Soft Computing

, Volume 23, Issue 3, pp 871–888 | Cite as

Physarum-energy optimization algorithm

  • Xiang FengEmail author
  • Yang LiuEmail author
  • Huiqun Yu
  • Fei Luo
Methodologies and Application


In general, the existing evolutionary algorithms are prone to premature convergence and slow convergence in coping with combinatorial optimization problems. So an intelligent optimization algorithm called physarum-energy optimization algorithm (PEO) is proposed and put TSP as the carrier in this paper. This algorithm consists of four parts: the physarum biological model, the energy model, the age factor model and the stochastic disturbance model. First, the high parallelism of PEO is enlightened from the physarum’s low complexity and high parallelism. Second, we present an energy mechanism model in PEO, which is mainly to develop the shortcomings of existing algorithm, such as slow convergence and lack of interaction capability. Third, inspired by the characteristic of ants’ spatiotemporal variations, the age factor mechanism is introduced to raise search capacity, which can control the convergence speed and precision ability of PEO. In addition, in order to avoid premature convergence, the stochastic disturbance mechanism is adopted into PEO. And also the feasibility and convergence of PEO has been analyzed and verified theoretically. Moreover, we compare the algorithm and other algorithms to TSPs of diverse scope. The experiment results show that PEO has the advantages of excellent global optimization, high optimization accuracy and high parallelism and is significantly better than other algorithms.


Physarum optimization algorithm Energy mechanism Age factor Traveling salesman problem 



This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61472139 and 61462073, the Information Development Special Funds of Shanghai Economic and Information Commission under Grant No. 201602008, the Open Funds of Shanghai Smart City Collaborative Innovation Center.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. Booker LB, Goldberg DE, Holland JH (1989) Classifier systems and genetic algorithms. Artif Intell 40(1–3):235–282CrossRefGoogle Scholar
  2. Chen W-N, Zhang J, Chung HSH et al (2010) A novel set-based particle swarm optimization method for discrete optimization problems. IEEE Trans Evol Comput 14(2):278–300CrossRefGoogle Scholar
  3. Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31CrossRefGoogle Scholar
  4. Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 1(1):53–66Google Scholar
  5. Duan Y, Ying S (2009) A particle swarm optimization algorithm with ant search for solving traveling salesman problem. In: International conference on computational intelligence and security, 2009. CIS’09, vol 2. IEEE, pp 137–141Google Scholar
  6. Feng X, Yang T, Yu H (2016) A new multi-colony fairness algorithm for feature selection. Soft Comput. doi: 10.1007/s00500-016-2257-0
  7. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95–99CrossRefGoogle Scholar
  8. Han K-H, Kim J-H (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6(6):580–593MathSciNetCrossRefGoogle Scholar
  9. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of IEEE international conference on neural networks, 1995, vol 4. IEEE, pp 1942–1948Google Scholar
  10. Laporte G (1992) The traveling salesman problem: an overview of exact and approximate algorithms. Eur J Oper Res 59(2):231–247MathSciNetCrossRefzbMATHGoogle Scholar
  11. Li K, Kang L, Zhang W, et al. (2008) Comparative analysis of genetic algorithm and ant colony algorithm on solving traveling salesman problem. In: IEEE international workshop on semantic computing and systems, 2008. WSCS’08. IEEE, pp 72–75Google Scholar
  12. Liang JJ, Kai Qin A, Suganthan PN et al (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295CrossRefGoogle Scholar
  13. Liu L, Song Y, Zhang H et al (2015) Physarum optimization: a biology-inspired algorithm for the steiner tree problem in networks. IEEE Trans Comput 64(3):818–831MathSciNetCrossRefzbMATHGoogle Scholar
  14. Mavrovouniotis M, Yang S (2011) A memetic ant colony optimization algorithm for the dynamic travelling salesman problem. Soft Comput 15(7):1405–1425CrossRefGoogle Scholar
  15. Mersch DP, Crespi A, Keller L (2013) Tracking individuals shows spatial fidelity is a key regulator of ant social organization. Science 340(6136):1090–1093CrossRefGoogle Scholar
  16. Nakagaki T, Yamada H, Tóth Á (2000) Intelligence: maze-solving by an amoeboid organism. Nature 407(6803):470–470CrossRefGoogle Scholar
  17. Nguyen HD, Yoshihara I, Yamamori K et al (2007) Implementation of an effective hybrid ga for large-scale traveling salesman problems. IEEE Trans Syst Man Cybern Part B (Cybern) 37(1):92–99CrossRefGoogle Scholar
  18. Prügel-Bennett A, Tayarani-Najaran M-H (2012) Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimization problem. IEEE Trans Evol Comput 16(3):319–338CrossRefGoogle Scholar
  19. Shuang B, Chen J, Li Z (2011) Study on hybrid ps-aco algorithm. Appl Intell 34(1):64–73CrossRefGoogle Scholar
  20. Simopoulos DN, Kavatza SD, Vournas CD (2006) Unit commitment by an enhanced simulated annealing algorithm. IEEE Trans Power Syst 21(1):68–76CrossRefGoogle Scholar
  21. Song Y, Liu L, Ma H et al (2014) A biology-based algorithm to minimal exposure problem of wireless sensor networks. IEEE Trans Netw Serv Manag 11(3):417–430CrossRefGoogle Scholar
  22. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359MathSciNetCrossRefzbMATHGoogle Scholar
  23. Tayarani-Najaran M-H, Prügel-Bennett A (2015a) Anatomy of the fitness landscape for dense graph-colouring problem. Swarm Evol Comput 22:47–65CrossRefGoogle Scholar
  24. Tayarani-Najaran M-H, Prügel-Bennett A (2015b) Quadratic assignment problem: a landscape analysis. Evol Intell 8(4):165–184CrossRefGoogle Scholar
  25. Tayarani-Najaran M-H, Prügel-Bennett A (2016) An analysis of the fitness landscape of travelling salesman problem. Evol Comput 24(2):347–384CrossRefGoogle Scholar
  26. Tayarani-Najaran M-H, Yao X, Xu H (2015) Meta-heuristic algorithms in car engine design: a literature survey. IEEE Trans Evol Comput 19(5):609–629CrossRefGoogle Scholar
  27. Tero A, Takagi S, Saigusa T et al (2010) Rules for biologically inspired adaptive network design. Science 327(5964):439–442MathSciNetCrossRefzbMATHGoogle Scholar
  28. Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82CrossRefGoogle Scholar
  29. Zhang J, Xiong W (2009) An improved particle swarm optimization algorithm and its application for solving traveling salesman problem. In: 2009 WRI world congress on computer science and information engineering, vol 4. IEEE, pp 612–616Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringEast China University of Science and TechnologyShanghaiChina
  2. 2.Smart City Collaborative Innovation CenterShanghai Jiao Tong UniversityShanghaiChina

Personalised recommendations