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A Priority-Based Genetic Representations for Bicriteria Network Design Optimizations

  • Lin LinEmail author
  • Jingsong Zhao
  • Sun Lu
  • Mitsuo Gen
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

Network design is one of the most important and most frequently encountered classes of optimization problems. It is a combinatory field in combinatorial optimization and graph theory. A lot of optimization problems in network design arose directly from everyday practice in engineering and management. Furthermore, network design problems are also important for complexity theory, an area in the common intersection of mathematics and theoretical computer science which deals with the analysis of algorithms. Recent advances in evolutionary algorithms (EAs) are interested to solve such practical network problems. However, various network optimization problems typically cannot be solved analytically. Usually we must design the different algorithm for the different type of network optimization problem depending on the characteristics of the problem. In this paper, we investigate the recent related researches, design and validate effective priority-based genetic representations for the typical network models, such as shortest path models (node selection and sequencing), spanning tree models (arc selection) and maximum flow models (arc selection and flow assignment) etc., that these models covering the most features of network optimization problems. Thereby validate that EA approaches can be effectively and widely used in network design optimization.

Keywords

Evolutionary Algorithm (EA) Shortest path model Spanning tree model Maximum flow model Bicriteria network design 

Notes

Acknowledgements

This work is partly supported by the National Natural Science Foundation of China under Grant 61572100, and in part by the Grant-in-Aid for Scientific Research (C) of Japan Society of Promotion of Science (JSPS) No. 15K00357.

References

  1. 1.
    Abbasi S, Taghipour M (2015) An ant colony algorithm for solving bi-criteria network flow problems in dynamic networks. IT Eng 3(5):34–48Google Scholar
  2. 2.
    Ahuj RK, Magnanti TL, Orlin JB (1993) Network flows. Prentice Hall, New JerseyGoogle Scholar
  3. 3.
    Climaco JCN, Craveirinha JMF, Pascoal MMB (2003) A bicriterion approach for routing problems in multimedia networks. Networks 41(4):206–220MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Craveirinha J, Maco J et al (2013) A bi-criteria minimum spanning tree routing model for mpls/overlay networks. Telecommun Syst 52(1):1–13CrossRefGoogle Scholar
  5. 5.
    Davis L, Orvosh D et al (1993) A genetic algorithm for survivable network design. In: Proceedings of 5th international conference on genetic algorithms, pp 408–415Google Scholar
  6. 6.
    Deb BK (2010) Optimization for engineering design: algorithms and examples. Prentice-Hall, New DelhiGoogle Scholar
  7. 7.
    Deb K (1989) Genetic algorithms in multimodal function optimization. Master’s thesis, University of AlabamaGoogle Scholar
  8. 8.
    Deb K, Thiele L et al (2001) Scalable test problems for evolutionary multiobjective optimization. Wiley, ChichesterzbMATHGoogle Scholar
  9. 9.
    Dorigo M (1992) Optimization, learning and natural algorithms. PhD thesis, Politecnico di MilanoGoogle Scholar
  10. 10.
    Duhamel C, Gouveia L et al (2012) Models and heuristics for the k-degree constrained minimum spanning tree problem with node-degree costs. Networks 60(1):1–18MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fawcett H (2014) Manual of political economy. Macmillan and co., LondonGoogle Scholar
  12. 12.
    Fogel LJ, Owens AJ, Walsh MJ (1966) Artificial intelligence through simulated evolution. Wiley, New YorkzbMATHGoogle Scholar
  13. 13.
    Fonseca C, Fleming P (1995) An overview of evolutionary algorithms in multiobjective optimization. IEEE Trans Evol Comput 3(1):1–16Google Scholar
  14. 14.
    Garey MR, Johnson DS (1979) Computers and intractability: a guide to the theory of np-completeness. W.H. Freeman, New YorkzbMATHGoogle Scholar
  15. 15.
    Gen M (2006) Genetic algorithms and their applications. Springer, LondonGoogle Scholar
  16. 16.
    Gen M, Cheng R, Oren SS (2000) Network design techniques using adapted genetic algorithms. Springer, LondonCrossRefzbMATHGoogle Scholar
  17. 17.
    Gen M, Cheng R, Lin L (2008) Network models and optimization: multiobjective genetic algorithm approach. Springer, LondonzbMATHGoogle Scholar
  18. 18.
    Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Pub. Co., BostonzbMATHGoogle Scholar
  19. 19.
    Hansen P (1979) Bicriterion path problems. In: Proceedings of 3rd conference multiple criteria decision making theory and application, pp 109–127Google Scholar
  20. 20.
    Hao X, Gen M et al (2015) Effective multiobjective EDA for bi-criteria stochastic job-shop scheduling problem. J Intell Manufact 28:1–13Google Scholar
  21. 21.
    Holland J (1975) Adaptation in Natural and Artificial System. MIT Press, Ann ArborGoogle Scholar
  22. 22.
    Holland JH (1976) Adaptation. In: Rosen R, Snell FM (eds) Progress in theoretical biology IVGoogle Scholar
  23. 23.
    Hwang CL, Yoon K (1994) Multiple attribute decision making. Springer, HeidelbergGoogle Scholar
  24. 24.
    Ishibuchi H, Murata T (1998) A multi-objective genetic local search algorithm and its application to flowshop scheduling. Comput Ind Eng 28(3):392–403Google Scholar
  25. 25.
    Kennedy J, Eberhart R (2011) Particle swarm optimization. In: Proceeding of the IEEE international conference on neural networks, Piscataway, pp 1942–1948Google Scholar
  26. 26.
    Kennedy J, Eberhart R (2011) Particle swarm optimization. Morgan Kaufmann, San FranciscoGoogle Scholar
  27. 27.
    Koza JR (1992) Genetic programming, the next generation. MIT Press, CambridgeGoogle Scholar
  28. 28.
    Koza JR (1994) Genetic programming II (videotape): the next generation. MIT Press, CambridgeGoogle Scholar
  29. 29.
    Liang W, Schweitzer P, Xu Z (2013) Approximation algorithms for capacitated minimum forest problems in wireless sensor networks with a mobile sink. IEEE Trans Comput 62(10):1932–1944MathSciNetCrossRefGoogle Scholar
  30. 30.
    Lin L (2006) Node-based genetic algorithm for communication spanning tree problem. IEICE Trans Commun 89(4):1091–1098CrossRefGoogle Scholar
  31. 31.
    Lin L, Gen M (2008) An effective evolutionary approach for bicriteria shortest path routing problems. IEEJ Trans Electron Inf Syst 128(3):416–423Google Scholar
  32. 32.
    Mathur R, Khan I, Choudhary V (2013) Genetic algorithm for dynamic capacitated minimum spanning tree. Comput Technol Appl 4(3):404Google Scholar
  33. 33.
    Medhi D, Pioro M (2004) Routing, flow, and capacity design in communication and computer networks. Morgan Kaufmann Publishers, San FranciscozbMATHGoogle Scholar
  34. 34.
    Piggott P, Suraweera F (1995) Encoding graphs for genetic algorithms: an investigation using the minimum spanning tree problem. Springer, HeidelbergGoogle Scholar
  35. 35.
    Raidl GR, Julstrom B (2003) Edge-sets: an effective evolutionary coding of spanning trees. IEEE Trans Evol. Comput. 7(3):225–239CrossRefGoogle Scholar
  36. 36.
    Rechenberg I (1973) Optimieriung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, StuttgartGoogle Scholar
  37. 37.
    Ruiz E, Albareda-Sambola M et al (2015) A biased random-key genetic algorithm for the capacitated minimum spanning tree problem. Comput Oper Res 57:95–108MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: International conference on genetic algorithms, pp 93–100Google Scholar
  39. 39.
    Schwefel HPP (1995) Evolution and Optimum Seeking: The Sixth Generation. Wiley, New YorkGoogle Scholar
  40. 40.
    Srinivas N, Deb K (1995) Multiobjective function optimization using nondominated sorting genetic algorithms. IEEE Trans Evol Comput 2(3):221–248Google Scholar
  41. 41.
    Steiner S, Radzik T (2008) Computing all efficient solutions of the biobjective minimum spanning tree problem. Comput Oper Res 35(1):198–211MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Steuer RE (1986) Multiple criteria optimization theory computation and application Wiley series in probability and mathematical statistics. Probability and mathematical statistics. Wiley, New YorkGoogle Scholar
  43. 43.
    Torkestani JA (2013) Degree constrained minimum spanning tree problem: a learning automata approach. J Supercomput 64(1):226–249CrossRefzbMATHGoogle Scholar
  44. 44.
    Torkestani JA, Meybodi MR (2012) A learning automata-based heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs. J Supercomput 59(2):1035–1054CrossRefGoogle Scholar
  45. 45.
    Torkestani JA, Rezaei Z (2013) A learning automata based approach to the bounded-diameter minimum spanning tree problem. J Chin Inst Eng 36(6):749–759CrossRefGoogle Scholar
  46. 46.
    Vo\(\beta \) S, Martello S, et al (2012) Meta-heuristics: Advances and trends in local search paradigms for optimizationGoogle Scholar
  47. 47.
    Zandieh M (2011) A novel imperialist competitive algorithm for bi-criteria scheduling of the assembly flowshop problem. Int J Prod Res 49(11):3087–3103CrossRefGoogle Scholar
  48. 48.
    Zhang Q, Ding L (2016) A new crossover mechanism for genetic algorithms with variable-length chromosomes for path optimization problems. Expert Syst Appl 60:183–189CrossRefGoogle Scholar
  49. 49.
    Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary methods for design, optimization and control with applications to industrial problems. Proceedings of the Eurogen 2001, Athens, Greece, SeptemberGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Fuzzy Logic Systems InstituteTokyoJapan
  3. 3.Key Laboratory for Ubiquitous Network and Service Software of Liaoning ProvinceDalianPeople’s Republic of China

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