Solving the anti-covering location problem using Lagrangian relaxation

Computers and Operations Research

Volumn 24, Issue 2, 1997, Pages 127-140

  Murray, Alan T ^a   Church, Richard L ^b,c  

^a QUEENSLAND UNIVERSITY OF TECHNOLOGY   (Australia)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c Department of Geography ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANTI COVERING LOCATION PROBLEM; LAGRANGIAN RELAXATION;

COMBINATORIAL MATHEMATICS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; HEURISTIC PROGRAMMING; OPTIMIZATION;

LAGRANGE MULTIPLIERS;

EID: 0031076801     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0305-0548(96)00048-2     Document Type: Article

References (53)

1. Garey M. and Johnson D., Computers and Intractability: A guide to the Theory of NP-Completeness. Freeman and Company, New York, 1979.
2. Beasley, J., Lagrangean relaxation. In Modern Heuristic Techniques for Combinatorial Problems, ed. Colin Reeves. Wiley and Sons, New York, 1993.
3. Moon, I.D. and Chaudhry, S., An analysis of network location problems with distance constraints. Management Science, 1984, 30, 290-307.
4. Murray, A. and Church, R., Using proximity restrictions for locating undesirable facilities. Revised for, Studies in Locational Analysis, 1996.
5. Nemhauser, G. and Wolsey, L., Integer and Combinatorial Optimization. Wiley, New York, 1988.
6. Pardalos, P. and Xue, J., The maximal clique problem. Journal of Global Optimization, In press.
7. Edmonds, J., Covers and packings in a family of sets. Bulletin of the American Mathematical Society, 1962, 68, 494-499.
8. Balas, E. and Xue, J., Minimum weighted coloring of triangulated graphs, with application to maximum weight vertex packing and clique finding in arbitrary graphs. SIAM Journal on Computing, 1991, 20, 209-221.
9. Balas, E. and Yu, C., Finding a maximum clique in an arbitrary graph. SIAM Journal on Computing, 1986, 15, 1054-1068.
10. Christofides, N., Graph Theory: An Algorithmic Approach. Academic Press, New York, 1975.
11. Chaudhry, S., McCormick, S. and Moon, I.D., Locating independent facilities with maximum weight: greedy heuristics. Omega, 1986, 14, 383-389.
12. Joseph, D., Meidanis, J. and Tiwari, P., Determining DNA sequence similarity using maximal independent set algorithms for interval graphs. In Algorithm Theory-SWAT '92, eds O. Nurmi and E. Ukkonen, pp. 326-337. Springer, Berlin, 1992.
13. Barahona, F., Weintraub, A. and Epstein, R., Habitat dispersion in forest planning and the stable set problem. Operations Research, 1992, 40, 1 S14-S21.
14. Weintraub, A., Barahona, F. and Epstein, R., A column generation algorithm for solving general forest planning problems with adjacency constraints. Forest Science, 1994, 40, 142-161.
15. Kuby, M., Programming models for facility dispersion: the p-dispersion and maxisum dispersion problems. Geographical Analysis, 1987, 19, 315-329.
16. Erkut, E., The discrete p-dispersion problem. European Journal of Operational Research, 1990, 46, 48-60.
17. Erkut, E., Francis, R. and Lowe, T., A multimedian problem with interdistance constraints. Environment and Planning B, 1988, 15, 181-190.
18. Moon, I.D. and Papayanopoulos, L., Minimax location of two facilities with minimum separation: interactive graphical solutions. Journal of the Operational Research Society, 1991, 42, 685-694.
19. White, D., The maximal dispersion problem and the "first point outside the neighborhood" heuristic. Computers and Operations Research, 1991, 18, 43-50.
20. White, D., Location of two facilities with minimal separation. Journal of the Operational Research Society, 1993, 44, 1053-1057.
21. Ravi, S., Rosenkrantz, D. and Tayi, G., Heuristic and special case algorithms for dispersion problems. Operations Research, 1994, 42, 299-310.
22. Burns, J., The maximal independent set problem for cubic planar graphs. Networks, 1989, 19, 373-378.
23. Yu, C. and Chen, G., The weighted maximal independent set problem in permutation graphs. BIT, 1992, 32, 609-618.
24. Liu, J., Maximal independent sets in bipartite graphs. Journal of Graph Theory, 1993, 17, 495-507.
25. Nemhauser, G. and Sigismondi, G., A strong cutting plane/branch and bound algorithm for node packing. Journal of the Operational Research Society, 1992, 43, 444-457.
26. Burke, L., A neural design for the solution of the maximal independent set problem. European Journal of Operational Research, 1992, 62, 186-193.
27. Gendreau, M., Soriano, P. and Salvail, L., Solving the maximum clique problem using a tabu search approach. Annals of Operations Research, 1993, 41, 385-403.
28. Fleischer, M., Parallel processing, martingales, and simulated annealing: and information theoretic approach to optimization. Paper presented at TIMSIORSA Boston, April 24-27, 1994.
29. Held, M. and Karp, R., The traveling-salesman problem and minimum spanning trees. Operations Research, 1970, 18, 1138-1162.
30. Held, M. and Karp, R., The traveling-salesman problem and minimum spanning trees: Part II. Mathematical Programming, 1971, 1, 6-25.
31. Fisher, M., The Lagrangean relaxation method for solving integer programming problems. Management Science, 1981, 27, 1-18.
32. Cornuejols, G., Fisher, M. and Nemhauser, G., Location of bank accounts to optimize float: an analytical study of exact and approximate algorithms. Management Science, 1977, 23, 789-810.
33. Narula, S., Ogbu, U. and Samuelsson, H., An algorithm for the p-median problem. Operations Research, 1977, 25, 709-713.
34. Hanjoul, P. and Peeters, D., A comparison of two dual-based procedures for solving the p-median problem. European Journal of Operational Research, 1985, 20, 387-396.
35. Fisher, M., An applications oriented guide to Lagrangean relaxation. Interfaces, 1985, 15, 10-21.
36. Williams, H., Model building in mathematical programming. 3rd edn. Wiley and Sons, England, 1990.
37. Murray, A., Modeling adjacency conditions in spatial optimization problems. Ph.D. dissertation. Department of Geography, University of California, Santa Barbara, 1995.
38. Williams, H., Experiments in the formulation of integer programming problems. Mathematical Programming Study, 1974, 2, 180-197.
39. Murray, A. and Church, R., Constructing and selecting adjacency constraints. INFOR, 1996, 34.
40. Held, M., Wolfe, P. and Crowder, H., Validation of subgradient optimization. Mathematical Programming, 1974, 6, 62-88.
41. Beasley, J., A Lagrangian heuristic for set-covering problems. Naval Research Logistics, 1990, 37, 151-164.
42. Gerrard, R. and Church, R., Analyzing tradeoffs between zonal constraints and accessibility in facility location. Computers and Operations Research, 1994, 21, 79-99.
43. Goffin, J., On convergence rates of subgradient optimization methods. Mathematical Programming, 1977, 13, 329-347.
44. Padberg, M., On the facial structure of set packing polyhedra. Mathematical Programming, 1973, 5, 199-215.
45. Meneghin, B., Kirby, M. and Jones, J. G., An algorithm for writing adjacency constraints efficiently in linear programming models. In The 1988 Symposium on Systems Analysis in Forest Resources, pp.46-53. U.S. Forest Service Rocky Mountain Forest and Range Experiment Station General Technical Report RM-161, 1988.
46. Jones, J.G., Meneghin, B. and Kirby, M., Formulating adjacency constraints in linear optimization models for scheduling projects in tactical planning. Forest Science, 1991, 37, 1283-1297.
47. Balas, E. and Padberg, M., Set partitioning: a survey. SIAM Review, 1976, 18, 710-760.
48. Grotschel, M. and Wakabayashi, Y., Facets of the clique partitioning polytope. Mathematical Programming, 1990, 47, 367-387.
49. De Amorim, S., Barthelemy, J. and Ribeiro, C., Clustering and clique partitioning: simulated annealing and Tabu search approaches. Journal of Classification, 1992, 9, 17-41.
50. Toregas, C., Swain, R., ReVelle, C. and Bergman, L., The location of emergency service facilities. Operations Research, 1971, 19, 1363-1373.
51. Swain, R., A decomposition algorithm for a class of facility location problems. Ph.D. dissertation, Cornell University, Ithaca, NY, 1971.
52. Migereko, D., An analysis of the coffee cooperative marketing system in Busoga, Uganda: transportation and facilities location. Masters thesis, Department of Geography, University of California, Santa Barbara, 1983.
53. Waters, N. M., Methodology for servicing the geography of urban fire: an exploration with reference to London, Ontario. Ph.D. thesis. Department of Geography. The University of Western Ontario, London, Ontario, Canada, 1977.