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TECHNICAL PAPERS

Two- and Three-Dimensional Path Optimization for Production Machinery

[+] Author and Article Information
W. A. Khan

Faculty of Mechanical Engineering, GIK Institute of Engineering Sciences and Technology, Topi-23460, N.W.F.P, Pakistan

D. R. Hayhurst

Department of Mechanical Engineering, UMIST, Manchester, England, UK

J. Manuf. Sci. Eng 122(1), 244-252 (Apr 01, 1999) (9 pages) doi:10.1115/1.538901 History: Received February 01, 1998; Revised April 01, 1999
Copyright © 2000 by ASME
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References

Khan, W. A., 1990, Investigation of Tool Path Sequencing Problem in Hierarchical CIM Environment, Ph.D. thesis, University of Sheffield, Sheffield, UK.
Khan,  W. A., and Hayhurst,  D. R., 1991, “Computer Aided Part Program Segmentation and Reconstruction for Minimization of Machine Tool Residence Time,” Int. J. Comput. Integr. Manuf., 4, No. 5, pp. 300–314.
Kalpakjian, S., 1992, Manufacturing Engineering and Technology, 2nd Ed., Addison-Wesley Publishing Company, New York, USA.
Chryssolouris, G., 1992, Manufacturing Systems—Theory and Practice, Springer Verlag, New York.
Alting, L., 1994, Manufacturing Engineering Processes, 2nd Ed., Marcel Dekker, New York.
Dantzig,  G. B., , 1954, “Solution of a Large Scale Traveling Salesman Problem,” Oper. Res., 2, pp. 393–410.
Johnson,  D. S., , 1989, “Optimization by Simulated Annealing: An Experimental Evaluation (Part I), Graph Partitioning,” Oper. Res., 37, No. 6, pp. 865–892.
Johnson,  D. S., , 1991, “Optimization by Simulated Annealing: An Experimental Evaluation (Part II), Graph Partitioning,” Oper. Res., 39, No. 3, pp. 378–406.
Johnson, D. S., et al., 1997, The Traveling Salesman Problem: A Case Study. Local Search in Combinatorial Optimization, Aarts, E., and Lenstra, J. K., eds., John Wiley & Sons.
Hoffman, A. J., and Wolfe, P., 1997, “History,” in The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization, Lawler, E. L., Lenstra, J. K., Rinooy Kan, A. H. G., and Shmoys, D. B., eds., John Wiley, Chichester.
Andreou, D. A., 1987, Heuristic Strategies for Large Traveling Salesman Problem Applicable to the Traveling Sequence Optimization of Industrial Robots, Ph.D. thesis, Drexel University, USA.
Reinelt, G., 1994, “The Traveling Salesman: Computational Solutions for TSP Applications,” Lecture Notes in Computer Science, Vol. 840, Springer Verlag.
Khan,  W. A., Hayhurst,  D. R., and Cannings,  C., 1999, “Probabilistic Shortest Path Determination Under Approach and Exit Constraints,” Eur. J. of Operational Res., 117, pp. 310–325.
Khan, W. A., Khan, M. A., and Hayhurst, D. R., 1998, “Use of Technological Constraints as Enumeration Criteria for the Solution of TSP Applicable to Production Machinery,” submitted for publication in Journal of Engineering Manufacture: Proceedings of the Institution of Mechanical Engineers, UK.
Kirkpatric,  S., Gelatt,  C. D., and Vecchi,  M. P., 1983, “Optimization by Simulated Annealing,” Science, 220, pp. 671–680.
Lundy,  M., 1985, “Application of Annealing Algorithm to Combination Problems in Statistics,” Biometrika, 72, pp. 191–198.
Lundy, M., and Mees, A., 1986, “Convergence of the Annealing Algorithm,” Math. Program., 34 .
Khan, W. A., 1996, “Path Optimisation for Computer Numerical Control Machines,” Proceedings 36th Annual Convention of the Institution of Engineers, Pakistan.
Metropolis,  N., Rosenbluth,  A. W., Rosenbluth,  M. N., and Teller,  A. H., 1953, “Equation of State Calculation by Fast Computing Machines,” J. Chem. Phys., 21, pp. 1087–1092.
Reinelt, G., 1998, “The TSPLIB: A Library of TSP Problem Instances,” reinelt@ares.iwr.Uni-Heidelberg.DE.

Figures

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Variation of acceptable error with error probability for 100 nodes TSP
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Variation of control parameter with iterations for 100 nodes classical TSP
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Variation of control parameter and its effect on allowable iterations applicable to 100–500 nodes TSP
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Initial path for 100 node classical TSP
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Final path for 100 node classical TSP at BULL DPX 20/600 workstation
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Initial path for nodes distributed along the periphery of a cube
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Final path for nodes distributed along the periphery of a cube
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Initial path for 100 randomly distributed nodes
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Final path for 100 randomly distributed nodes
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Initial path for 500 randomly distributed nodes
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Final path for 500 randomly distributed nodes
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Convergence behavior of 100–500 nodes TSPs at BULL DPX 20/600 workstation
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Execution time for fixed iteration termination of 100–500 node TSPs
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Initial path for nodes distributed along the periphery of a sphere
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Final path for nodes distributed along the periphery of a sphere
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Final path for 100 nodes classical TSP at Pentium based personal computer
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Initial path for 100 nodes distributed along the periphery of a circle
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Final path for 100 nodes distributed along the periphery of a circle
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Final path for 500 randomly distributed nodes solved at Pentium based personal computer

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