Advertisement

Optimization Problems and Algorithms

  • Yujun Zheng
  • Xueqin Lu
  • Minxia Zhang
  • Shengyong Chen
Chapter

Abstract

Optimization problems occur in almost everywhere of our society. According to the form of solution spaces, optimization problems can be classified into continuous optimization problems and combinatorial optimization problems. Algorithms for optimization problems, according to whether they can guarantee the exact optimal solutions, can be classified into exact algorithms and heuristic algorithms. This chapter presents a brief overview of optimization problems and then introduces some well-known optimization algorithms, which lays the foundation of this book.

References

  1. 1.
    Bell JE, McMullen PR (2004) Ant colony optimization techniques for the vehicle routing problem. Adv Eng Inf 18:41–48.  https://doi.org/10.1016/j.aei.2004.07.001CrossRefGoogle Scholar
  2. 2.
    D, K (2005) An idea based on honey bee swarm for numerical optimization. Technical report, Erciyes UniversityGoogle Scholar
  3. 3.
    Dantzig BG (1998) Linear programming and extensions. Princeton University Press, PrincetonGoogle Scholar
  4. 4.
    Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B 26:29–41.  https://doi.org/10.1109/3477.484436CrossRefGoogle Scholar
  5. 5.
    Durran D (1999) Numerical methods for wave equations in geophysical fluid dynamics. Springer, BerlinGoogle Scholar
  6. 6.
    Eberhart R, Yuhui S (2001) Tracking and optimizing dynamic systems with particle swarms. Proc IEEE Congr Evol Comput 1:94–100.  https://doi.org/10.1109/CEC.2001.934376CrossRefGoogle Scholar
  7. 7.
    Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68.  https://doi.org/10.1177/003754970107600201CrossRefGoogle Scholar
  8. 8.
    Goldberg DE, Deb K (1991) A comparative analysis of selection schemes used in genetic algorithms. Found Genetic Algorithms 1:69–93.  https://doi.org/10.1016/B978-0-08-050684-5.50008-2MathSciNetCrossRefGoogle Scholar
  9. 9.
    Henry HJ (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. University of Michigan Press, Ann ArborGoogle Scholar
  10. 10.
    Kennedy J, Eberhart R (1995) Particle swarm optimization. IEEE Int Conf Neural Netw 4:1942–1948.  https://doi.org/10.1109/ICNN.1995.488968CrossRefGoogle Scholar
  11. 11.
    Kennedy J, Mendes R (2006) Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Trans Syst Man Cybern C 36:515–519.  https://doi.org/10.1109/TSMCC.2006.875410CrossRefGoogle Scholar
  12. 12.
    Kirkpatrick S, Jr DG, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680.  https://doi.org/10.1126/science.220.4598.671MathSciNetCrossRefGoogle Scholar
  13. 13.
    Liang JJ, Qu BY, Suganthan PN (2014) Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Technical report, Computational Intelligence Laboratory, Zhengzhou UniversityGoogle Scholar
  14. 14.
    Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579.  https://doi.org/10.1016/j.amc.2006.11.033MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Mehrabian A, Lucas C (2006) A novel numerical optimization algorithm inspired from weed colonization. Ecol Inf 1:355–366.  https://doi.org/10.1016/j.ecoinf.2006.07.003CrossRefGoogle Scholar
  16. 16.
    Oftadeh R, Mahjoob M, Shariatpanahi M (2010) A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search. Comput Math Appl 60:2087–2098.  https://doi.org/10.1016/j.camwa.2010.07.049CrossRefzbMATHGoogle Scholar
  17. 17.
    Potvin JY (1996) Genetic algorithms for the traveling salesman problem. Ann Op Res 63:337–370CrossRefGoogle Scholar
  18. 18.
    Rajendran C, Ziegler H (2004) Ant-colony algorithms for permutation flowshop scheduling to minimize makespan/total flowtime of jobs. Eur J Op Res 155:426–438.  https://doi.org/10.1016/S0377-2217(02)00908-6CrossRefzbMATHGoogle Scholar
  19. 19.
    Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: A gravitational search algorithm. Inf Sci 179:2232–2248.  https://doi.org/10.1016/j.ins.2009.03.004CrossRefzbMATHGoogle Scholar
  20. 20.
    Shao Z, Pi D, Shao W (2017) A novel discrete water wave optimization algorithm for blocking flow-shop scheduling problem with sequence-dependent setup times. Swarm Evol Comput.  https://doi.org/10.1016/j.swevo.2017.12.005.(onlinefirst)
  21. 21.
    Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12:702–713.  https://doi.org/10.1109/TEVC.2008.919004CrossRefGoogle Scholar
  22. 22.
    Srinivas M, Patnaik L (1994) Genetic algorithms - a survey. Computer 27:17–26.  https://doi.org/10.1109/2.294849CrossRefGoogle Scholar
  23. 23.
    Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359.  https://doi.org/10.1023/A:1008202821328MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Tan Y, Zhu Y (2010) Fireworks algorithm for optimization. In: Advances in swarm intelligence, Lecture Notes in Computer Science, vol 6145. Springer, pp 355–364.  https://doi.org/10.1007/978-3-642-13495-1_44Google Scholar
  25. 25.
    Wu XB, Liao J, Wang ZC (2015) Water wave optimization for the traveling salesman problem. In: Huang DS, Bevilacqua V, Premaratne P (eds) Intelligent computing theories and methodologies. Springer, Cham, pp 137–146 (2015).  https://doi.org/10.1007/978-3-319-22180-9_14CrossRefGoogle Scholar
  26. 26.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm. In: Nature inspired cooperative strategies for optimization, Studies in computational intelligence, vol 284. pp 65–74.  https://doi.org/10.1007/978-3-642-12538-6_6CrossRefGoogle Scholar
  27. 27.
    Zhao F, Liu H, Zhang Y, Ma W, Zhang C (2018) A discrete water wave optimization algorithm for no-wait flow shop scheduling problem. Expert Syst Appl 91:347–363.  https://doi.org/10.1016/j.eswa.2017.09.028CrossRefGoogle Scholar
  28. 28.
    Zheng S, Janecek A, Tan Y (2013) Enhanced fireworks algorithm. In: Proceedings of IEEE Congress on Evolutionary Computation. pp 2069–2077.  https://doi.org/10.1109/CEC.2013.6557813
  29. 29.
    Zheng YJ (2015) Water wave optimization: a new nature-inspired metaheuristic. Comput Op Res 55:1–11.  https://doi.org/10.1016/j.cor.2014.10.008MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Zheng YJ, Zhang B (2015) A simplified water wave optimization algorithm. In: Proceedings of IEEE Congress on Evolutionary Computation. pp 807–813.  https://doi.org/10.1109/CEC.2015.7256974

Copyright information

© Springer Nature Singapore Pte Ltd. and Science Press, Beijing 2019

Authors and Affiliations

  • Yujun Zheng
    • 1
  • Xueqin Lu
    • 2
  • Minxia Zhang
    • 2
  • Shengyong Chen
    • 2
  1. 1.Hangzhou Institute of Service EngineeringHangzhou Normal UniversityHangzhouChina
  2. 2.College of Computer Science and TechnologyZhejiang University of TechnologyHangzhouChina

Personalised recommendations