Advertisement

Heuristics for Nonlinear Assignment Problems

  • Stefan Voss
Part of the Combinatorial Optimization book series (COOP, volume 7)

Abstract

Given two sets of elements, assignment problems require a mapping of the elements of one set to those of the other. Distinguishing between bijective and injective mappings we may classify two main areas, i.e., assignment and semiassignment problems. Nonlinear assignment problems (NAPs) are those (semi-) assignment problems where the objective function is nonlinear.

In combinatorial optimization many NAPs are natural extensions of the linear (semi-) assignment problem and include, among others, the quadratic assignment problem (QAP) and its variants. Due to the intrinsic complexity not only of the QAP and related NAPs heuristics are a primary choice when it comes to the successful solution of these problems in time boundaries deemed practical. In this paper we survey existing heuristic approaches for various NAPs.

Keywords

Local Search Simulated Annealing Tabu Search Assignment Problem Quadratic Assignment Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. [Aarts and Lenstra, 1997]
    Aarts, E. and Lenstra, J., editors (1997). Local Search in Combinatorial Optimization. Wiley, Chichester.MATHGoogle Scholar
  2. [Ahuja et al., 1995]
    Ahuja, R., Orlin, J., and Tivari, A. (1995). A greedy genetic algorithm for the quadratic assignment problem. Working paper 3826–95, Sloan School of Management, MIT.Google Scholar
  3. [Angel and Zissimopoulos, 1998]
    Angel, E. and Zissimopoulos, V. (1998). On the quality of local search for the quadratic assignment problem. Discrete Applied Mathematics, 82:15–25.MathSciNetMATHCrossRefGoogle Scholar
  4. [Balas and Saltzman, 1991]
    Balas, E. and Saltzman, M. (1991). An algorithm for the three-index assignment problem. Operations Research, 39:150–161.MathSciNetMATHCrossRefGoogle Scholar
  5. [Bandelt et al., 1994]
    Bandelt, H.-J., Crama, Y., and Spieksma, F. (1994). Approximation algorithms for multidimensional assignment problems with decomposable costs. Discrete Applied Mathematics, 49:25–50.MathSciNetMATHCrossRefGoogle Scholar
  6. [Bartolomei-Suarez and Egbelu, 2000]
    Bartolomei-Suarez, S. and Egbelu, P. (2000). Quadratic assignment problem with adaptable material handling devices. International Journal of Production Research, 38:855–874.MATHCrossRefGoogle Scholar
  7. [Battiti, 1996]
    Battiti, R. (1996). Reactive search: Toward self-tuning heuristics. In Rayward-Smith, V., Osman, I., Reeves, C., and Smith, G., editors, Modern Heuristic Search Methods, pages 61–83, Chichester. Wiley.Google Scholar
  8. [Battiti and Tecchiolli, 1992]
    Battiti, R. and Tecchiolli, G. (1992). Parallel biased search for combinatorial optimization: genetic algorithms and tabu. Microprocessors and Microsystems, 16:351–367.CrossRefGoogle Scholar
  9. [Battiti and Tecchiolli, 1994a]
    Battiti, R. and Tecchiolli, G. (1994a). The reactive tabu search. ORSA Journal on Computing, 6:126–140.MATHCrossRefGoogle Scholar
  10. [Battiti and Tecchiolli, 1994b]
    Battiti, R. and Tecchiolli, G. (1994b). Simulated annealing and tabu search in the long run: a comparison on QAP tasks. Computer and Mathematical Applications, 28:1–8.MATHCrossRefGoogle Scholar
  11. [Bazaraa and Kirca, 1983]
    Bazaraa, M. and Kirca, O. (1983). A branch-andbound heuristic for solving the quadratic assignment problem. Naval Research Logistics Quarterly, 30:287–304.MathSciNetMATHCrossRefGoogle Scholar
  12. [Bazaraa and Sherali, 1980]
    Bazaraa, M. and Sherali, H. (1980). Bender’s partitioning scheme applied to a new formulation of the quadratic assignment problem. Naval Research Logistics Quarterly, 27:29–41.MathSciNetMATHCrossRefGoogle Scholar
  13. [Bersini and Varela, 1991]
    Bersini, H. and Varela, F. (1991). The immune recruitment mechanism: A selective evolutionary strategy. In Proceedings of the 4th International Conference on GeneticAlgorithms, San Mateo. Morgan Kaufmann.Google Scholar
  14. [Block, 1978]
    Block, T. (1978). A new construction algorithm for facilities layout. Journal of Engineering Production, 2:111–126.Google Scholar
  15. [Boender et al., 1982]
    Boender, C., Kan, A. R., Timmer, A., and Stougie, L. (1982). A stochastic method for global optimization. Mathematical Programming, 22:125–140.MathSciNetMATHCrossRefGoogle Scholar
  16. [Bölte, 1994]
    Bölte, A. (1994). Modelle und Verfahren zur innerbetrieblichen Standortplanung. Physica, Heidelberg.CrossRefGoogle Scholar
  17. [Bonomi and Lutton, 1986]
    Bonomi, E. and Lutton, J.-L. (1986). The asymptotic behavior of quadratic sum assignment problems: A statistical mechanics approach. European Journal of Operational Research, 26:295–300.MathSciNetMATHCrossRefGoogle Scholar
  18. [Brown et al., 1989]
    Brown, E., Huntley, L., and Spillance, R. (1989). A parallel genetic heuristic for the quadratic assignment problem. In Schaffer, J., editor, Proceedings of the 3rd International Conference on Genetic Algorithms, Arlington, pages 406–415, San Mateo. Morgan Kaufmann.Google Scholar
  19. [Bruijs, 1984]
    Bruijs, P. (1984). On the quality of heuristic solutions to a 19x19 quadratic assignment problem. European Journal of Operational Research, 17:21–30.MathSciNetMATHCrossRefGoogle Scholar
  20. [Buffa et al., 1964]
    Buffa, E., Armour, G., and Vollmann, T. (1964). Allocating facilities with CRAFT. Harvard Business Review, 42 (2):136–158.Google Scholar
  21. [Burkard and Bönniger, 1983]
    Burkard, R. and Bönniger, T. (1983). A heuristic for quadratic boolean programs with applications to quadratic assignment problems. European Journal of Operational Research, 13:374–386.MathSciNetMATHCrossRefGoogle Scholar
  22. [Burkard and Çela, 1995]
    Burkard, R. and Çela, E. (1995). Heuristics for biquadratic assignment problems and their computational comparison. European Journal of Operational Research, 83:283–300.MATHCrossRefGoogle Scholar
  23. [Burkard and Çela, 1998]
    Burkard, R. and Çela, E. (1998). Quadratic and three-dimensional assignments: An annotated bibliography. In Dell’Amico, M., Maffioli, F., and Martello, S., editors, Annotated Bibliographies in Combinatorial Optimization, pages 373–392, Chichester. Wiley.Google Scholar
  24. [Burkard et al., 1994]
    Burkard, R., Çela, E., and Klinz, B. (1994). On the biquadratic assignment problem. In Pardalos, P. and Wolkowicz, H., editors, Quadratic Assignment and Related Problems, pages 117–146, Providence. AMS.Google Scholar
  25. [Burkard et al., 1998]
    Burkard, R., Çela, E., Pardalos, P., and Pitsoulis, L. (1998). The quadratic assignment problem. In Pardalos, P. and Du, D.-Z., editors, Handbook of Combinatorial Optimization, pages 241–338, Boston. Kluwer.Google Scholar
  26. [Burkard and Derigs, 1980]
    Burkard, R. and Derigs, U. (1980). Assignment and matching problems: Solution methods with FORTRAN programs, volume 184 of Lecture Notes in Economics and Mathematical Systems. Springer, Berlin.MATHGoogle Scholar
  27. [Burkard and Fincke, 1982]
    Burkard, R. and Fincke, U. (1982). On random quadratic bottleneck assignment problems. Mathematical Programming, 23:227–232.MathSciNetMATHCrossRefGoogle Scholar
  28. [Burkard and Fincke, 1983]
    Burkard, R. and Fincke, U. (1983). The asymptotic probabilistic behavior of quadratic sum assignment problems. Zeitschrift für Operations Research, 27:73–81.MathSciNetMATHGoogle Scholar
  29. [Burkard et al., 1991]
    Burkard, R., Karisch, S., and Rendl, F. (1991). QAPLIB - a quadratic assignment problem library. European Journal of Operational Research, 55:115 – 119.MATHCrossRefGoogle Scholar
  30. [Burkard et al., 1997]
    Burkard, R., Karisch, S., and Rendl, F. (1997). QAPLIB - a quadratic assignment problem library. Journal of Global Optimization, 10:391–403.Google Scholar
  31. [Burkard and Rendl, 1984]
    Burkard, R. and Rendl, F. (1984). A thermodynamically motivated simulation procedure for combinatorial optimization problems. European Journal of Operational Research, 17:169–174.MATHCrossRefGoogle Scholar
  32. [Burkard and Stratmann, 1978]
    Burkard, R. and Stratmann, K.-H. (1978). Numerical investigations on quadratic assignment problems. Naval Research Logistics Quarterly, 25:129–148.MATHCrossRefGoogle Scholar
  33. [Çela, 1998]
    Çela, E. (1998). The QuadraticAssignmentProblem:Theory andAlgorithms. Kluwer, Dordrecht.MATHGoogle Scholar
  34. [Chakrapani and Skorin-Kapov, 1992]
    Chakrapani, J. and Skorin-Kapov, J. (1992). A connectionist approach to the quadratic assignment problem. Computers & Operations Research, 19:287–295.MATHCrossRefGoogle Scholar
  35. [Chakrapani and Skorin-Kapov, 1993]
    Chakrapani, J. and Skorin-Kapov, J. (1993). Massively parallel tabu search for the quadratic assignment problem. Annals of Operations Research, 41:327–342.MATHCrossRefGoogle Scholar
  36. [Cheh et al., 1991]
    Cheh, K., Goldberg, J., and Askin, R. (1991). A note on the neighborhood structure in simulated annealing. Computers & Operations Research, 18:537–547.MATHCrossRefGoogle Scholar
  37. [Chhajed and Lowe, 1992]
    Chhajed, D. and Lowe, T. (1992). M-median and m-center problems with mutual communication: solvable special cases. Operations Research, 40:56–66.MathSciNetCrossRefGoogle Scholar
  38. [Chiang and Chiang, 1998]
    Chiang, W.-C. and Chiang, C. (1998). Intelligent local search strategies for solving facility layout problems with the quadratic assignment problem formulation. European Journal of Operational Research, 106:457–488.MATHCrossRefGoogle Scholar
  39. [Choi et al., 1999]
    Choi, W., Kang, H., and Baek, T. (1999). A turbine-blade balancing problem. International Journal of Production Economics, 6061:405–410.CrossRefGoogle Scholar
  40. [Colorni and Maniezzo, 1999]
    Colorni, A. and Maniezzo, V. (1999). The ant system applied to the quadratic assignment problem. IEEE Transactions on Knowledge and Data Engineering, 11:769–778.CrossRefGoogle Scholar
  41. [Connolly, 1990]
    Connolly, D. (1990). An improved annealing scheme for the QAP. European Journal of Operational Research, 46:93–100.MathSciNetMATHCrossRefGoogle Scholar
  42. [Conway and Venkataramanan, 1994]
    Conway, D. and Venkataramanan, M. (1994). Genetic search and the dynamic facility layout problem. Computers & Operations Research, 21:955–960.MATHCrossRefGoogle Scholar
  43. [Crama and Spieksma, 1992]
    Crama, Y. and Spieksma, F. (1992). Approximation algorithms for three-dimensional assignment problems with triangle inequalities. European Journal of Operational Research, 60:273–279.MATHCrossRefGoogle Scholar
  44. [Cung et al., 1996]
    Cung, V.-D., Mautor, T., Michelon, P., and Tavares, A. (1996). A scatter search based approach for the quadratic assignment problem. Working paper 96/037, PRiSM Laboratory, University of Versailles.Google Scholar
  45. [Daduna and Voß, 1995]
    Daduna, J. and Voß, S. (1995). Practical experiences in schedule synchronization. In Daduna, J., Branco, I., and Paixao, J., editors, Computer-Aided Transit Scheduling, volume 430 of Lecture Notes in Economics and Mathematical Systems, pages 39–55. Springer, Berlin.CrossRefGoogle Scholar
  46. [de Abreu et al., 1999]
    de Abreu, N., Querido, T., and Boaventura-Netto, P. (1999). REDINV- SA: A simulated annealing for the quadratic assignment problem. RAIRO Recherche Operationelle, 33:249–274.MATHCrossRefGoogle Scholar
  47. [Dell’Amico et al., 1999]
    Dell’Amico, M., Lodi, A., and Maffioli, F. (1999). Solution of the cumulative assignment problem with a well-structured tabu search method. Journal of Heuristics, 5:123–143.MATHCrossRefGoogle Scholar
  48. [Derigs et al., 1999]
    Derigs, U., Kabath, M., and Zils, M. (1999). Adaptive genetic algorithms for dynamic autoconfiguration of genetic search algorithms. In Voss, S., Martello, S., Osman, I., and Roucairol, C., editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 231–248. Kluwer, Boston.CrossRefGoogle Scholar
  49. [Domschke, 1989]
    Domschke, W. (1989). Schedule synchronization for public transit networks. OR Spektrum, 11:17–24.MATHCrossRefGoogle Scholar
  50. [Domschke and Drexl, 1996]
    Domschke, W. and Drexl, A. (1996). Logistik: Standorte, fourth ed. Oldenbourg, München.Google Scholar
  51. [Domschke et al., 1992]
    Domschke, W., Forst, P., and Voß, S. (1992). Tabu search techniques for the quadratic semi-assignment problem. In Fandel, G., Gulledge, T., and Jones, A., editors, New Directioris for Operations Research in Manufacturing, pages 389– 405. Springer, Berlin.Google Scholar
  52. [Domschke and Krispin, 1997]
    Domschke, W. and Krispin, G. (1997). Location and layout planning — a survey. OR Spektrum, 19:181–202.MathSciNetMATHCrossRefGoogle Scholar
  53. [Dorigo et al., 1999]
    Dorigo, M., Maniezzo, V., and Colorni, A. (1999). Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man and Cybernetics, 26:29–41.Google Scholar
  54. [Dowsland, 1993]
    Dowsland, K. (1993). Simulated annealing. In Reeves, C., editor, Modern Heuristic Techniques for Combinatorial Problems, pages 20–69. Blackwell: Halsted Pr.Google Scholar
  55. [Dueck and Scheuer, 1990]
    Dueck, G. and Scheuer, T. (1990). Threshold accepting: a general purpose optimization algorithm appearing superior to simulated annealing. Journal of Computational Physics, 90:161–175.MathSciNetMATHCrossRefGoogle Scholar
  56. [Duin and Voß, 1999]
    Duin, C. and Voß, S. (1999). The pilot method, a strategy for heuristic repetition with application to the Steiner problem in graphs. Networks, 34:181–191.MathSciNetMATHCrossRefGoogle Scholar
  57. [Dutta et al., 1982]
    Dutta, A., Koehler, G., and Whinston, A. (1982). On optimal allocation in a distributed processing environment. Management Science, 28:839–853.MATHCrossRefGoogle Scholar
  58. [Dutta and Sahu, 1982]
    Dutta, K. and Sahu, S. (1982). A multi-goal heuristic for facilities design problem: MUGHAL. International Journal of Production Research, 20:147–154.CrossRefGoogle Scholar
  59. [Dyer et al., 1986]
    Dyer, M., Frieze, A., and McDiarmid, C. (1986). On linear programs with random costs. Mathematical Programming, 35:3–16.MathSciNetMATHCrossRefGoogle Scholar
  60. [Edwards et al., 1970]
    Edwards, H., Gillett, B., and Hale, M. (1970). Modular allocation technique (MAT). Management Science, 17:161–169.CrossRefGoogle Scholar
  61. [Eishafei, 1977]
    Elshafei, A. (1977). Hospital layout as a quadratic assignment problem. Operational Research Quarterly, 28:167–179.MATHCrossRefGoogle Scholar
  62. [Ernst, 1978]
    Ernst, W. (1978). Verfahren zur Fabrikplanung im MenschRechner-Dialog am Bildschirm. Krausskopf, Mainz.Google Scholar
  63. [Fathi and Ginjupalli, 1993]
    Fathi, Y. and Ginjupalli, K. (1993). A mathematical model and a heuristic procedure for the turbine balancing problem. European Journal of Operational Research, 63:336–342.CrossRefGoogle Scholar
  64. [Feo et al., 1991]
    Feo, T., Venkatraman, K., and Bard, J. (1991). A grasp for a difficult single machine scheduling problem. Computers & Operations Research, 18:635–643.MATHCrossRefGoogle Scholar
  65. [Fiechter et al., 1992]
    Fiechter, C., Rogger, A., and de Werra, D. (1992). Basic ideas of tabu search with an application to traveling salesman and quadratic assignment. Ricerca Operativa, 62:5–28.Google Scholar
  66. [Fink and Voß, 1998]
    Fink, A. and Voß, S. (1998). Applications of modem heuristic search methods to continuous flow-shop scheduling problems. Working paper, Technische Universität Braunschweig, Germany.Google Scholar
  67. [Fink and Voß, 1999]
    Fink, A. and Voß, S. (1999). Generic metaheuristics application to industrial engineering problems. Computers & Industrial Engineering, 37:281–284.CrossRefGoogle Scholar
  68. [Fleurent and Ferland, 1994]
    Fleurent, C. and Ferland, J. (1994). Genetic hybrids for the quadratic assignment problem. In Pardalos, P. and Wolkowicz, H., editors, Quadratic Assignment and Related Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 173–187. American Mathematical Society, Providence.Google Scholar
  69. [Fleurent and Glover, 1999]
    Fleurent, C. and Glover, F. (1999). Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS Journal on Computing, 11:198–204.MathSciNetMATHCrossRefGoogle Scholar
  70. [Frenk et al., 1985]
    Frenk, J., van Houweninge, M., and Kan, A. R. (1985). Asymptotic properties of the quadratic assignment problem. Mathematics of Operations Research, 16:223–239.Google Scholar
  71. [Frieze and Yadegar, 1981 ]
    Frieze, A. and Yadegar, J. (1981). An algorithm for solving 3-dimensional assignment problems with applications to scheduling a teaching practice. Operations Research, 32:989–995.MATHGoogle Scholar
  72. [Frieze et al., 1989]
    Frieze, A., Yadegar, J., El-Horbaty, S., and Parkinson, D. (1989). Algorithms for assignment problems on an array processor. Parallel Computing, 11:151–162.MathSciNetMATHCrossRefGoogle Scholar
  73. [Gambardella et al., 1999]
    Gambardella, L., Taillard, E., and Dorigo, M. (1999). Ant colonies for the QAP. Journal of the Operational Research Society, 50:167–176.MATHGoogle Scholar
  74. [Gavish, 1991]
    Gavish, B. (1991). Manifold search techniques applied to quadratic assignment problems (QAP). Working paper, Owen Graduate School of Management, Vanderbilt University, Nashville.Google Scholar
  75. [Gen et al., 1999]
    Gen, M., Ida, K., and Lee, C.-Y. (1999). Hybridized neural network and genetic algorithms for solving nonlinear integer programming problem. In SEAL’98, volume 1585 of Lecture Notes in Computer Science, pages 421–429. Springer, Berlin.Google Scholar
  76. [Gilmore, 1962]
    Gilmore, P. (1962). Optimal and suboptimal algorithms for the quadratic assignment problem. J. SIAM, 10:305–313.MathSciNetMATHGoogle Scholar
  77. [Glover, 1995]
    Glover, F. (1995). Scatter search and star-paths: beyond the genetic metaphor. OR Spektrum, 17:125–137.MATHCrossRefGoogle Scholar
  78. [Glover and Laguna, 1997]
    Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer, Dordrecht.MATHCrossRefGoogle Scholar
  79. [Goldberg, 1989]
    Goldberg, D. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading.MATHGoogle Scholar
  80. [Golden and Skiscim, 1986]
    Golden, B. and Skiscim, C. (1986). Using simulated annealing to solve routing and location problems. Naval Research Logistics Quarterly, 33:261–279.MathSciNetMATHCrossRefGoogle Scholar
  81. [Graves and Whinston, 1970]
    Graves, G. and Whinston, A. (1970). An algorithm for the quadratic assignment problem. Management Science, 17:453–471.CrossRefGoogle Scholar
  82. [Haghani and Chen, 1998]
    Haghani, A. and Chen, M.-C. (1998). Optimizing gate assignments at airport terminals. Transportation Research A, 32:437–454.Google Scholar
  83. [Hamam and Hindi, 2000]
    Hamam, Y. and Hindi, K. (2000). Assignment of program modules to processors: A simulated annealing approach. European Journal of Operational Research, 122:509–513.MATHCrossRefGoogle Scholar
  84. [Heragu, 1997]
    Heragu, S. (1997). Facilities Design. PWS, Boston.Google Scholar
  85. [Heragu and Alfa, 1992]
    Heragu, S. and Alfa, A. (1992). Experimental analysis of simulated annealing based algorithms for the facility layout problem. European Journal of Operational Research, 57:190–202.MATHCrossRefGoogle Scholar
  86. [Hillier and Conners, 1966]
    Hillier, F. and Conners, M. (1966). Quadratic assignment problem algorithms and the location of indivisable facilities. Management Science, 13:42–57.CrossRefGoogle Scholar
  87. [Holland, 1975]
    Holland, J. (1975). Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor.Google Scholar
  88. [Huntley and Brown, 1991]
    Huntley, C. and Brown, D. (1991). A parallel heuristic for quadratic assignment problems. Computers & Operations Research, 18:275–289.MATHCrossRefGoogle Scholar
  89. [Jajodia et al., 1992]
    Jajodia, S., Minis, I., Harhalakis, G., and Proth, J. (1992). CLASS: Computerized layout solutions using simulated annealing. International Journal of Production Research, 30:95–108.MATHCrossRefGoogle Scholar
  90. [Johnson et al., 1989]
    Johnson, D., Aragon, C., McGeoch, L., and Schevon, C. (1989). Optimization by simulated annealing: an experimental evaluation; part 1, graph partitioning. Operations Research, 37:865–892.MATHCrossRefGoogle Scholar
  91. [Johnson et al., 1988]
    Johnson, D., Papadimitriou, C., and Yannakakis, M. (1988). How easy is local search? J. Comput. System Sci., 37:79–100.MathSciNetMATHCrossRefGoogle Scholar
  92. [Kelly et al., 1994]
    Kelly, J., Laguna, M., and Glover, F. (1994). A study of diversification strategies for the quadratic assignment problem. Computers & Operations Research, 21:885–893.MATHCrossRefGoogle Scholar
  93. [Kirkpatrick et al., 1983]
    Kirkpatrick, S., Jr., C. G., and Vecchi, M. (1983). Optimization by simulated annealing. Science, 220:671–680.MathSciNetMATHCrossRefGoogle Scholar
  94. [Klemt and Stemme, 1988]
    Klemt, W.-D. and Stemme, W. (1988). Schedule synchronization for public transit networks. In Daduna, J. and Wren, A., editors, Computer-Aided Transit Scheduling, volume 308 of Lecture Notes in Economics and Mathematical Systems, pages 327–335. Springer, Berlin.Google Scholar
  95. [Kusiak and Heragu, 1987]
    Kusiak, A. and Heragu, S. (1987). The facility layout problem. European Journal of Operational Research, 29:229–251.MathSciNetMATHCrossRefGoogle Scholar
  96. [Land, 1963]
    Land, A. (1963). A problem of assignment with interrelated costs. Operational Research Quarterly, 14:185–198.CrossRefGoogle Scholar
  97. [Laporte and Mercure, 1988]
    Laporte, G. and Mercure, H. (1988). Balancing hydraulic turbine runners: A quadratic assignment problem. European Journal of Operational Research, 35:378–381.CrossRefGoogle Scholar
  98. [Lashari and Jaisingh, 1980]
    Lashari, R. and Jaisingh, S. (1980). A heuristic approach to quadratic assignment problems. Journal of the Operational Research Society, 31:845–850.Google Scholar
  99. [Laursen, 1993]
    Laursen, P. (1993). Simulated annealing for the QAP - optimal tradeoff between simulation time and solution quality. European Journal of Operational Research, 69:238 – 243.CrossRefGoogle Scholar
  100. [Lawler, 1963]
    Lawler, E. (1963). The quadratic assignment problem. Management Science, 9:586–599.MathSciNetMATHCrossRefGoogle Scholar
  101. [Lee and Moore, 1967]
    Lee, R. and Moore, J. (1967). CORELAP - computerized relationship layout planning. Journal of Industrial Engineering, 18:195–200.Google Scholar
  102. [Li and Pardalos, 1992]
    Li, Y. and Pardalos, P. (1992). Generating quadratic assignment test problems with known optimal permutations. Computational Optimization and Applications, 1:163–184.MathSciNetMATHCrossRefGoogle Scholar
  103. [Li et al., 1994]
    Li, Y., Pardalos, P., and Resende, M. (1994). A greedy randomized adaptive search procedure for the quadratic assignment problem. In Pardalos, P. and Wolkowicz, H., editors, Quadratic Assignment and Related Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, pages 237–261. American Mathematical Society, Providence.Google Scholar
  104. [Lutton and Bonomi, 1986]
    Lutton, J. and Bonomi, E. (1986). The asymptotic behavior of a quadratic sum assignment problems: a sta-tistical mechanics approach. European Journal of Operational Research, 26:295–300.MathSciNetMATHCrossRefGoogle Scholar
  105. [Magirou and Milis, 1989]
    Magirou, V. and Milis, J. (1989). An algorithm for the multiprocessor assignment problem. Operations Research Letters, 8:351–356.MathSciNetMATHCrossRefGoogle Scholar
  106. [Magos, 1996]
    Magos, D. (1996). Tabu search for the planar three-index assignment problem. Journal of Global Optimization, 8:35–48.MathSciNetMATHCrossRefGoogle Scholar
  107. [Magos and Miliotis, 1994]
    Magos, D. and Miliotis, P. (1994). An algorithm for the planar three-index assignment problem. European Journal of Operational Research, 77:141–153.MATHCrossRefGoogle Scholar
  108. [Malucelli, 1993]
    Malucelli, F. (1993). Quadratic assignment problems: solution methods and applications. PhD thesis, Universita di Pisa.Google Scholar
  109. [Maniezzo, 1999]
    Maniezzo, V. (1999). Exact and approximate nondeterministic tree-search procedures for the quadratic assignment problem. INFORMS Journal on Computing, 11:358–369.MathSciNetMATHCrossRefGoogle Scholar
  110. [Maniezzo et al., 1995]
    Maniezzo, V., Dorigo, M., and Colorni, A. (1995). Algodesk: An experimental comparison of eight evolutionary heuristics applied to the quadratic assignment problem. European Journal of Operational Research, 81:188–204.MATHCrossRefGoogle Scholar
  111. [Mason and Rönnqvist, 1997]
    Mason, A. and Rönnqvist, M. (1997). Solution methods for the balancing ofjet turbines. Computers & Operations Research, 24:153–167.MATHCrossRefGoogle Scholar
  112. [Mavridou et al., 1998]
    Mavridou, T., Pardalos, P., Pitsoulis, L., and Resende, M. (1998). A GRASP for the biquadratic assignment problem. European Journal of Operational Research, 105:613–621.MATHCrossRefGoogle Scholar
  113. [Moretti Tomasin et al., 1988]
    Moretti Tomasin, E., Pianca, P., and Sorato, A. (1988). Heuristic algorithms for the quadratic semi-assignment problem. Ricerca Operativa, 18:65–89.Google Scholar
  114. [Mühlenbein, 1989]
    Mühlenbein, H. (1989). Varying the probability of mutation in the genetic algorithm. In Schaffer, J., editor, Proceedings of the Third International Conference on Genetic Algorithms, pages 416–421, San Mateo. Morgan Kaufmann.Google Scholar
  115. [Müller-Merbach, 1970]
    Müller-Merbach, H. (1970). Optimale Reihenfolgen. Springer, Berlin.CrossRefGoogle Scholar
  116. [Murphey et al., 1998]
    Murphey, R., Pardalos, P., and Pitsoulis, L. (1998). A parallel GRASP for the data association multidimensional assignment problem. In Pardalos, P., editor, Parallel Processing ofDiscrete Problems, volume 106 of IMA Volumes in Mathematics and its Applications, pages 159–180. Springer, Berlin.Google Scholar
  117. [Murtagh et al., 1982]
    Murtagh, B., Jefferson, T., and Somprasit, V. (1982). A heuristic procedure for solving the quadratic assignment problem. European Journal of Operational Research, 9:71–76.MATHCrossRefGoogle Scholar
  118. [Murthy et al., 1992]
    Murthy, K., Pardalos, P., and Li, Y. (1992). A local search algorithm for the quadratic assignment problem. Informatica, 3:524–538.MathSciNetMATHGoogle Scholar
  119. [Nissen, 1993]
    Nissen, V. (1993). A new efficient evolutionary algorithm for the quadratic assignment problem. In Hansmann, K.-W., Bachem, A., Jarke, M., Katzenberger, W., and Marusev, A., editors, Operations Research Proceedings 1992, pages 259 – 267, Berlin. Springer.Google Scholar
  120. [Nissen, 1994]
    Nissen, V. (1994). Evolutionäre Algorithmen. DUV, Wiesbaden.MATHCrossRefGoogle Scholar
  121. [Nissen and Paul, 1993]
    Nissen, V. and Paul, H. (1993). A modification of threshold accepting and its application to the quadratic assignment problem. OR Spektrum, 17:205–210.Google Scholar
  122. [Nugent et al., 1968]
    Nugent, C., Vollmann, T., and Ruml, J. (1968). An experimental comparison of techniques for the assignment of facilities to locations. Operations Research, 16:150–173.CrossRefGoogle Scholar
  123. [Pardalos et al., 1994]
    Pardalos, P., Burkard, R., and Wolkowicz, H. (1994). The quadratic assignment problem: A survey and recent developments. In Pardalos, P. and Wolkowicz, H., editors, Quadratic Assignment and Related Problems, pages 142, Providence. AMS.Google Scholar
  124. [Pardalos et al., 1995]
    Pardalos, P., Pitsoulis, L., and Resende, M. (1995). A parallel grasp implementation for solving the quadratic assignment problem. In Ferreira, A. and Rolim, J., editors, Parallel Algorithms for Irregular Problems: State of the Art, pages 115–133. Kluwer, Boston.Google Scholar
  125. [Pardalos et al., 1997]
    Pardalos, P., Pitsoulis, L., and Resende, M. (1997). Fortran subroutines for approximate solution of sparse quadratic assignment problems using grasp. ACM Transactions on Mathematical Software, 23:196–208.MathSciNetMATHCrossRefGoogle Scholar
  126. [Pardalos and Wolkowicz, 1994]
    Pardalos, P. and Wolkowicz, H., editors (1994). Quadratic Assignment and Related Problems, volume 16 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence.MATHGoogle Scholar
  127. [Paulli, 1993]
    Paulli, J. (1993). Information utilization in simulated annealing and tabu search. Committee on Algorithms Bulletin, 22:28–34.Google Scholar
  128. [Peng et al., 1996]
    Peng, T., Huanchen, W., and Dongme, Z. (1996). Simulated annealing for the quadratic assignment problem: A further study. Computers & Industrial Engineering, 31:925–928.CrossRefGoogle Scholar
  129. [Pitsoulis et al., 2000]
    Pitsoulis, L., Pardalos, P., and Hearn, D. (2000). Approximate solutions to the turbine balancing problem. European Journal of Operational Research, (to appear)Google Scholar
  130. [Poore and Rijavec, 1994]
    Poore, A. and Rijavec, N. (1994). A parallel heuristic for quadratic assignment problems. Journal of Computing and Information Technology, 2:25–37.Google Scholar
  131. [Queyranne, 1986]
    Queyranne, M. (1986). Performance ratio of polynomial algorithms for triangle-inequality quadratic assignment problems. OperationsResearchLetters, 4:231–234.MathSciNetMATHGoogle Scholar
  132. [Resende et al., 1996]
    Resende, M., Pardalos, P., and Li, Y. (1996). Fortran subroutines for approximate solution of dense quadratic assignment problems using grasp. ACM Transactions on Mathematical Software, 22:104–118.MATHCrossRefGoogle Scholar
  133. [Rhee, 1988a]
    Rhee, W. (1988a). A note on asymptotic properties of the quadratic assignment problem. Operations Research Letters, 7:197–200.MathSciNetMATHCrossRefGoogle Scholar
  134. [Rhee, 1988b]
    Rhee, W. (1988b). Stochastic analysis of the quadratic assignment problem. Mathematics of Operations Research, 16:223–239.MathSciNetCrossRefGoogle Scholar
  135. [Rosenblatt, 1979]
    Rosenblatt, M. (1979). The facilities layout problem: A multi-goal approach. International Journal ofProduction Research, 17:323–332.CrossRefGoogle Scholar
  136. [Sahni and Gonzalez, 1976]
    Sahni, S. and Gonzalez, T. (1976). P-complete approximation problems. Journal of the ACM (Association for Computing Machinery), 23:555–565.MathSciNetMATHCrossRefGoogle Scholar
  137. [Schäffer and Yannakakis, 1991]
    Schäffer, A. and Yannakakis, M. (1991). Simple local search problems that are hard to solve. SIAM Journal on Computing, 20:56–87.MathSciNetMATHCrossRefGoogle Scholar
  138. [Seehof and Evans, 1967]
    Seehof, J. and Evans, W. (1967). Automated layout design program. Journal of Industrial Engineering, 18:690–695.Google Scholar
  139. [Sharpe et al., 1985]
    Sharpe, R., Marksjo, B., Mitchell, J., and Crawford, J. (1985). An interactive model for the layout of buildings. Applied Mathematical Modeling, 9:207–214.CrossRefGoogle Scholar
  140. [Simeone, 1986]
    Simeone, B. (1986). An asymptotically exact algorithm for equipartition problems. Discrete Applied Mathematics, 14:283–293.MathSciNetMATHCrossRefGoogle Scholar
  141. [Sinclair, 1993]
    Sinclair, M. (1993). Comparison of the performance of modem heuristics for combinatorial optimization on real data. Computers & Operations Research, 20:687–695.MATHCrossRefGoogle Scholar
  142. [Skorin-Kapov, 1990]
    Skorin-Kapov, J. (1990). Tabu search applied to the quadratic assignment problem. ORSA Journal on Computing, 2:33–45.MATHCrossRefGoogle Scholar
  143. [Skorin-Kapov, 1994]
    Skorin-Kapov, J. (1994). Extensions of a tabu search adaptation to the quadratic assignment problem. Computers & Operations Research, 21:855–866.MathSciNetMATHCrossRefGoogle Scholar
  144. [Smith, 1995]
    Smith, K. (1995). Solving the generalized quadratic assignment problem using a self-organizing process. In Proceedings of the IEEE International Conference on Neural Networks (ICNN), pages 1876–1879. Vol. 4, Perth.CrossRefGoogle Scholar
  145. [Smith, 1999]
    Smith, K. (1999). Neural networks for combinatorial optimization: A review of more than a decade of research. INFORMS Journal on Computing, 11:15–34.MathSciNetMATHCrossRefGoogle Scholar
  146. [Smith et al., 1998]
    Smith, K., Palaniswami, M., and Krishnamoorthy, M. (1998). Neural techniques for combinatorial optimization with applications. IEEE Transactions on Neural Networks, 9:1301–1318.CrossRefGoogle Scholar
  147. [Sondergeld and Voß, 1993]
    Sondergeld, L. and Voß, S. (1993). Solving quadratic assignment problems using the cancellation sequence method. Working paper, TH Darmstadt.Google Scholar
  148. [Sondergeld and Voß, 1996]
    Sondergeld, L. and Voß, S. (1996). A star-shaped diversification approach in tabu search. In Osman, I. and Kelly, J., editors, Meta-Heuristics: Theory and Applications, pages 489–502. Kluwer, Boston.CrossRefGoogle Scholar
  149. [Starke et al., 1999]
    Starke, J., Schanz, M., and Haken, H. (1999). Treatment of combinatorial optimization problems using selection equations with cost terms. part ii. NP-hard three-dimensional assignment problems. Physica D, 134:242–252.MathSciNetMATHCrossRefGoogle Scholar
  150. [Steinberg, 1961]
    Steinberg, L. (1961). The backboard wiring problem: A placement algorithm. SIAM Review, 3:37–50.MathSciNetMATHCrossRefGoogle Scholar
  151. [Stützle and Hoos, 1999]
    Stützle, T. and Hoos, H. (1999). The max-min ant system and local search for combinatorial optimization problems. In Voss, S., Martello, S., Osman, I., and Roucairol, C., editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 313–329. Kluwer, Boston.CrossRefGoogle Scholar
  152. [Taillard, 1991]
    Taillard, E. (1991). Robust taboo search for the quadratic assignment problem. Parallel Computing, 17:443–455.MathSciNetCrossRefGoogle Scholar
  153. [Taillard, 1995]
    Taillard, E. (1995). Comparison of iterative searches for the quadratic assignment problem. Location Science, 3:87–105.MATHCrossRefGoogle Scholar
  154. [Taillard, 1998]
    Taillard, E. (1998). FANT: Fast ant system. Working paper, IDSIA, Lugano.Google Scholar
  155. [Taillard, 2000]
    Taillard, E. (2000). An introduction to ant systems. In Laguna, M. and Gonzalez-Velarde, J., editors, Computing Tools for Modeling, Optimization and Simulation, pages 131–144. Kluwer, Boston.CrossRefGoogle Scholar
  156. [Taillard and Voß, 1999]
    Taillard, E. and Voß, S. (1999). Popmusic. Working paper, University of Applied Sciences of Western Switzerland.Google Scholar
  157. [Talbi et al., 1999]
    Talbi, E.-G., Hafidi, Z., and Geib, J.-M. (1999). Parallel tabu search for large optimization problems. In Voss, S., Martello, S., Osman, I., and Roucairol, C., editors, Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization, pages 345–358. Kluwer, Boston.CrossRefGoogle Scholar
  158. [Tam, 1992]
    Tam, K. (1992). Genetic algorithms, function optimization, and facility layout design. European Journal of Operational Research, 63:322–346.MATHCrossRefGoogle Scholar
  159. [Tate and Smith, 1995]
    Tate, D. and Smith, A. (1995). A genetic approach to the quadratic assignment problem. Computers & Operations Research, 22:73–83.MATHCrossRefGoogle Scholar
  160. [Torki et al., 1996]
    Torki, A., Yajima, Y., and Enkawa, T. (1996). A low-rank bilinear programming approach for sub-optimal solution of the quadratic assignment problem. European Journal of Operational Research, 94:384–391.MATHCrossRefGoogle Scholar
  161. [Tsuchiya et al., 1996]
    Tsuchiya, K., Bharitkar, S., and Takefuji, Y. (1996). A neural network approach to facility layout problems. European Journal of Operational Research, 89:556–563.MATHCrossRefGoogle Scholar
  162. [Urban, 1998]
    Urban, T. (1998). Solution procedures for the dynamic facility layout problem. Annals of Operations Research, 76:323–342.MATHCrossRefGoogle Scholar
  163. [Vollmann et al., 1968]
    Vollmann, T., Nugent, C., and Zartler, R. (1968). A computerized model for office layout. Journal of Industrial Engineering, 19:321–327.Google Scholar
  164. [Voß, 1992]
    Voß, S. (1992). Network design formulations in schedule synchronization. In Desrochers, M. and Rousseau, J.-M., editors, Computer-Aided Transit Scheduling, volume 386 of Lecture Notes in Economics and Mathematical Systems, pages 137 – 152. Springer, Berlin.Google Scholar
  165. [Voß, 1993]
    Voß, S. (1993). Tabu search: applications and prospects. In Du, D.-Z. and Pardalos, P., editors, Network Optimization Problems, pages 333 – 353. World Scientific, Singapore.Google Scholar
  166. [Voß, 1995]
    Voß, S. (1995). Solving quadratic assignment problems using the reverse elimination method. In Nash, S. and Sofer, A., editors, The Impact of Emerging Technologies on Computer Science and Operations Research, pages 281 – 296. Kluwer, Dordrecht.Google Scholar
  167. [Voß, 1996]
    Voß, S. (1996). Observing logical interdependencies in tabu search: Methods and results. In Rayward-Smith, V., Osman, I., Reeves, C., and Smith, G., editors, Modern Heuristic Search Methods, pages 41–59, Chichester. Wiley.Google Scholar
  168. [Wäscher and Chamoni, 1987]
    Wäscher, G. and Chamoni, P. (1987). MICROLAY: An interactive computer program for factory layout planning on microcomputers. European Journal of Operational Research, 31:185–193.MATHCrossRefGoogle Scholar
  169. [West, 1983]
    West, D. (1983). Algorithm 608: Approximate solution of the quadratic assignment problem. ACM Transactions on Mathematical Software, 9:461466.Google Scholar
  170. [White, 1996]
    White, D. (1996). A lagrangean relaxation approach for a turbine design quadratic assignment problem. Journal of the Operational Research Society, 47:766–775.MATHGoogle Scholar
  171. [Wilhelm and Ward, 1987]
    Wilhelm, M. and Ward, T. (1987). Solving quadratic assignment problems by ’simulated annealing’ . IIETransactions, 19:107– 119.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Stefan Voss
    • 1
  1. 1.Wirtschaftsinformatik und InformationsmanagementTechnische Universität Braunschweig Allgemeine BetriebswirtschaftslehreBraunschweigGermany

Personalised recommendations