Skip to main content
SpringerLink
Log in

Problems of discrete optimization: Challenges and main approaches to solve them

  • Systems Analysis
  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

This paper briefly reviews the current state of the art in the field of discrete optimization problems. Emphasis is on the generalization of the experience gained at the V. M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine in research and development of solution methods and software for various classes of complicated discrete programming problems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Artemenko and I. V. Sergienko, “A P-method of solving integer linear programming problems with Boolean variables,” Dokl. AN USSR, Ser. A, No. 4, 72–75 (1980).

  2. O. V. Volkovich, V. A. Roschin, and I. V. Sergienko, “On models and methods of solving integer quadratic programming problems,” Kibernetika, No. 3, 1–15 (1987).

  3. V. V. Glushkova and V. P. Shylo, “Problems of optimal arrangement of switching equipment,” in: Mathematical Methods of Decision-Making under Uncertainty [in Russian], V. M. Glushkov Inst. Cybernetics, AS USSR, Kiev (1990), pp. 69–71.

    Google Scholar 

  4. L. F. Gulyanitskii, I. V. Sergienko, and A. N. Khodzinskii, “Problems of development and analysis of parallel discrete optimization methods,” in: Programming Languages and Parallel Computers: Algorithms and Algorithmic Languages [in Russian], Nauka, Moscow (1990), pp. 62–78.

    Google Scholar 

  5. V. A. Emelichev and V. A. Perepelitsa, “Complexity of discrete multicriterion problems,” Diskret. Matem., Issue 1, 6, 3–33 (1994).

    MATH  MathSciNet  Google Scholar 

  6. V. A. Emelichev and D. P. Podkopaev, “Stability and regularization of vector problems of integer linear programming,” Diskret. Analiz Issled. Oper., Ser. 2, 8, No. 1, 47–69 (2001).

    MATH  MathSciNet  Google Scholar 

  7. Yu. I. Zhuravlyov, Selected Scientific Works [in Russian], Magistr, Moscow (1998).

    Google Scholar 

  8. N. Z. Shor, I. V. Sergienko, V. P. Shylo, et al., Problems of Optimal Design of Reliable Networks [in Ukrainian], Naukova Dumka, Kiev (2005).

    Google Scholar 

  9. M. M. Kovalev and V. M. Kotov, “Suboptimal algorithms in integer programming,” Dokl. AN BSSR, 26, 969–972 (1982).

    MATH  MathSciNet  Google Scholar 

  10. N. K. Maksishko and V. A. Perepelitsa, Analysis and Prediction of the Evolution of Economic Systems [in Russian], Poligraph, Zaporozhye (2006).

    Google Scholar 

  11. M. Minou, Mathematical Programming: Theory and Algorithms, J. Wiley and Sons, New York (1986).

    Google Scholar 

  12. V. S. Mikhalevich and V. L. Volkovich, Computational Methods of the Analysis and Design of Complex Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  13. V. S. Mikhalevich and A. I. Kuksa, Methods of Sequential Optimization in Discrete Network Problems of Optimal Resource Allocation [in Russian], Nauka, Moscow (1983).

    Google Scholar 

  14. V. S. Mikhalevich, V. A. Trubin, and N. Z. Shor, Optimization Problems of Production and Transportation Scheduling [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  15. M. V. Mikhalevich and I. V. Sergienko, Simulation of Transition Economy: Models, Methods, and Information Technologies [in Russian], Naukova Dumka, Kiev (2005).

    Google Scholar 

  16. C. H. Papadimitriu and K. Steiglitz, Combinatorial Optimization: Algorithms and Complexity, Prentice Hall (1987).

  17. I. V. Sergienko, Mathematical Models and Methods for Solving Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1988).

    Google Scholar 

  18. I. V. Sergienko and N. F. Kaspshitskaya, Models and Methods of Solving Combinatory Optimization Problems on a Computer [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  19. I. V. Sergienko, L. N. Kozeratskaya, and T. T. Lebedeva, Stability and Parametric Analyses of Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1995).

    Google Scholar 

  20. I. V. Sergienko, T. T. Lebedeva, and V. A. Roshchin, Approximate Methods of Solving Discrete Optimization Problems [in Russian], Naukova Dumka, Kiev (1980).

    Google Scholar 

  21. I. V. Sergienko, T. T. Lebedeva, and N. V. Semenova, “Existence of solutions in vector optimization problems,” Cybern. Syst. Analysis, Vol. 36, No. 6, 823–828 (2000).

    Article  MATH  Google Scholar 

  22. I. V. Sergienko, I. V. Parasyuk, and N. I. Tukalevskaya, Computer-Aided Data Processing Systems [in Russian], Naukova Dumka, Kiev (1976).

    Google Scholar 

  23. I. V. Sergienko, and N. V. Filonenko, “Solution of some stability problems in integer linear programming,” Dokl. AN USSR, Ser. A, No. 6, 79–82 (1982).

  24. I. V. Sergienko, V. P. Shilo, and V. A. Roshchin, “RESTART technology for solving discrete optimization problems,” Cybern. Syst. Analysis, Vol. 36, No. 5, 659–666 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  25. I. V. Sergienko, V. P. Shilo, and V. A. Roshchin, “Optimization parallelizing for discrete programming problems,” Cybern. Syst. Analysis, Vol. 40, No. 2, 184–189 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  26. I. V. Sergienko, and V. P. Shylo, Discrete Optimization Problems: Challenges, Solution Techniques, and Analysis [in Russian], Naukova Dumka, Kiev (2003).

    Google Scholar 

  27. I. V. Sergienko, “A method of solving extremum problems,” Avtomatika, No. 5, 15–21 (1964).

  28. I. V. Sergienko, Computer Science in Ukraine: Development and Problems [in Ukrainian], Naukova Dumka, Kiev (1999).

    Google Scholar 

  29. I. V. Sergienko, Computer Science and Computer Technologies [in Ukrainian], Naukova Dumka, Kiev (2004).

    Google Scholar 

  30. I. Sergienko and V. Koval’, “SKIT: A Ukrainian supercomputer project,” Visn. NAN Ukrainy, No. 8, 3–13 (2005).

  31. A. Schrijver, Theory of Linear and Integer Programming, John Wiley and Sons (1986).

  32. V. P. Shilo, “The method of global equilibrium search,” Cybern. Syst. Analysis, Vol. 35, No. 1, 68–74 (1999).

    MATH  MathSciNet  Google Scholar 

  33. V. P. Shilo, “Results of the experimental investigation of the efficiency of the global-equilibrium-search method,” Cybern. Syst. Analysis, Vol. 35, No. 2, 253–261 (1999).

    MATH  MathSciNet  Google Scholar 

  34. V. P. Shylo, “Solution of multidimensional knapsack problems by global equilibrium search,” in: Theory of Optimal Solutions [in Russian], V. M. Glushkov Inst. Cybern., NAS Ukraine, Kiev (2000), pp. 10–13.

    Google Scholar 

  35. V. P. Shilo, “New lower bounds of the size of error-correcting codes for the Z-channel,” Cybern. Syst. Analysis, Vol. 38, No. 1, 13–16 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  36. V. P. Shylo, “Exact solution of the problem of creating code maximum-size error-correcting,” in: Computer Mathematics [in Russian], V. M. Glushkov Inst. Cybern., NAS Ukraine, No. 2, 145–152, Kiev (2000).

  37. V. P. Shylo and D. A. Boyarchuk, “Algorithm of creating a covering with independent sets,” in: Computer Mathematics [in Russian], V. M. Glushkov Inst. Cybern., NAS Ukraine, No. 2, 151–157, Kiev (2001).

  38. O. V. Shylo, “Algorithm of global equilibrium search to solve the scheduling problem,” in: Computer Mathematics [in Russian], V. M. Glushkov Inst. Cybern., NAS Ukraine, No. 2, 150–160, Kiev (2004).

  39. O. V. Shylo, “Algorithm of global equilibrium search to solve the p-median problem,” in: Theory of Optimal Solutions [in Russian], No. 3, 150–158, V. M. Glushkov Inst. Cybern., NAS Ukraine, Kiev (2004).

    Google Scholar 

  40. Yu. Yu. Chervak, Optimization. Unimprovable Choice [in Ukrainian], Uzhgorod National University, Uzhgorod (2002).

    Google Scholar 

  41. E. H. L. Aarts and J. K. Lenstra, Local Search in Combinatorial Optimization, J. Wiley and Sons, Chichester (1997).

    MATH  Google Scholar 

  42. M. M. Amini, B. Alidaee, and G. A. Kochenberger, “A scatter search approach to unconstrained binary quadratic programs,” in: D. Corne, M. Dorigo, and F. Glover (eds.), New Ideas in Optimization, McGraw-Hill, London (1999), pp. 317–329.

    Google Scholar 

  43. D. Applegate, R. Bixby, V. Chvatal, et al., The Traveling Salesman Problem, Techn. Rep. DIMACS, Rutgers Univ., New Brunswick, NJ (1994).

    Google Scholar 

  44. E. Balas, S. Ceria, and G. Cornuejols, “Mixed 0-1 programming by lift-and-project in a branch-and-cut framework,” Manag. Sci., 42, 1229–1246 (1996).

    MATH  Google Scholar 

  45. E. Balas and A. Vazacopoulus, “Guided local search with shifting bottleneck for job-shop scheduling,” Manag. Sci., 44(2), 262–275 (1998).

    MATH  Google Scholar 

  46. R. Battiti and M. Protasi, “Reactive search, a history sensitive heuristic for MAX-SAT,” ACM J. Exper. Algorithms, No. 3, 23–39 (1997).

  47. R. Battiti and G. Tecchiolli, “Local search with memory: benchmarking RTS,” Prepr., Univ. di Trento (1994).

  48. R. Battiti and G. Tecchiolli, “The reactive tabu search,” ORSA J. Comput., 6, No. 2, 126–140 (1996).

    Google Scholar 

  49. J. E. Beasley, “Heuristic algorithms for the unconstrained binary quadratic programming problem,” Working Paper, The Management School, Imperial College, London, England (1998).

    Google Scholar 

  50. S. Binato, W. J. Hery, D. Loewenstern, et al., “GRASP for job shop scheduling,” in: Essays and Surveys on Metaheuristics, Kluwer, Acad. Publ., Boston (2001), pp. 59–79.

    Google Scholar 

  51. E. Bonabeau, M. Dorigo, and G. Theraulaz, Swarm Intelligence: from Natural to Artificial Systems, Oxford Univ. Press, New York (1999).

    MATH  Google Scholar 

  52. E. Bonomi and J. L. Lutton, “The n-sity traveling salesman problem: statistical mechanics and the Metropolis algorithm,” SIAM Rev., 26, No. 4, 551–568 (1984).

    Article  MATH  MathSciNet  Google Scholar 

  53. A. Caprara and A. Fischetti, “Branch and cut algorithms,” in: M. Dell’Amico, F. Maffioli, S. Martellochapter, et al. (eds.), Annot. Bibliogr. in Combin. Optim. (1997).

  54. G. Caprossi and P. Hansen, “Variable neighborhood search for extremal graphs,” The AutoGraphix System, Discrete Math., 212, 29–44 (2000).

    Google Scholar 

  55. V. Cerny, “Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm,” J. Optim. Theory Appl., 45, 41–51 (1985).

    Article  MATH  MathSciNet  Google Scholar 

  56. P. C. Chu and J. E. Beasley, “A genetic algorithm for the multidimensional knapsack problem,” J. Heuristic, 4, 63–86 (1998).

    Article  MATH  Google Scholar 

  57. C. Cordier, H. Marchand, R. Laundy, et al., “Bc-opt: a branch-and-cut code for mixed integer programs,” Math. Program., 86(2), 335–353 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  58. S. Coy, B. Golden, and E. Wasil, “A computational study of smoothing heuristics for the traveling salesman problem,” Eur. J. Oper. Res., 124(1), 15–27 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  59. G. A. Croes, “A method for solving traveling salesman problems,” Oper. Res., 6, 791–812 (1958).

    MathSciNet  Google Scholar 

  60. M. Dorigo and L. M. Gambardella, “Ant colony system: a cooperative learning approach to the traveling salesman problem,” IEEE Trans. Evolut. Comput., 1(1), 53–66 (http://iridia.ulb.ac.be/mdorigo/ACO/ACO.html) (1997).

    Article  Google Scholar 

  61. T. A. Feo and M. G. C. Resende, “Greedy randomised adaptive search procedures,” J. Global Optimiz., 6, 109–133 (1989).

    Article  MathSciNet  Google Scholar 

  62. A. G. Ferreira and J. Zerovnik, “Bounding the probability of success of stochastic methods for global optimization,” Comput. Math. Appl., 25, 1–8 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  63. L. Gambardella, E. Taillard, and M. Dorigo, “Ant colonies for the quadratic assignment problem,” Oper. Res. Soc., 50, 167–176 (www.idsia.ch/∼luca) (1999).

    Article  MATH  Google Scholar 

  64. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, New York (1979).

    MATH  Google Scholar 

  65. M. Gendreau, A. Hertz, and G. Laporte, “New insertion and postoptimization procedures for the traveling salesman problem,” Oper. Res., 40, 1086–1094 (1992).

    MATH  MathSciNet  Google Scholar 

  66. N. L. J. Ulder, E. H. L. Aarts, H. J. Bandelt et al., “Genetic local search algorithms for the traveling salesman problem,” Proc. 1st Intern. Workshop on Parallel Problem Solving from Nature (1990), pp. 109–116.

  67. E. Girlich and M. Kowaljow, Nichtlineare discrete optimizierung, Acad.-Verlag, Berlin (1981).

    Google Scholar 

  68. F. Glover, “A template for scatter search and path relinking,” in: J. K. Hao, E. Lutton, E. Ronald, et al. (eds.), Artificial Evolution, Lect. Notes Comp. Sci., 1363, Springer-Verlag, Berlin (1998), pp. 13–54.

    Chapter  Google Scholar 

  69. F. Glover, “Tabu search. I,” ORSA J. Comput., No. 1, 190–206 (1989).

  70. F. Glover, “Tabu search. II,” ORSA J. Comput., No. 2, 4–32 (1989).

  71. F. Glover, A. Lokketangen, and D. Woodruff, “Scatter search to generate diverse MIP solutions,” in: M. Laguna and J. L. Gonzalez-Velarde (eds.), Computing Tools for Modeling, Optim. and Simul.: Interfaces in Comp. Sci. and Oper. Res., Kluwer Acad. Publ., Boston (2000), pp. 299–317.

    Google Scholar 

  72. F. Glover and M. Laguna, Tabu Search, Kluwer Acad. Publ., Boston (1997).

    MATH  Google Scholar 

  73. J. Grabowski, E. Nowicki, and S. Zdralka, “A block approach for single machine scheduling with release dates and due dates,” Eur. J. Oper. Res., 26(2), 278–285 (1986).

    Article  MATH  Google Scholar 

  74. M. Grotschel and O. Holland, “Solution of large-scale traveling salesman problems,” Math. Program., 51(2), 141–202 (1991).

    Article  MathSciNet  Google Scholar 

  75. J. Gu and X. Huang, “Efficient local search with search space smoothing: a case study of the traveling salesman problem,” IEEE Trans. Syst., Man., Cybernetics, 24(5), 728–735 (1994).

    Article  Google Scholar 

  76. P. Hansen and N. Mladenovic, “Variable neighborhood search for the p-median,” Location Sci., 5(4), 207–226 (1997).

    Article  MATH  Google Scholar 

  77. P. Hansen, N. Mladenovic, and D. Perez-Brito, “Variable neighborhood decomposition search,” J. Heuristics, 7(3), 335–350 (2001).

    Article  MATH  Google Scholar 

  78. J. Holland, Adaptation in Natural and Artificial Systems, Univ. of Michigan Press, Ann Arbor (1975).

    Google Scholar 

  79. J. J. Hopfield and D. W. Tank, ““Neural” computation of decisions in optimization problems,” Biol. Cybernetics, 52, 141–152 (1985).

    MATH  MathSciNet  Google Scholar 

  80. M. Junger, G. Reinelt, and S. Thienel, “Practical problem solving with cutting plane algorithms in combinatorial optimization,” Combinatorial Optimization: DIMACS Ser. in Discrete Math. and Theor. Comput. Sci., 20, 111–152, AMS (1995).

    MathSciNet  Google Scholar 

  81. O. Kariv and S. L. Hakimi, “An algorithmic approach to network location problems; Part 2. The p-medians,” SIAM J. Appl. Math., 37, 539–560 (1969).

    Article  MathSciNet  Google Scholar 

  82. R. M. Karp, “The probabilistic analysis of some combinatorial search algorithms,” in: J. F. Trumb (ed.), Algorithms and Complexity, Acad. Press, New York (1976), pp. 1–16.

    Google Scholar 

  83. K. Katayama and H. Narihisha, “Performance of simulated annealing-based heuristic for unconstrained binary quadratic programming problem,” Eur. J. Oper. Res., 134, No. 1, 103–119 (2001).

    Article  MATH  Google Scholar 

  84. B. W. Kernighan and S. Lin, “An efficient heuristic procedure for partitioning graphs,” Bell Syst. Tech., 49, 291–307 (1970).

    MATH  Google Scholar 

  85. S. Kirkpatrick, C. D. Gelatti, and M. P. Vecchi, “Optimization by simulated annealing,” Science, 220, 671–680 (1983).

    Article  MathSciNet  Google Scholar 

  86. S. Lin, “Computer solutions of the traveling salesman problem,” Bell Syst. Tech. J., 44, 2245–2269 (1965).

    MATH  Google Scholar 

  87. S. Lin and B. W. Kernighan, “An effective heuristic algorithm for the traveling salesman problem,” Oper. Res., 21, 498–516 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  88. A. Lodi, K. Allemand, and T. M. Leibling, “An evolutionary heuristics for quadratic 0-1 programming,” Eur. J. Oper. Res., 119, 662–670 (1999).

    Article  MATH  Google Scholar 

  89. R. Marti, H. Lourenco, and M. Laguna, “Assigning proctors to exams with scatter search,” in: M. Laguna and J. L. Gonzalez-Velarde (eds.), Computing Tools for Modeling, Optim. and Simul.: Interfaces in Comput. Sci. and Oper. Res., Kluwer Acad. Publ., Boston (2000), pp. 215–227.

    Google Scholar 

  90. P. Merz and B. Freisleben, “Greedy and local search heuristics for unconstrained binary quadratic programming,” J. Heuristics, 8, 197–213 (2002).

    Article  MATH  Google Scholar 

  91. P. Merz and B. Freisleben, “Fitness landscapes, memetic algorithms and greedy operators for graph bipartitioning,” Evolut. Comput., 8, No. 1, 61–91 (2000).

    Article  Google Scholar 

  92. N. Mladenovic and P. Hansen, “Variable neighborhood search,” Comput. Oper. Res., 24(11), 1097–1100 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  93. E. Nowicki and C. Smutnicki, “A fast taboo search algorithm for the job shop problem,” Manag. Sci., 42(6), 797–813 (1996).

    MATH  Google Scholar 

  94. M. Ohlsson, C. Peterson, and B. Soderberg, “Neural networks for optimization problems with inequality constraints: the knapsack problem,” Neural Comput., No. 5, 331–339 (1993).

  95. D. S. Johnson, C. R. Aragon, L. A. McGeoch, et al. (eds.), “Optimization by simulated annealing: an experimental evaluation. Part I,” in: Graph Partitioning, Oper. Res., 37, 865–892 (1989).

  96. D. S. Johnson, C. R. Aragon, L. A. McGeoch, et al. (eds.), “Optimization by simulated annealing: an experimental evaluation. Part II,” in: Graph Coloring and Number Partitioning, Oper. Res., 39, 378–406 (1991).

  97. M. A. Osorio, F. Glover, and P. Hammer, “Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions,” Techn. Rep., Hearin Center for Enterprise Science, HCES-08-00 (2000).

  98. I. Osman and J. Kelly, “Meta-heuristics: an overview,” in: I. Osman and J. Kelly (eds.), Meta-Heuristics: Theory and Applications, Kluwer Acad. Publ., Boston (1996).

    Google Scholar 

  99. I. Osman and G. Laporte (eds.), “Metaheuristics in combinatorial optimization,” in: Ann. Oper. Res., Baltzer, Amsterdam (1996).

  100. M. Padberg and G. Rinaldi, “A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems,” SIAM Rev., 33(1), 60–100 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  101. G. Palubeckis, “Multistart tabu search strategies for the unconstrained binary quadratic programming problem,” Ann. Oper. Res., 131, 259–282 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  102. P. M. Pardalos and G. A. Rodgers, “Branch and bound algorithm for the maximum clique problem,” Comput. Oper. Res., 19, 363–375 (1992).

    Article  MATH  Google Scholar 

  103. P. M. Pardalos and J. Xue, “The maximum clique problem,” J. Global Optimiz., 4, 301–328 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  104. F. Pezzella and E. Merelli, “A tabu search method guided by shifting bottleneck for the job shop scheduling problem,” Eur. J. Oper. Res., 120, 297–310 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  105. C. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Optimization, Halsted Press, New York (1993).

    Google Scholar 

  106. M. Resende, “Greedy randomized adaptive search procedures (GRASP),” Techn. Rep., AT&T Labs. Res., 98.41.1, Florham Park, NJ (www.research.att.com) (1998).

  107. M. G. C. Resende and R. A. Werneck, “GRASP with path-relinking for the p-median problem,” AT&T Labs. Res., Techn. Rep., TD-5E53XL, Sept. 18 (2002).

  108. E. Rolland, D. A. Schilling, and J. R. Current, “An efficient tabu search procedure for the p-median problem,” Eur. J. Oper. Res., 96, 329–342 (1996).

    Article  Google Scholar 

  109. B. DeBacker, V. Fumon, P. Shaw et al. (eds.), “Solving vehicle routing problems using constraint programming and metaheuristics,” Heuristics, 6(4), 501–523 (2000).

  110. V.A. Emelichev, E. Girlich, Yu. V. Nikulin et al. (eds.), “Stability and regularization of vector problems of integer linear programming,” Optimization, 51(4), 645–676 (2002).

  111. E. Tsang and C. Voudouris, “Fast local search and guided local search and their application to British Telecom’s workforce scheduling problem,” Oper. Res. Lett., 20, 119–127 (1997).

    Article  MATH  Google Scholar 

  112. P. J. M. Van Laarhoven, E. H. L. Aarts, and J. K. Lenstra, “Job shop scheduling by simulated annealing,” Oper. Res., 40(1), 113–125 (1992).

    MATH  MathSciNet  Google Scholar 

  113. M. Vasquez and Hao Jin-Kao, A Hybrid Approach for the 0-1 Multidimensional Knapsack Problem, Washington, Seattle (2001).

  114. C. Voudouris and E. Tsang, “Guided local search and its application to the traveling salesman problem,” Eur. J. Oper. Res., 113, 469–499 (1999).

    Article  MATH  Google Scholar 

  115. C. Voudouris and E. Tsang, “Partial constraint satisfaction problems and guided local search,” in: Proc. 2nd Intern. Conf. Prac. Appl. Constr. Technol. (1996), pp. 337–356.

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kiev, Ukraine

    I. V. Sergienko & V. P. Shylo

Authors
  1. I. V. Sergienko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. P. Shylo
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The study was partially sponsored by the grant UKM2-2812-KV-06 (SRDF Cooperative Grants Program).

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–25, July–August 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sergienko, I.V., Shylo, V.P. Problems of discrete optimization: Challenges and main approaches to solve them. Cybern Syst Anal 42, 465–482 (2006). https://doi.org/10.1007/s10559-006-0086-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-006-0086-3

Keywords

Search

Navigation