numerical optimization,” in IEEE Congress on Evolutionary Computation, 2005, pp.

1785–1791.

[55] A. Auger and N. Hansen, “A restart cma evolutionary strategy with increasing pop-ulation size,” in IEEE Congress on Evolutionary Computation, 2005, pp. 1769–1776.

[56] J. W. Allen and F. W. Bruce, Power Generation, Operation, and Control. New York: Wiley, 1984.

[57] D. C. Walters and G. B. Sheble’, “Genetic algorithm solution of economic dispatch with valve point loading,” IEEE Transaction on Power Systems, vol. 8, no. 3, pp.

1325–1332, August 1993.

[58] G. B. Sheble and K. Brittig, “Refined genetic algorithm - economic-dispatch exam-ple,” IEEE Transactions on Power System, vol. 10, no. 1, pp. 117–124, 1995.

[59] P. H. Chen and H. C. Chang, “Large-scale economic-dispatch by genetic algorithm,”

IEEE Transactions on Power System, vol. 10, no. 4, pp. 1919–1926, 1995.

[60] S. Baskar, P. Subbaraj, and M. V. C. Rao, “Hybrid real coded genetic algorithm solu-tion to economic dispatch problem,” Computers and Electrical Engineering, vol. 29, no. 3, pp. 407–419, 2003.

[61] T. Yalcinoz, H. Altun, and M. Uzam, “Economic dispatch solution using a genetic algorithm based on arithmetic crossover,” in IEEE Power Tech Conference, 2001.

[62] J. T, J. K, J. DN, and R. T, “Evolutionary programming techniques for different kinds of economic dispatch problems,” Electric Power Systems Research, vol. 73, no. 2, pp. 169–176, 2005.

[63] N. Shinha, R. Chakrabarti, and P. K. Chattopadhyay, “Evolutionary programming technique for economic load dispatch,” IEEE Transactions on Evolutionary Compu-tation, vol. 7, no. 1, pp. 83–94, 2003.

[64] H. T. Yang, P. C. Yang, and C. L. Huang, “Evolutionary programming based eco-nomic dispatch for units with non-smooth fuel cost functions,” IEEE Transactions on Power System, vol. 11, no. 1, pp. 112–117, 1996.

[65] K. P. Wong and J. Yuryevich, “Evolutionary-programming-based algorithm for environmentally-constrained economic dispatch,” IEEE Transactions on Power Sys-tem, vol. 13, no. 2, pp. 301–306, 1998.

[66] Z. L. Gaing, “Particle swarm optimization to solving the economic dispatch consid-ering the generator constraints,” IEEE Transactions on Power System, vol. 18, no. 3, pp. 1187–1195, 2003.

[67] T. A. A. Victoire and A. E. Jeyakumar, “Hybrid pso-sqp for economic dispatch with valve-point effect,” Electric Power Systems Research, vol. 71, no. 1, pp. 51–59, 2004.

[68] J. B. Park, K. S. Lee, J. R. Shin, and K. Y. Lee, “A particle swarm optimization for economic dispatch with nonsmooth cost functions,” IEEE Transactions on Power System, vol. 20, no. 1, pp. 34–42, 2005.

[69] T. A. A. Victoire and A. E. Jeyakumar, “Discussion of ”particle swarm optimiza-tion to solving the economic dispatch considering the generator constraints”,” IEEE Transactions on Power System, vol. 19, no. 4, pp. 2121–2122, 2004.

[70] W. M. Lin, F. S. Cheng, and M. T. Tsay, “An improved tabu search for economic dispatch with multiple minima,” IEEE Transactions on Power System, vol. 17, no. 1, pp. 108–112, 2002.

[71] Y.-M. Park, J. R. Won, and J. B. Park, “New approach to economic load dispatch based on improved evolutionary programming,” Eng. Intell. Syst. Elect. Eng. Com-mun, vol. 6, no. 2, pp. 103–110, June 1998.

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