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fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Hu, X.; Zhang, J.; Li, Y. (2008)
Publisher: Springer
Languages: English
Types: Article
Subjects: QA75, QA76

Classified by OpenAIRE into

ACM Ref: ComputingMethodologies_ARTIFICIALINTELLIGENCE, MathematicsofComputing_NUMERICALANALYSIS
Research into ant colony algorithms for solving continuous optimization problems forms one of the most\ud significant and promising areas in swarm computation. Although traditional ant algorithms are designed for combinatorial\ud optimization, they have shown great potential in solving a wide range of optimization problems, including continuous\ud optimization. Aimed at solving continuous problems effectively, this paper develops a novel ant algorithm termed "continuous orthogonal ant colony" (COAC), whose pheromone deposit mechanisms would enable ants to search for\ud solutions collaboratively and effectively. By using the orthogonal design method, ants in the feasible domain can explore\ud their chosen regions rapidly and e±ciently. By implementing an "adaptive regional radius" method, the proposed\ud algorithm can reduce the probability of being trapped in local optima and therefore enhance the global search capability and accuracy. An elitist strategy is also employed to reserve the most valuable points. The performance of the COAC is\ud compared with two other ant algorithms for continuous optimization of API and CACO by testing seventeen functions\ud in the continuous domain. The results demonstrate that the proposed COAC algorithm outperforms the others.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [1] Deneubourg J L, Aron S, Goss S, Pasteels J M. The selfspeed and avoid trapping in local optima and converge organizing exploratory pattern of the Argentine ant. Journal prematurely. (b) The best region becomes a region of Insect Behavior, 1990, 3: 159{168. with a larger radius in the current iteration. (c) If the [2] Goss S, Aron S, Deneubourg J L, Pasteels J M. Self-
    • organized shortcuts in the Argentine ant. Naturwisradius is smaller than the prede¯ned value, it will be senschaften, 1989, 76(12): 579{581. reset to a random value that may be larger than the [3] Dorigo M, StuÄtzle T. Ant Colony Optimization. the MIT previous one. Press, 2003.
    • For unimodal functions, the radiuses are gradually [4] Dorigo M, Gambardella L M. Ant colony system: A cooper-
    • ative learning approach to the traveling salesman problem. reduced except for f4 in Fig.7. For multimodal func- IEEE. Trans. Evol. Comput., 1997, 1(1): 53{66. tions and f4, whose global optima are harder to ¯nd, [5] Toth P, Vigo D. The Vehicle Routing Problem. SIAM Monothe radiuses °uctuate with step changes. Each step graphs on Discrete Mathematics and Applications, Philadel-
    • phia, Society for Industrial & Applied Mathematics, 2001. jump accompanies a great reduction of the function [6] Gambardella L M, Taillard E¶ D, Agazzi G. MACS-VRPTW: values, where large radiuses can help jump out of lo- A Multiple Ant Colony System for Vehicle Routing Problems cal optima. with Time Windows. New Ideas in Optimization, Corne
    • 3) As the graphs are drawn by radiuses and function D, Dorigo M, Glover F (eds.), London, McGraw Hill, 1999,
    • pp.63{76. values of the best results, the radiuses are unchanged [7] Zhang J, Hu X M, Tan X, Zhong J H, Huang Q. Impleif no better results have been found. Hence, horizon mentation of an ant colony optimization technique for job lines are shown in the graph, such as the radiuses of shop scheduling problem. Transactions of the Institute of f1 and f3 etc. Measurement and Control, 2006, 28(1): 1{16.
    • [8] Zecchin A C, Simpson A R, Maier H R, Nixon J B. Paramet-
    • It can be seen from the graphs that the sizes of the ric study for an ant algorithm applied to water distribution radiuses control the accuracy of the resulting function system optimization. IEEE Trans. Evol. Comput., 2005, 9: value. The smaller the radiuses, the higher the accu- 175{191. racy of the result is achieved. [9] Parpinelli R S, Lopes H S, Freitas A A. Data mining with
    • Comput., 2002, 4: 321{332. 7 Conclusions [10] Sim K M, Sun W H. Ant colony optimization for routing and
    • This paper has developed a novel algorithm, contin- Systems, Man, and Cybernetics | Part A: System and Huuous orthogonal ant colony (COAC), to solve continu- mans, 2003, 33: 560{572.
    • [11] Bilchev G, Parmee I C. The ant colony metaphor for searchous optimization problems. It utilizes the orthogonal ing continuous design spaces. In Proc. the AISB Workshop design method for ant colony optimization (ACO) to on Evolutionary Computation, University of She±eld, UK, search the continuous domain completely and e®ec- LNCS 933, Springer-Verlag, Berlin, Germany, 1995, pp.25{ tively. 39.
    • [12] Wodrich M, Bilchev G. Cooperative distributed search: The
    • The performance of the proposed COAC algorithm ant's way. Control and Cybernetics, 1997, 3: 413{446. has been compared with that of two other ant algo- [13] Mathur M, Karale S B, Priye S, Jyaraman V K, Kulkarni B rithms, API and CACO, in solving seventeen contin- D. Ant colony approach to continuous function optimization. uous functions. The results show that the proposed Ind. Eng. Chem. Res., 2000, 39: 3814{3822.
    • [14] Holland J H. Adaptation in Natural and Arti¯cial Systems. COAC algorithm is among the fastest and the most Second Edition (First Edition, 1975), Cambridge: the MIT accurate in solving unimodal functions. Although Press, MA, 1992. [15] Monmarch¶e N, Venturini G, Slimane M. On how Pachy- Conference/Exhibition on High Performance Computing in
    • condyla apicalis ants suggest a new search algorithm. Future the Asia-Paci¯c Region, May 2000, 2: 659{663.
    • Generation Computer Systems, 2000, 16: 937{946. [36] Liang X B. Orthogonal designs with maximal rates. IEEE [16] Dr¶eo J, Siarry P. Continuous interacting ant colony algo- Trans. Information Theory, 2003, 49(10): 2468{2503.
    • rithm based on dense heterarchy. Future Generation Com- [37] Tanaka H. Simple genetic algorithm started by orthogonal
    • puter Systems, 2004, 20: 841{856. design of experiments. In Proc. SICE Annual Conference [17] Dr¶eo J, Siarry P. A new ant colony algorithm using the heter- in Sapporp, August 2004, pp.1075{1078.
    • archical concept aimed at optimization of multiminima con- [38] Salomon R. Reevaluating genetic algorithm performance un-
    • tinuous functions. In Proc. ANTS 2002, Brussels, Belgium, der coordinate rotation of benchmark functions. BioSys-
    • LNCS 2463, 2002, pp.216{221. tems, 1996, 39: 263{278. [18] Socha K. ACO for continuous and mixed-variable optimiza-
    • tion. In Proc. ANTS 2004, Brussels, Belgium, LNCS 3172, Xiao-Min Hu received her
    • 2004, pp.25{36. BSc. degree in computer science [19] Socha K, Dorigo M. Ant colony optimization for continuous in 2006 from Sun Yat-Sen Univer-
    • domains. Eur. J. Oper. Res., 2008, 185(3): 1155{1173. sity, Guangzhou, China. She is cur[20] Pourtakdoust S H, Nobahari H. An extension of ant colony rently a Ph.D. candidate majored
    • ANTS 2004, Brussels, Belgium, LNCS 3172, 2004, pp.294{ in computer application and tech-
    • 301. nology in Sun Yat-Sen University. [21] Kong M, Tian P. A binary ant colony optimization for the Her research interests include arti¯-
    • Security (CIS'05), Xi'an, China, LNAI 3801, 2005, pp.682{ biological information.
    • 687. [22] Kong M, Tian P. A direct application of ant colony optimiza- Jun Zhang received the Ph.D.
    • In Proc. ANTS 2006, Brussels, Belgium, LNCS 4150, 2006, degree in electrical engineering from
    • pp.324{331. City University of Hong Kong, in [23] Chen L, Shen J, Qin L, Chen H J. An improved ant colony 2002. From 2003 to 2004, he was a
    • algorithm in continuous optimization. Journal of Systems Brain Korean 21 Postdoctoral Fel-
    • Science and Systems Engineering, 2003, 12(2): 224{235. low in the Department of EECS, [24] Dr¶eo J, Siarry P. An ant colony algorithm aimed at dynamic Korea Advanced Institute of Science
    • continuous optimization. Appl. Math. Comput., 2006, 181: and Technology (KAIST). Since
    • 2004, he has been with the Sun Yat[25] Feng Y J, Feng Z R. An immunity-based ant system for con-
    • and Cybernetics, Shanghai, August 26{29, 2004, pp.1050{ Computer Science. He has authored three research book
    • 1054. chapters and over 50 refereed technical papers in his re[26] Shelokar P S, Siarry P, Jayaraman V K, Kulkarni B D. Parti- search areas. His research interests include genetic algo-
    • continuous optimization. Appl. Math. Comput., 2006, doi:
    • 10.1016/j.amc. 2006.09.098. cash °ow optimization and nonlinear time series analysis [27] Rao C R. Factorial experiments derivable from combinato- and prediction.
    • rial arrangements of arrays. J. Royal Statist. Soc., 1947,
    • 9(Suppl.): 128{139. Yun Li received the B.S. de[28] Bush K A. Orthogonal arrays [Dissertation]. University of gree in radio electronics science
    • North Carolina, Chapel Hill, 1950. from Sichuan University, Chengdu, [29] Math Stat Res Group, Chinese Acad Sci. Orthogonal De- China, in 1984, an M.Sc. de-
    • sign. Bejing: People Education Pub., 1975. (in Chinese) gree in electronic engineering from [30] Fang K T, Wang Y. Number-Theoretic Methods in Statis- University of Electronic Science
    • tics. New York: Chapman & Hall, 1994. [31] Hedayat A S, Sloane N J A, Stufken J. Orthogonal Arrays: and Technology of China (UESTC),
    • Theory and Applications. New York: Springer-Verlag, 1999. Chengdu, in 1987, and a Ph.D. de[32] Nathanson M B. Elementary Methods in Number Theory. gree in computing and control en-
    • New York: Springer-Verlag, 2000. gineering from University of Strath[33] Zhang Q, Leung Y W. An orthogonal genetic algorithm for clyde, Glasgow, U.K., in 1990. From 1989 to 1990, he
    • Computation, 1999, 3(1): 53{62. for Industrial Systems and Control Limited, Glasgow, U.K. [34] Leung Y W, Wang W. An orthogonal genetic algorithm with He became a lecturer at the University of Glasgow in 1991.
    • Evol. Comput., 2001, 5(1): 41{53. In 2002, he served as a visiting professor at Kumamoto [35] Ho S Y, Chen J H. A genetic-based systematic reasoning University, Japan. He is currently a senior lecturer at Uni-
    • orthogonal array crossover. In Proc. the Fourth Internal 1996, he independently invented the \inde¯nite scatter1) /* Initialization phase */
    • countE := 0 2) /* Orthogonal exploration phase */
    • For each region j do visitj := 0 End-for
    • For k := 1 to m do
    • Choose the next region j according to (1) (2)
    • visitj := visitj + 1
    • countE := countE + 1
    • countE := 0
    • End-if 3) /* Global modulation phase */
    • countG := 0 SjR := ; Sj0R = ; For j := 1 to ¹ do
    • rank j := 0
    • Add region j to SjR End-for For i :=1 to à £ ¹ do
    • Find the region j with the minimum value satis¯ed 1) f10 and f11
    • 1 yi = 1 + (xi + 1);
    • 8 p(xi ¡ a)j;
    • > u(xi; a; p; j) = < 0; The value of p is equal to 5, 7, and 10 respectively from
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

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