Advertisement

Springer Nature is making Coronavirus research free. View research | View latest news | Sign up for updates

Parallel decomposition of combinatorial optimization problems using electro-optical vector by matrix multiplication architecture

  • 155 Accesses

  • 5 Citations

Abstract

A new state space representation for a class of combinatorial optimization problems, related to minimal Hamiltonian cycles, enables efficient implementation of exhaustive search for the minimal cycle in optimization problems with a relatively small number of vertices and heuristic search for problems with large number of vertices. This paper surveys structures for representing Hamiltonian cycles, the use of these structures in heuristic optimization techniques, and efficient mapping of these structures along with respective operators to a newly proposed electrooptical vector by matrix multiplication (VMM) architecture. Record keeping mechanisms are used to improve solution quality and execution time of these heuristics using the VMM. Finally, the utility of a low-power VMM based implementation is evaluated.

This is a preview of subscription content, log in to check access.

References

  1. 1.

    Larrinaga P, Kuijpers CMH, (1999) Murga: Genetic algorithms for the travelling salesman problem: a review of representations and operators. Artif Intell Rev 129–170

  2. 2.

    Tamir DE, Shaked NT, Wilson PJ, Dolev S (2009) High-speed and low-power electro-optical DSP coprocessor. J Opt Soc Am A 26:A11–A20

  3. 3.

    Karhi D, Tamir DE (2009) Caching in the TSP search space. In: Next generation applied intelligence, Tainan, Taiwan, pp 221–230

  4. 4.

    Wang L, Maciejewski AA, Siegel HJ, Roychowdhury VP (2005) A study of five parallel approaches to a genetic algorithm for the traveling salesman problem. Intell Autom Soft Comput 11(4):217–234

  5. 5.

    Shaked NT, Messika S, Dolev S, Rosen J (2007) Optical solution for bounded NP-complete problems. Appl Opt 46(5):711–724

  6. 6.

    Jog P, Suh JY, Van Gucht D (1989) The effects of population size, heuristic crossover and local improvement on a genetic algorithm for the traveling salesman problem. In: 3rd int’l conf genetic algorithms, pp 110–115

  7. 7.

    Goodman GW (1996) Introduction to Fourier optics. McGraw-Hill, New York

  8. 8.

    Feitelson DG (1988) Optical computing: a survey for computer scientists. MIT Press, Cambridge

  9. 9.

    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of NP-completeness. Freeman, New York

  10. 10.

    Johnson DS, McGeoch LA (1997) The traveling salesman problem: a case study in local optimization. Local Search in Combinatorial Optimization. Wiley, New York, pp 215–310

  11. 11.

    Applegate DL, Bixby RE, Vasek C, Cook WJ (2007) The traveling salesman problem: a computational study. Princeton University Press, Princeton

  12. 12.

    Gutfreund D, Shaltiel R, Ta-Shma A (2007) If NP languages are hard on the worst-case, then it is easy to find their hard instances. Comput Complex 16(4):412–441

  13. 13.

    Reinelt G (1991) TSPLIB—a traveling salesman problem library. ORSA J Comput 3(4):376–384; http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/

  14. 14.

    Haist T, Osten W (2007) An optical solution for the traveling salesman problem. Opt Express 15:10473–10482

  15. 15.

    Held M, Karp RM (1970) The traveling salesman problem and minimum spanning trees. Oper Res 18:1138–1162

  16. 16.

    Anonymous, Concorde TSP Solver, http://www.tsp.gatech.edu/concorde.html

  17. 17.

    Pearl J (1984) Heuristics: Intelligent search strategies for computer problem solving. Addison-Wesley, Reading

  18. 18.

    Russell SJ, Norvig P (1995) Artificial intelligence: a modern approach. Prentice-Hall, New York

  19. 19.

    Xi B, Liu Z, Raghavachari M, Xia C, Zhang L (2004) A smart hill-climbing algorithm for application server configuration. In: Proceedings of the 13th international conference on world wide web, pp 287–296

  20. 20.

    Vose MD (1999) The simple genetic algorithm: foundations and theory. MIT Press, Cambridge

  21. 21.

    Glover F, Laguna M (1997) Tabu search. Kluwer Academic, Norwell

  22. 22.

    Kennedy J, Eberhart RC (2001) Swarm intelligence. Academic Press, San Diego

  23. 23.

    Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

  24. 24.

    Zilberstein S (1996) Using anytime algorithms in intelligent systems. AI Mag 17(3):73–83

  25. 25.

    Ramos T, Cozman G (2005) Anytime anyspace probabilistic inference. Int J Approx Reason 38(1):53–80

  26. 26.

    Aarts E, Lenstra J (2003) Local search in combinatorial optimization. Princeton University Press, Princeton

  27. 27.

    Ursache L (2007) Representation models for solving TSP with genetic algorithms. In: Proceedings of CNMI, Bacău, pp 291–298

  28. 28.

    Or I (1976) Traveling salesman types combinatorial problems and their relations to the logistics of regional blood banking. PhD thesis, Northwestern University

  29. 29.

    Borovska P (2006) Solving the travelling salesman problem in parallel by genetic algorithm on multicomputer cluster. In: Int conf on computer systems and technologies, pp 1–6

  30. 30.

    Gang P, Iimura I, Nakatsuru T, Nakayama S (2005) Efficiency of local genetic algorithm in parallel processing. In: Sixth international conference on parallel and distributed computing, applications and technologies, pp 620–623

  31. 31.

    Langdon WB, Banzhaf W (2008) A SIMD interpreter for genetic programming on GPU graphics cards. In: EuroGP, pp 73–85

  32. 32.

    Inoue T, Sano M, Takahashi Y (1997) Design of a processing element of a SIMD computer for genetic algorithms. In: Proceedings of the high-performance computing on the information superhighway, pp 688–691

  33. 33.

    Vega-Rodriguez MA, Gutierrez-Gil R, Avila-Roman JM, Sanchez-Perez JM, Gomez-Pulido JA (2005) Genetic algorithms using parallelism and FPGAs: the TSP as case study. In: International conference workshops on parallel processing, pp 573–579

  34. 34.

    Collings N, Sumi R, Weible KJ, Acklin B, Xue W (1993) The use of optical hardware to find good solutions of the travelling salesman problem (TSP). Proc SPIE 1806:637–641

  35. 35.

    Shaked NT, Tabib T, Simon G, Messika S, Dolev S, Rosen J (2007) Optical binary-matrix synthesis for solving bounded NP-complete combinatorial problems. Opt Eng 46(10):1–11

  36. 36.

    Oltean M (2008) Solving the Hamiltonian path problem with a light-based computer. Nat Comput 7(1):57–70

  37. 37.

    Oltean M, Muntean O (2008) Solving NP-complete problems with delayed signals: an overview of current research directions. In: Proceedings of 1st international workshop on optical supercomputing, pp 115–128

  38. 38.

    Pitsoulis L, Resende M (1995) Greedy randomized adaptive search procedures. J Glob Optim 6(2):109–133

  39. 39.

    Lowell D, El Lababedi B, Novoa C, Tamir DE (2009) The locality of reference of genetic algorithms and probabilistic reasoning. In: The international conference on artificial intelligence and pattern recognition, Florida, pp 221–228

Download references

Author information

Correspondence to Dan E. Tamir.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Tamir, D.E., Shaked, N.T., Geerts, W.J. et al. Parallel decomposition of combinatorial optimization problems using electro-optical vector by matrix multiplication architecture. J Supercomput 62, 633–655 (2012). https://doi.org/10.1007/s11227-010-0517-9

Download citation

Keywords

  • Optical super computing
  • Parallel processing
  • Combinatorial optimization
  • Hamiltonian cycles
  • The traveling salesman problem
  • Heuristic search