Computational bounds for local search in combinatorial optimization

Computational Mathematics and Mathematical Physics

Volumn 48, Issue 5, 2008, Pages 747-763

  Kochetov, Yu A ^a  

^a SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

Local search; Metaheuristics; Overview; PLS complete problems

Indexed keywords

EID: 44149121444     PISSN: 09655425     EISSN: 15556662     Source Type: Journal    
DOI: 10.1134/S0965542508050059     Document Type: Article

References (65)

1. T. T. Arkhipova and I. V. Sergienko, "Formalization and Solution of Certain Computing-Process-Organization Problems in Data Processing Systems," Kibernetika, No. 5, 11-18 (1973).
2. T. T. Arkhipova and I. V. Sergienko, "Method of Feasible Directions and the Descent-Vector Method in Integer Programming," Kibernetika, No. 5, (1975).
3. V. A. Volkonskii, L. V. Levina, A. B. Pomanskii, et al., "An Iterative Method for Integer Programming Problems," Dokl. Akad. Nauk SSSR 169, 1289-1292 (1966).
4. M. R. Garey and D. S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness (Freeman, San Francisco, 1979; Mir, Moscow, 1982).
5. V. A. Emelichev, M. M. Kovalev, and A. M. Kononenko, "Two Methods for Approximate Solution of Linear Integer Programming Problems with Boolean Variables," in Automated Control Systems (TsNIITU, Minsk, 1971), Vol. 5 [in Russian].
6. Yu. I. Zhuravlev, "Local Algorithms for the Calculation of Information," Kibernetika, No. 1, 12-19 (1965).
7. M. M. Kovalev and V. A. Pir'yanovich, "Random Search for Locally Optimal Plans of Discrete Optimization Problems," in Improvement of the Planning and Management of the National Economy (NIIEMP, Minsk, 1975) [in Russian].
8. A. A. Korbut, I. Kh. Sigal, and Yu. Yu. Finkel'shtein, "Hybrid Methods in Discrete Programming," Izv. Akad. Nauk SSSR. Tekh. Kibern., No. 1, 65-77 (1988).
9. Yu. A. Kochetov, "Probabilistic Local Search Methods for Discrete Optimization Problems," in Discrete Mathematics and Applications (Mosk. Gos. Univ., Moscow, 2001), pp. 87-117 [in Russian].
10. Yu. A. Kochetov, M. G. Pashchenko, and A. V. Plyasunov, "On the Complexity of Local Search in the p-Median Problem," Diskret. Anal. Issled. Operats., Ser. 2 12(2), 44-71 (2005).
11. G. S. Lbov, "Choice of Effective System of Dependent Features," Vychisl. Sist., No. 19, 21-34 (1965).
12. C. H. Papadimitriou and K. Steiglitz, Combinatorial Optimization (Prentice Hall, Englewood Cliffs, 1982; Mir, Moscow, 1985).
13. L. A. Rastrigin, "Random Search: Specific Features, Historical Stages, and Prejudice," Vopr. Kibern., No. 33, 3-16 (1978).
14. I. V. Sergienko, "Application of the Descent-Vector Method to Integer Programming Problems," Upr. Sist. Mashiny, No. 3 (1975).
15. I. V. Sergienko and M. F. Kaspshitskaya, Models and Methods for Computer Solution of Combinatorial Optimization Problems (Naukova Dumka, Kiev, 1981) [in Russian].
16. I. Kh. Sigal, "Sequence of Applying Approximate Algorithms in a Combined Algorithm for Solving the Traveling Salesman Problem," Zh. Vychisl. Mat. Mat. Fiz. 29, 1714-1721 (1989).
17. V. A. Trubin, "Method for Solving Integer Linear Programming Problems of a Special Form," Dokl. Akad. Nauk SSSR 189, 552-554 (1969).
18. Yu. Yu. Finkel'shtein, Approximate Methods and Applied Discrete Programming Problems (Nauka, Moscow, 1976) [in Russian].
19. Yu. Yu. Finkel'shtein, "One Class of Discrete Programming Problems," Ekon. Mat. Methods 4, 652-655 (1968).
20. Yu. Yu. Finkel'shtein, "On the Solution of Special Discrete Programming Problems," Ekon. Mat. Methods 1, 262-270 (1965).
21. L. R. Ford, Jr. and D. R. Fulkerson, Flows in Networks (Princeton Univ. Press, Princeton, 1962; Mir, Moscow, 1966).
22. V. P. Cherenin and V. R. Khachaturov, "Solution of One Class of Facility Location Problems by Sequential Calculations," in Economic Mathematical Methods (Nauka, Moscow, 1965), No. 2, pp. 279-290 [in Russian].
23. E. H. L. Aarts, J. H. M. Korst, and P. J. M. van Laarhoven, "Simulated Annealing," in Local Search in Combinatorial Optimization (Wiley, Chichester, 1997), pp. 91-120.
24. R. K. Ahuja, O. Ergun, J. B. Orlin, and A. P. Punnen, "A Survey of Very Large-Scale Neighborhood Search Techniques," Discrete Appl. Math. 123, Issues 1-3, 75-102 (2002).
25. E. Alekseeva, Yu. Kochetov, and A. Plyasunov, "Complexity of Local Search for the p-Median Problem," Eur. J. Operat. Res. (2007).
26. E. Angel and V. Zissimopoulos, "On the Classification of NP-Complete Problems in Terms of Their Correlation Coefficient," Discrete Appl. Math. 9, 261-277 (2000).
27. S. Arora, P. Raghavan, and S. Rao, "Approximation Schemes for Euclidean k-Medians and Related Problems," Proceedings of 30th Annual ACM Symposium on Theory of Computing (1998), pp. 106-113.
28. G. Ausiello, P. Crescenzi, G. Gambosi, et al., Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties (Springer-Verlag, Berlin, 1999).
29. F. Bock, "An Algorithm for Solving "Traveling-Salesman" and Related Network Optimization Problems," Bulletin of 14th National Meeting of the Operations Research Society of America (1958), p. 897.
30. R. E. Burkard, V. G. Deineko, and G. J. Woeginger, "The Traveling Salesman Problem and the PQ-Tree," Proceedings of IPCOV (Lect. Notes Comput. Sci., Vol. 184) (Springer-Verlag, Berlin, 1996), pp. 490-504.
31. Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques, Ed. by E. K. Burke and G. Kendall (Springer-Verlag, Berlin, 2005).
32. G. A. Croes, "A Method for Solving Traveling Salesman Problems," Operat. Res. 6, 791-812 (1958).
33. A. Fabrikant, C. Papadimitriou, and K. Talwar, "The Complexity of Pure Nash Equilibria," Proceedings of 36th Annual ACM Symposium on Theory of Computing (Chicago, IL, USA, 2004), pp. 604-612.
34. C. M. Fiduccia and R. M. Mattheyses, "A Linear-Time Heuristic for Improving Network Partitions," Proceedings of 19th Design Automation Conference (IEEE Comput. Soc., Los Alamitos, CA, 1982), pp. 175-181.
35. S. T. Fischer, "A Note on the Complexity of Local Search Problems," Inf. Process. Lett. 53, 69-75 (1995).
36. M. L. Fridman, D. S. Johnson, L. A. McGeoch, and G. Ostheimer, "Data Structures for Traveling Salesman," J. Algorithms 18, 432-479 (1995).
37. L. K. Grover, "Local Search and the Local Structure of NP-Complete Problems," Operat. Res. Lett. 12, 235-244 (1992).
38. S. Guha and S. Khuller, "Greedy Strikes Back: Improved Facility Location Algorithms," J. Algorithms 31, 228-248 (1999).
39. G. Gutin, "Exponential Neighborhood Local Search for the Traveling Salesman Problem," Comput. Operat. Res. 26, 313-320 (1999).
40. G. Gutin and A. Yeo, "Small Diameter Neighborhood Graphs for the Traveling Salesman Problem: Four Moves from Tour to Tour," Comput. Operat. Res. 26, 321-327 (1999).
41. D. S. Johnson and L. A. McGeoch, "The Traveling Salesman Problem: A Case Study," Local Search in Combinatorial Optimization (Wiley, Chichester, 1997), pp. 215-310.
42. D. S. Johnson, "Local Optimization and the Traveling Salesman Problem," Automata, Languages, and Programming (Springer-Verlag, Berlin, 1990) (Lect. Notes Comput. Sci. Vol. 443), pp. 446-461.
43. D. S. Johnson, C. H. Papadimitriou, and M. Yannakakis, "How Easy Is Local Search?" J. Comput. Syst. Sci. 37, 79-100 (1988).
44. B. W. Kernighan and S. Lin, "An Efficient Heuristic Procedure for Partitioning Graphs," Bell Syst. Tech. J. 49, 291-307 (1970).
45. Yu. Kochetov and D. Ivanenko, "Computationally Difficult Instances for the Uncapacitated Facility Location Problem," Metaheuristics: Progress as Real Solvers, Ed. by T. Ibaraki, et al. (Springer-Verlag, Berlin, 2005), pp. 351-367.
46. B. Korte and J. Vygen, Combinatorial Optimization: Theory and Algorithms (Springer-Verlag, Berlin, 2005).
47. M. W. Krentel, "Structure in Locally Optimal Solutions," Proceedings of 30th Annual Symposium on Foundations of Computer Sciences, Research Triangle Park, NC, USA (1989), pp. 216-222.
48. M. W. Krentel, "On Finding and Verifying Locally Optimal Solutions," SIAM J. Comput. 19, 742-751 (1990).
49. S. Lin and B. W. Kernighan, "An Efficient Heurstic Algorithm for the Traveling-Salesman Problem," Operat. Res. 21, 498-516 (1973).
50. T. A. J. Nicholson, "A Sequential Method for Discrete Optimization Problems and Its Application to the Assignment, Traveling Salesman, and Tree Scheduling Problems," J. Inst. Math. Appl. 13, 362-375 (1965).
51. J. B. Orlin, A. P. Punnen, and A. Schulz, "Approximate Local Search in Combinatorial Optimization," SIAM J. Comput. 33, 1201-1214 (2004).
52. I. H. Osman and G. Laporte, "Metaheuristics: A Bibliography," Ann. Operat. Res. 63, 513-628 (1996).
53. C. H. Papadimitriou, "The Complexity of the Lin-Kernighan Heuristic for the Traveling Salesman Problem," SIAM J. Comput. 21, 450-463 (1992).
54. A. P. Punnen, "The Traveling Salesman Problem: New Polynomial Approximation Algorithms and Domination Analysis," Res. Rep. (St. John Univ., New Brunswick, 1996).
55. Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, Ed. by C.C. Ribeiro and P. Hansen (Kluwer. Academic, Boston, 1998).
56. A. A. Schäffer and M. Yannakakis, "Simple Local Search Problems That Are Hard to Solve," SIAM J. Comput. 20(1), 56-87 (1991).
57. P. F. Stadler, "Correlation in Landscapes of Combinatorial Optimization Problems," Europhys. Lett. 20, 479-482 (1992).
58. P. F. Stadler and W. Schnabl, "The Landscape of the Traveling Salesman Problem," Phys. Lett. A 161, 337-344 (1992).
59. C. A. Tovey, "Low Order Polynomial Bounds on the Expected Performance of Local Improvement Algorithms," Math. Program. 35, 193-224 (1986).
60. C. A. Tovey, "Local Improvement on Discrete Structures," Local Search in Combinatorial Optimization (Wiley, Chichester, 1997), pp. 57-90.
61. M. G. A. Verhoeven, P. C. J. Swinkels, and E. H. L. Aarts, Parallel Local Search and the Traveling Salesman Problem, Working Paper (Philips Res. Labs., Eindhoven, 1995).
62. T. Vredeveld and J. K. Lenstra, "On Local Search for the Generalized Graph Coloring Problem," Operat. Res. Lett. 31, 28-34 (2003).
63. P. Weiner, S. L. Savage, and A. Bagchi, "Neighborhood Search Algorithms for Guaranteeing Optimal Traveling Salesman Tours Must Be Inefficient," J. Comput. Syst. Sci. 12, 25-35 (1976).
64. M. Yannakakis, "Computational Complexity," Local Search in Combinatorial Optimization (Wiley, Chichester, 1997), pp. 19-55.
65. G. Ausello and M. Protasi, "Local Search Reducibility and Approximability of NP-Optimization Problems," Information Proc. Lett., 54, 73-79 (1995).