This paper presents a new method to isomorphism identification based on two novel evolutionary approaches—ant algorithm (AA) and artificial immune system (AIS). Salient features of the two evolutionary approaches are their efficient, robust and general-purpose algorithms for isomorphism identification despite its nondeterministic polynomial (NP) hard nature. First, based on the rearrangement of the vertexes in kinematic chains, the isomorphism identification of kinematic chains is transformed into a degree-reducible traveling salesman problem (TSP), so that the dimension and complexity can be largely decreased. Then AA and AIS algorithms are adopted to solve the transformed TSP. At last, characteristics of the two evolutionary approaches are discussed based on case studies.
1.
Zhang, W. J., 1991, “An Object-Oriented Mechanism Definition and Description With a Genetic Mechanism Model,” Technical Report No. BM-1.91, TU Delft, The Netherlands.
2.
Zhang
, W. J.
, and Breteler
, A. J.
, 1996
, “An Approach to Mechanism Topology Identification With Consideration of Design Progression
,” J. Mech. Eng. Sci.
, 211
(3
), pp. 175
–183
.3.
Shin
, J. K.
, and Krishnamurty
, S.
, 1994
, “On Identification and Canonical Numbering of Pin-Jointed Kinematic Chains
,” ASME J. Mech. Des.
, 116
(1
), pp. 182
–188
.4.
Kobler, J., Schoning, U. J., and Toran, J., 1993, The Graph Isomorphism Problems: Its Structural Complexity, Birkhauser, Boston.
5.
Tischler
, C. R.
, Samual
, A. E.
, and Hunt
, K. H.
, 1995
, “Kinematic Chain for Robot Hands—1. Orderly Number-Synthesis
,” Mech. Mach. Theory
, 30
(8
), pp. 1193
–1215
.6.
Davis, L., 1991, Handbook of Genetic Algorithms, Van Nostrand Reinbold, New York.
7.
Zhou, J., Cha, J. Z., and Xiao, R. B., 1998, Intelligent Design, Higher Education Press, Beijing (in Chinese).
8.
Bonabeau
, E.
, Dorigo
, M.
, and Theraulaz
, G.
, 2000
, “Inspiration for Optimization From Social Insect Behavior
,” Nature (London)
, 6
, pp. 39
–42
.9.
Xiao
, R. B.
, and Wang
, L.
, 2002
, “Artificial Immune System: Principle, Models, Analysis and Perspectives
,” Chin. J. Comput.
, 25
(12
), pp. 1281
–1293
.10.
Dobrjanskyi
, L.
, and Freudenstein
, F.
, 1989
, “Some Applications of Group Theory to the Enumeration and Structural Analysis of Basic Kinematic Chains
,” ASME J. Mech., Transm., Autom. Des.
, 111
, pp. 494
–497
.11.
Wilson, R., 1972, Introduction to Graph Theory, 3rd ed., Longman, London.
12.
Gambardella, L. M., and Dorigo, M., 1996, “Solving Symmetric and Asymmetric TSPs by Ant Colony,” Proceedings of the IEEE Conference on Evolution Computation, IEEE Press, New York, pp. 622–627.
13.
Dorigo
, M.
, and Gambardella
, L. M.
, 1997
, “Ant Colony System: a Cooperative Learning Approach to Traveling Salesman Problem
,” IEEE Trans. Evol. Comput.
, 1
(1
), pp. 73
–81
.14.
Xiao, R. B., and Tao, Z. W., 2003, “Co-Evolutionary Ant Algorithm and Application in Multi-Objective Optimization Problems,” ASME 2003 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, Chicago, IL, DETC2003/CIE-48258.
15.
Dorigo
, M.
, Bonabeau
, E.
, and Theraulaz
, G.
, 2000
, “Ant Algorithms and Stigmergy
,” Future Generation Comput. Syst.
, 16
, pp. 851
–871
.16.
Xiao, R. B., He, J. H., Chang, M., and Shi, H. M., 2001, “An Ant Algorithm Approach to the Isomorphism Identification of Mechanism Kinematic Chains,” ASME 2001 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, Pittsburgh, PA, DETC2001/CIE21674.
17.
Endoh, S., Toma, N., and Yamada, K., 1998, “Immune Algorithm for n-TSP,” Proc. of 1998 IEEE International Conference on Systems, Man, and Cybernetics, San Diego, CA, pp. 3844–3849.
18.
Chun
, J. S.
, Kim
, M. K.
, and Jung
, H. K.
, 1997
, “Shape Optimization of Electromagnetic Devices Using Immune Algorithm
,” IEEE Trans. Magn.
, 33
(2
), pp. 1876
–1879
.19.
Huang
, S. J.
, 2000
, “An Immune Based Optimization Method to Capacitor Placement in a Radial Distribution System
,” IEEE Trans. Power Deliv.
, 15
(2
), pp. 744
–749
.20.
Xiao, R. B., Wang, L., and Fan, Z., 2002, “An Artificial Immune System Based Isomorphism Identification Method for Mechanism Kinematic Chains,” ASME 2002 Design Engineering Technical Conferences and Computers and Information in Engineering Conference, ASME, Montreal, Canada, DETC2002/DAC-34063.
21.
Mruthyunjaya
, T. S.
, and Balasubramanzan
, H. R.
, 1987
, “In Quest of a Reliable and Efficient Computational Test for Detection of Isomorphism in Kinematic Chains
,” Mech. Mach. Theory
, 22
(2
), pp. 131
–140
.22.
Grefenstette, J., Gopal, R., and Gucht, D. V., 1985, “Genetic Algorithms for the Traveling Salesman Problem,” Proc. of 1st Int. Conf. On Genetic Algorithms and Their Applications, Law Erlbaum, Hillsdale, NJ, pp. 160–168.
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