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Combinatorial Optimization Problems in Planning and Decision Making pp 1–14Cite as

Introduction

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Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 173))

Abstract

We formulate the research problems which are a generalization of our earlier results in the field of intractable combinatorial optimization problems. On the basis of these problems, we have created a hierarchical model of planning and decision making for objects with a network representation of technological processes and limited resources (Chap. 9). We say that the problem is intractable if it is NP-hard (NP-hard in the strong sense) or such for which an exact polynomial time solution algorithm has not been yet obtained. To solve such problems efficiently, we developed a methodology of PSC-algorithms construction meaning the algorithms which necessarily include the following: sufficient conditions (signs) of a feasible solution optimality, verification of which can be implemented only at the stage of a feasible solution construction by a polynomial algorithm (the first polynomial component of the PSC-algorithm). The second polynomial component of the PSC-algorithm is an approximation algorithm with polynomial complexity. For NP-hard (NP-hard in the strong sense) combinatorial optimization problems, a PSC-algorithm may include an exact algorithm for its solving in case if sufficient conditions were found, satisfying of which during this algorithm execution turns it into a polynomial complexity algorithm (Chaps. 4 and 5). We also give a brief overview of the monograph’s chapters content.

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References

  1. Zgurovsky, M.Z., Pavlov, A.A.: Prinyatie Resheniy v Setevyh Sistemah s Ogranichennymi Resursami (Пpинятиe peшeний в ceтeвыx cиcтeмax c oгpaничeнными pecypcaми; Decision Making in Network Systems with Limited Resources). Naukova dumka, Kyiv (2010) (in Russian)

    Google Scholar 

  2. Pavlov, A.A. (ed.): Konstruktivnye Polinomialnye Algoritmy Resheniya Individualnyh Zadach iz Klassa NP (Кoнcтpyктивныe пoлинoмиaльныe aлгopитмы peшeния индивидyaльныx зaдaч из клacca NP; Constructive Polynomial Algorithms for Solving Individual Problems from the Class NP). Tehnika, Kyiv (1993) (in Russian)

    Google Scholar 

  3. Pavlov, A.A., Pavlova, L.A.: PDC-algorithms for intractable combinatorial problems. Theory and methodology of design. “Karpatskij region” shelf #15, Uzhhorod (1998)

    Google Scholar 

  4. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co, San Francisco (1979). https://doi.org/10.1137/1024022

    Article  Google Scholar 

  5. Jain, A.S., Meeran, S.: Deterministic job-shop scheduling: past, present and future. Eur. J. Oper. Res. 113, 390–434 (1999). https://doi.org/10.1016/S0377-2217(98)00113-1

    Article  MATH  Google Scholar 

  6. Pinedo, M.L.: Scheduling: Theory, Algorithms, and Systems. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-26580-3

    Book  Google Scholar 

  7. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: Sequencing and scheduling: Algorithms and complexity. In: Graves, S.C., Rinnooy Kan, A.H.G., Zipkin, P.H. (eds.) Logistics of Production and Inventory. Handbook in Operations Research and Management Science, vol. 4, pp. 445–522. North-Holland, Amsterdam (1993). https://doi.org/10.1016/s0927-0507(05)80189-6

    Chapter  Google Scholar 

  8. Fisher, H., Thompson, G.L.: Probabilistic learning combinations of local job-shop scheduling rules. In: Muth, J.F., Thompson, G.L. (eds.) Industrial Scheduling, pp. 225–251. Prentice-Hall, Englewood Cliffs (1963)

    Google Scholar 

  9. Lawrence, S.: Supplement to resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques. GSIA, Carnegie-Mellon University, Pittsburgh (1984)

    Google Scholar 

  10. Panwalkar, S.S., Iskander, W.: A survey of scheduling rules. Oper. Res. 25(1), 45–61 (1977). https://doi.org/10.1287/opre.25.1.45

    Article  MathSciNet  MATH  Google Scholar 

  11. Grabot, B., Geneste, L.: Dispatching rules in scheduling: a fuzzy approach. Int. J. Prod. Res. 32(4), 903–915 (1994). https://doi.org/10.1080/00207549408956978

    Article  MATH  Google Scholar 

  12. Werner, F., Winkler, A.: Insertion techniques for the heuristic solution of the job-shop problem. Discrete Appl. Math. 58(2), 191–211 (1995). https://doi.org/10.1016/0166-218X(93)E0127-K

    Article  MathSciNet  MATH  Google Scholar 

  13. Morton, T.E., Pentico, D.W.: Heuristic Scheduling Systems: With Applications to Production Systems and Project Management. Wiley, New York (1993)

    Google Scholar 

  14. Sabuncuoglu, I., Bayiz, M.: A beam search based algorithm for the job shop scheduling problem. Research Report IEOR-9705. Bilkent University, Bilkent (1997)

    Google Scholar 

  15. Fisher, M.L., Rinnooy Kan, A.H.G.: The design, analysis and implementation of heuristics. Manag. Sci. 34(3), 263–265 (1988). https://doi.org/10.1287/mnsc.34.3.263

    Article  MathSciNet  Google Scholar 

  16. Glover, F., Greenberg, H.J.: New approaches for heuristic search: a bilateral linkage with artificial intelligence. Eur. J. Oper. Res. 39(2), 119–130 (1989). https://doi.org/10.1016/0377-2217(89)90185-9

    Article  MathSciNet  MATH  Google Scholar 

  17. Rodammer, F.A., White, K.P., Jr.: A recent survey of production scheduling. IEEE Trans. Syst. Man Cybern. 18(6), 841–851 (1988). https://doi.org/10.1109/21.23085

    Article  MathSciNet  Google Scholar 

  18. Sergienko, I.V., Kapitonova, Y.V., Lebedeva, T.T.: Informatika v Ukraine: Stanovlenie, Razvitie, Problemy (Инфopмaтикa в Укpaинe: cтaнoвлeниe, paзвитиe, пpoблeмы; Informatics in Ukraine: Formation, Development, Problems). Naukova dumka, Kyiv (1999) (in Russian)

    Google Scholar 

  19. Johnson, D.S., Papadimitriou, C.H., Yannakakis, M.: How easy is local search? J. Comput. Syst. Sci. 37(1), 79–100 (1988). https://doi.org/10.1016/0022-0000(88)90046-3

    Article  MathSciNet  MATH  Google Scholar 

  20. Yannakakis, M.: The analysis of local search problems and their heuristics. In: Choffrut, C., Lengauer, T. (eds.) STACS 90. Lecture Notes in Computer Science, vol. 415, pp. 298–311. Springer, Berlin (1990). https://doi.org/10.1007/3-540-52282-4_52

    Chapter  Google Scholar 

  21. Sergienko, I.V.: O primenenii metoda vektora spada dlya resheniya zadach optimizacii kombinatornogo tipa (O пpимeнeнии мeтoдa вeктopa cпaдa для peшeния зaдaч oптимизaции кoмбинaтopнoгo типa; On the application of the recession vector method to solve optimization problems of combinatorial type). Upravlyayuschie sistemy i mashiny 2, 86–94 (1975) (in Russian)

    Google Scholar 

  22. Bykov, A.Y., Artamonova, A.Y.: Modifikaciya metoda vektora spada dlya optimizacionno-imitacionnogo podhoda k zadacham proektirovaniya sistem zaschity informacii (Moдификaция мeтoдa вeктopa cпaдa для oптимизaциoннo-имитaциoннoгo пoдxoдa к зaдaчaм пpoeктиpoвaния cиcтeм зaщиты инфopмaции; A modified recession vector method based on the optimization-simulation approach to design problems of information security systems). Nauka i Obrazovanie of Bauman MSTU, vol. 1, pp. 158–175 (2015). https://doi.org/10.7463/0115.0754845 (in Russian)

  23. Shilo, V.P.: Metod globalnogo ravnovesnogo poiska (Meтoд глoбaльнoгo paвнoвecнoгo пoиcкa; Global equilibrium search method). Cybern. Syst. Anal. 35(1), 74–81 (1999) (in Russian)

    Google Scholar 

  24. Adams, J., Balas, E., Zawack, D.: The shifting bottleneck procedure for job-shop scheduling. Manag. Sci. 34(3), 391–401 (1988). https://doi.org/10.1287/mnsc.34.3.391

    Article  MathSciNet  MATH  Google Scholar 

  25. Balas, E., Lancia, G., Serafini, P., et al.: Job-shop scheduling with deadlines. J. Comb. Optim. 1(4), 329–353 (1998). https://doi.org/10.1023/A:1009750409895

    Article  MathSciNet  MATH  Google Scholar 

  26. Balas, E., Vazacopoulos, A.: Guided local search with shifting bottleneck for job-shop scheduling. Manag. Sci. 44(2), 262–275 (1998). https://doi.org/10.1287/mnsc.44.2.262

    Article  MATH  Google Scholar 

  27. Caseau, Y., Laburthe, F.: Disjunctive scheduling with task intervals. LIENS Technical Report 95-25. Laboratoire d’Informatique de l’ Ecole Normale Superieure, Paris (1995)

    Google Scholar 

  28. Demirkol, E., Mehta, S., Uzsoy, R.: A computational study of shifting bottleneck procedures for shop scheduling problems. J. Heuristics 3(2), 111–137 (1997). https://doi.org/10.1023/A:1009627429878

    Article  MATH  Google Scholar 

  29. Yamada, T., Nakano, R.: Job-shop scheduling by simulated annealing combined with deterministic local search. In: Osman, I.H., Kelly, J.P. (eds.) Meta-Heuristics: Theory and Applications, pp. 237–248. Springer, Boston (1996). https://doi.org/10.1007/978-1-4613-1361-8_15

    Chapter  Google Scholar 

  30. Falkenauer, E., Bouffouix, S.: A genetic algorithm for job-shop. In: Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, 9–11 April 1991. https://doi.org/10.1109/robot.1991.131689

  31. Nakano, R., Yamada, T.: Conventional genetic algorithm for job-shop problems. In: Kenneth, M.K., Booker, L.B. (eds.) Proceedings of the 4th International Conference on Genetic Algorithms and their Applications, San Diego (1991)

    Google Scholar 

  32. Aarts, E.H.L., Van Laarhooven, P.J.M., Ulder, N.L.J.: Local search based algorithms for job-shop scheduling. Working Paper. University of Technology, Eindhoven (1991)

    Google Scholar 

  33. Dorndorf, U., Pesch, E.: Evolution based learning in a job-shop scheduling environment. Comp. Oper. Res. 22(1), 25–40 (1995). https://doi.org/10.1016/0305-0548(93)E0016-M

    Article  MATH  Google Scholar 

  34. Grefenstette, J.J.: Incorporating problem specific knowledge into genetic algorithms. In: Davis, L. (ed.) Genetic Algorithms and Simulated Annealing, pp. 42–60. Pitman, London (1987)

    Google Scholar 

  35. Moscato, P.: On evolution, search, optimization, genetic algorithms and martial arts: towards memetic algorithms. C3P Report 826: Caltech Concurrent Computation Program, Caltech (1989)

    Google Scholar 

  36. Ulder, N.L.J., Aarts, E.H.L., Bandelt, H.-J., et al.: Genetic local search algorithm for the travelling salesman problem. Lect. Notes Comput. Sci. 496, 109–116 (1991)

    Article  Google Scholar 

  37. Fox, M.S.: Constraint-directed search: a case study of job shop scheduling. Dissertation, Carnegy Mellon University, Pittsburgh (1983)

    Google Scholar 

  38. Nuijten, W.P.M., Le Pape, C.: Constraint-based job-shop scheduling with ILOG SCHEDULER. J. Heuristics 3(4), 271–286 (1998). https://doi.org/10.1023/A:1009687210594

    Article  MATH  Google Scholar 

  39. Pesch, E., Tetzlaff, U.A.W.: Constraint propagation based scheduling of job shops. INFORMS J. Comput. 8(2), 144–157 (1996). https://doi.org/10.1287/ijoc.8.2.144

    Article  MATH  Google Scholar 

  40. Sadeh, N.: Look-ahead techniques for micro-opportunistic job shop scheduling. Dissertation, Carnegie Mellon University, Pittsburgh (1991)

    Google Scholar 

  41. Foo, S.Y., Takefuji, Y.: Integer linear programming neural networks for job-shop scheduling. In: IEEE International Conference on Neural Networks, San Diego, 24–27 July 1988

    Google Scholar 

  42. Foo, S.Y., Takefuji, Y.: Stochastic neural networks for solving job-shop scheduling: Part 1. problem representation. In: IEEE International Conference on Neural Networks, San Diego, 24–27 July 1988

    Google Scholar 

  43. Foo, S.Y., Takefuji, Y.: Stochastic neural networks for solving job-shop scheduling: part 2. Architecture and simulations. IEEE International Conference on Neural Networks, San Diego, 24–27 July 1988

    Google Scholar 

  44. Sabuncuoglu, I., Gurgun, B.: A neural network model for scheduling problems. Eur. J. Oper. Res. 93(2), 288–299 (1996). https://doi.org/10.1016/0377-2217(96)00041-0

    Article  MATH  Google Scholar 

  45. Zhou, D.N., Cherkassky, V., Baldwin, T.R., et al.: Scaling neural networks for job-shop scheduling. In: Proceedings of International Joint Conference on Neural Networks (IJCNN’90), San Diego, 17–21 June 1990, pp. 889–894. https://doi.org/10.1109/ijcnn.1990.137947

  46. Zhou, D.N., Cherkassky, V., Baldwin, T.R., et al.: A neural network approach to job-shop scheduling. IEEE Trans. Neural. Netw. 2(1), 175–179 (1991). https://doi.org/10.1109/72.80311

    Article  Google Scholar 

  47. Dorigo, M.: Optimization, learning and natural algorithms. Dissertation, Politecnico di Milano (1992)

    Google Scholar 

  48. Donati, A.V., Darley, V., Ramachandran, B.: An ant-bidding algorithm for multistage flowshop scheduling problem: optimization and phase transitions. In: Siarry, P., Michalewicz, Z. (eds.) Advances in Metaheuristics for Hard Optimization, pp. 111–136. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-72960-0_6

  49. Prabhakar, B., Dektar, K.N., Gordon, D.M.: The regulation of ant colony foraging activity without spatial information. PLoS Comput. Biol. 8(8), e1002670 (2012). https://doi.org/10.1371/journal.pcbi.1002670

    Article  MathSciNet  Google Scholar 

  50. Brucker, P., Hurink, J., Werner, F.: Improving local search heuristics for some scheduling problems—I. Discrete Appl. Math. 65(1–3), 97–122 (1996). https://doi.org/10.1016/0166-218X(95)00030-U

    Article  MathSciNet  MATH  Google Scholar 

  51. Brucker, P., Hurink, J., Werner, F.: Improving local search heuristics for some scheduling problems. Part II. Discrete Appl. Math. 72(1–2), 47–69 (1997). https://doi.org/10.1016/S0166-218X(96)00036-4

    Article  MathSciNet  MATH  Google Scholar 

  52. Lourenco, H.R.D.: A computational study of the job-shop and the flow-shop scheduling problems. Dissertation, Cornell University (1993)

    Google Scholar 

  53. Lourenco, H.R.D.: Job-shop scheduling: computational study of local search and large-step optimization methods. Eur. J. Oper. Res. 83(2), 347–364 (1995). https://doi.org/10.1016/0377-2217(95)00012-F

    Article  MATH  Google Scholar 

  54. Lourenco, H.R.D., Zwijnenburg, M.: Combining the large-step optimization with tabu-search: Application to the job-shop scheduling problem. In: Osman, I.H., Kelly, J.P. (eds.) Meta-Heuristics: Theory and Applications, pp. 219–236. Springer, Boston (1996). https://doi.org/10.1007/978-1-4613-1361-8_14

    Chapter  Google Scholar 

  55. Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for traveling salesman problem. Complex Syst. 5(3), 299–326 (1989)

    MathSciNet  MATH  Google Scholar 

  56. Martin, O., Otto, S.W., Felten, E.W.: Large-step Markov chains for TSP incorporating local search heuristics. Oper. Res. Lett. 11(4), 219–224 (1992). https://doi.org/10.1016/0167-6377(92)90028-2

    Article  MathSciNet  MATH  Google Scholar 

  57. Glover, F.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986). https://doi.org/10.1016/0305-0548(86)90048-1

    Article  MathSciNet  MATH  Google Scholar 

  58. Glover, F.: Heuristics for integer programming using surrogate constraints. Decis. Sci. 8(1), 156–166 (1977). https://doi.org/10.1111/j.1540-5915.1977.tb01074.x

    Article  Google Scholar 

  59. Glover, F.: Tabu search—part I. ORSA J. Comput. 1(3), 190–206 (1989). https://doi.org/10.1287/ijoc.1.3.190

    Article  MATH  Google Scholar 

  60. Glover, F.: Tabu search—part II. ORSA J. Comput. 2(1), 4–32 (1990). https://doi.org/10.1287/ijoc.2.1.4

    Article  MATH  Google Scholar 

  61. Glover, F., Laguna, M.: Tabu Search. Springer, Boston (1997). https://doi.org/10.1007/978-1-4615-6089-0

    Book  Google Scholar 

  62. Nowicki, E., Smutnicki, C.: A fast taboo search algorithm for the job-shop problem. Manag. Sci. 42(6), 797–813 (1996). https://doi.org/10.1287/mnsc.42.6.797

    Article  MATH  Google Scholar 

  63. Taillard, E.: Parallel taboo search technique for the job-shop scheduling problem. Internal Research Report ORWP89/11. Ecole Polytechnique Federale de Lausanne, Lausanne (1989)

    Google Scholar 

  64. Edelkamp, S., Schrödl, S.: Heuristic Search: Theory and Applications. Morgan Kaufmann Publishers, Waltham, MA (2012). https://doi.org/10.1016/c2009-0-16511-x

  65. Resende, M.G.C.: A GRASP for job shop scheduling. In: INFORMS National Meeting, pp. 23–31, San Diego, CA, 4–7 May 1997

    Google Scholar 

  66. Matsuo, H., Suh, C.J., Sullivan, R.S.: A controlled search simulated annealing method for the general job-shop scheduling problem. Working Paper. University of Texas, Austin (1988)

    Google Scholar 

  67. Van Laarhoven, P.J.M., Aarts, E.H.L., Lenstra, J.K.: Job-shop scheduling by simulated annealing. Report OS-R8809. Centrum voor Wiskunde en Informatica, Amsterdam (1988)

    Google Scholar 

  68. Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)

    MATH  Google Scholar 

  69. Michel, L., Hentenryck, P.V.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2012. Lecture Notes in Computer Science, vol. 7298, pp. 228–243. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-29828-8_15

    Chapter  Google Scholar 

  70. Schulte, C., Tack, G., Lagerkvist, M.Z.: Modeling and programming with Gecode. http://www.gecode.org/doc-latest/MPG.pdf (2018). Accessed 02 Apr 2018.

  71. Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009). https://doi.org/10.1017/cbo9780511801655

  72. Pavlov, A.A. (ed.): Osnovy Sistemnogo Analiza i Proektirovaniya ASU (Ocнoвы cиcтeмнoгo aнaлизa и пpoeктиpoвaния ACУ; Fundamentals of System Analysis and Design of Automated Control Systems). Vyshcha Shkola, Kyiv (1991) (in Russian)

    Google Scholar 

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Authors and Affiliations

  1. Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine

    Michael Z. Zgurovsky

  2. Faculty of Informatics and Computer Science, National Technical University of Ukraine, Kyiv, Ukraine

    Alexander A. Pavlov

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  1. Michael Z. Zgurovsky
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Correspondence to Michael Z. Zgurovsky .

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Zgurovsky, M.Z., Pavlov, A.A. (2019). Introduction. In: Combinatorial Optimization Problems in Planning and Decision Making. Studies in Systems, Decision and Control, vol 173. Springer, Cham. https://doi.org/10.1007/978-3-319-98977-8_1

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