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On Estimating LON-Based Measures in Cyclic Assignment Problem in Non-permutational Flow Shop Scheduling Problem

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Modelling and Performance Analysis of Cyclic Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 241))

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Abstract

In recent years, Fitness Landscape Analysis (FLA) has provided a variety of new methods to analyze problem instances, allowing for a better understanding of the challenges that operations research is facing. Many from the most promising FLA methods are based on Local Optima Networks (LON), a compact representation of a search space from the perspective of a optimization algorithms. In order to obtain a represantative LON, a solution space sampling procedure must be utilized. However, there is little known about the proper sampling methods—as well as the minimal ammout of computational effort required to sufficiently sample the space. In this chapter, we investigate the impact of the number of samples taken, on the obtained LON metrics for Cyclic Assignment Problem in non-permutational Flow Shop Scheduling Problem. The sampling process is performed in incremental steps, until the entire solution space is analyzed. After each step, LON measures are calculated. The results suggest a strong relation between the measure values and sampling effort.

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References

  1. Bożejko, W., Gnatowski, A., Idzikowski, R., Wodecki, M.: Cyclic flow shop problem with two-machine cells. Arch. Control. Sci. 27(2), 151–167 (2017)

    Article  MathSciNet  Google Scholar 

  2. Bożejko, W., Gnatowski, A., Klempous, R., Affenzeller, M., Beham, A.: Cyclic scheduling of a robotic cell. In: 2016 7th IEEE International Conference on Cognitive Infocommunications (CogInfoCom), pp. 379–384. IEEE (2016)

    Google Scholar 

  3. Bożejko, W., Gnatowski, A., Niżyński, T., Affenzeller, M., Beham, A.: Local optima networks in solving algorithm selection problem for TSP. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds.) Contemporary Complex Systems and Their Dependability. DepCoS-RELCOMEX 2018. Advances in Intelligent Systems and Computing, vol. 761, pp. 83–93. Springer, Cham (2019)

    Google Scholar 

  4. Bożejko, W., Pempera, J., Wodecki, M.: Minimal cycle time determination and golf neighborhood generation for the cyclic flexible job shop problem. Bull. Pol. Acad. Sci.: Tech. Sci. 66(3), 333–344 (2018)

    Google Scholar 

  5. Chaudhry, I.A., Khan, A.A.: A research survey: Review of flexible job shop scheduling techniques. Int. Trans. Oper. Res. 23(3), 551–591 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  6. Crama, Y., Kats, V., van de Klundert, J., Levner, E.: Cyclic scheduling in robotic flowshops. Ann. Oper. Res. 96(1), 97–124 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dawande, M., Geismar, H.N., Sethi, S.P., Sriskandarajah, C.: Sequencing and scheduling in robotic cells: recent developments. J. Sched. 8(5), 387–426 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dawande, M.W., Geismar, H.N., Suresh, P.S., Sriskandarajah, C., Sethi, S., Sriskandarajah, C.: Throughput Optimization in Robotic Cells. Springer, Boston (2007)

    MATH  Google Scholar 

  9. Gultekin, H., Coban, B., Akhlaghi, V.E.: Cyclic scheduling of parts and robot moves in m -machine robotic cells. Comput. Oper. Res. 90, 161–172 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hall, N.G., Kamoun, H., Sriskandarajah, C.: Scheduling in robotic cells: classification, two and three machine cells. Oper. Res. 45(3), 421–439 (1997)

    Article  MATH  Google Scholar 

  11. Humeau, J., Liefooghe, A., Talbi, E.G., Verel, S.: ParadisEO-MO: From fitness landscape analysis to efficient local search algorithms. Technical report RR-7871, INRIA. https://hal.inria.fr/hal-00665421v2. Accessed 30 March 2019

  12. Iclanzan, D., Daolio, F., Tomassini, M.: Data-driven local optima network characterization of QAPLIB instances. In: Proceedings of the 2014 conference on Genetic and evolutionary computation, pp. 453–460. ACM Press, New York (2014)

    Google Scholar 

  13. Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. In: Bessiere, C., De Raedt, L., Kotthoff, L., Nijssen, S., O’Sullivan, B., Pedreschi, D. (eds.) Data Mining and Constraint Programming: Foundations of a Cross-Disciplinary Approach, pp. 149–190. Springer International Publishing, Cham (2016)

    Chapter  Google Scholar 

  14. Lu, H., Shi, J., Fei, Z., Zhou, Q., Mao, K.: Measures in the time and frequency domains for fitness landscape analysis of dynamic optimization problems. Appl. Soft Comput. 51, 192–208 (2017)

    Article  Google Scholar 

  15. Naudts, B., Suys, D., Verschoren, A.: Epistasis as a basic concept in formal landscape analysis. In: Proceedings of the 7th International Conference on Genetic Algorithms, pp. 65–72. Morgan Kaufmann, Burlington (1997)

    Google Scholar 

  16. Newman, M.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Newman, M.E.J.: Mixing patterns in networks. Phys. Rev. E 67, 026126 (2003)

    Article  MathSciNet  Google Scholar 

  18. Ochoa, G., Veerapen, N.: Additional dimensions to the study of funnels in combinatorial landscapes. In: Proceedings of the 2016 on Genetic and Evolutionary Computation Conference—GECCO’16, pp. 373–380. ACM Press, New York (2016)

    Google Scholar 

  19. Ochoa, G., Veerapen, N.: Mapping the global structure of TSP fitness landscapes. J. Heuristics 24(3), 265–294 (2017)

    Article  Google Scholar 

  20. Ochoa, G., Verel, S., Daolio, F., Tomassini, M.: Local optima networks: a new model of combinatorial fitness landscapes. In: Richter, H., Engelbrecht, A. (eds.) Recent Advances in the Theory and Application of Fitness Landscapes, pp. 233–262. Springer, Berlin (2014)

    Chapter  Google Scholar 

  21. Peixoto, T.P.: The graph-tool python library. http://figshare.com/articles/graph_tool/1164194 (2014). Accessed 30 March 2019

  22. Reidys, C.M., Stadler, P.F.: Neutrality in fitness landscapes. Appl. Math. Comput. 117(2–3), 321–350 (2001)

    MathSciNet  MATH  Google Scholar 

  23. Rosé, H., Ebeling, W., Asselmeyer, T.: The density of states — a measure of the difficulty of optimisation problems. In: Guervós, J.J.M., Adamidis, P., Beyer, H.G., Schwefel, H.P., Fernández-Villacañas, J.L. (eds.) Parallel Problem Solving from Nature — PPSN IV. PPSN 1996. Lecture Notes in Computer Science, vol. 2439, pp. 208–217. Springer, Berlin (1996)

    Chapter  Google Scholar 

  24. Ruiz, R., Vázquez-Rodríguez, J.A.: The hybrid flow shop problem. Eur. J. Oper. Res. 205(1), 1–18 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  25. Sethi, S.P., Sriskandarajah, C., Sorger, G., Blazewicz, J., Kubiak, W.: Sequencing of parts and robot moves in a robotic cell. Int. J. Flex. Manuf. Syst. 4(3–4), 331–358 (1992)

    Article  Google Scholar 

  26. Shirakawa, S., Nagao, T.: Bag of local landscape features for fitness landscape analysis. Soft Comput. 20(10), 3787–3802 (2016)

    Article  Google Scholar 

  27. Stadler, P.F.: Fitness landscapes. In: Lässig, M., Valleriani, A. (eds.) Biological Evolution and Statistical Physics, pp. 183–204. Springer, Berlin (2002)

    Chapter  Google Scholar 

  28. Thomson, S.L., Ochoa, G., Daolio, F., Veerapen, N.: The effect of landscape funnels in QAPLIB instances. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion on—GECCO’17, pp. 1495–1500. ACM Press, New York (2017)

    Google Scholar 

  29. Tomassini, M., Verel, S., Ochoa, G.: Complex-network analysis of combinatorial spaces: the NK landscape case. Phys. Rev. E 78(6), 066114 (2008)

    Article  Google Scholar 

  30. Vassilev, V.K., Fogarty, T.C., Miller, J.F.: Information characteristics and the structure of landscapes. Evol. Comput. 8(1), 31–60 (2000)

    Article  Google Scholar 

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Acknowledgements

The chapter was partially supported by the National Science Centre of Poland, grant OPUS number DEC 2017/25/B/ST7/02181.

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Authors and Affiliations

  1. Department of Control Systems and Mechatronics, Faculty of Electronics, Wrocław University of Science and Technology, 27 Wybrzeże Wyspiańskiego St., 50-372, Wrocław, Poland

    Andrzej Gnatowski & Teodor Niżyński

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  1. Andrzej Gnatowski
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  2. Teodor Niżyński
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Correspondence to Andrzej Gnatowski .

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Editors and Affiliations

  1. Department of Control Systems and Mechatronics, Faculty of Electronics, Wrocław University of Science and Technology, Wrocław, Poland

    Wojciech Bożejko

  2. Department of Computer Science and Management, Faculty of Electronics and Computer Science, Koszalin University of Technology, Koszalin, Poland

    Grzegorz Bocewicz

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Gnatowski, A., Niżyński, T. (2020). On Estimating LON-Based Measures in Cyclic Assignment Problem in Non-permutational Flow Shop Scheduling Problem. In: Bożejko, W., Bocewicz, G. (eds) Modelling and Performance Analysis of Cyclic Systems. Studies in Systems, Decision and Control, vol 241. Springer, Cham. https://doi.org/10.1007/978-3-030-27652-2_4

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  • DOI: https://doi.org/10.1007/978-3-030-27652-2_4

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