The Journal of Supercomputing

, Volume 72, Issue 10, pp 3960–3992 | Cite as

Finding approximate solutions of NP-hard optimization and TSP problems using elephant search algorithm

  • Suash Deb
  • Simon FongEmail author
  • Zhonghuan Tian
  • Raymond K. Wong
  • Sabah Mohammed
  • Jinan Fiaidhi


A novel bio-inspired optimization algorithm called elephant search algorithm (ESA) has been applied to solve NP-hard problems including the classical traveling salesman problem (TS) in this paper. ESA emerges from the hybridization of evolutionary mechanism and dual balancing of exploitation and exploration. The design of ESA is inspired by the behavioral characteristics of elephant herds; hence, the name Elephant Search Algorithm which divides the search agents into two groups representing the dual search patterns. The male elephants are search agents that outreach to different dimensions of search space afar; the female elephants form groups of search agents doing local search at certain close proximities. By computer simulation, ESA is shown to outperform other metaheuristic algorithms over the popular benchmarking optimization functions which are NP-hard in nature. In terms of fitness values in optimization, ESA is ranked after Firefly algorithm showing superior performance over the other ones. The performance of ESA is most stable when compared to all other metaheuristic algorithms. When ESA is applied to the traveling salesman problem, different ratios of gender groups yield different results. Overall, ESA is shown to be capable of providing approximate solutions in TSP.


Elephant search algorithm Metaheuristic Bio-inspired optimization 



The authors are thankful for the financial support from the Research Grant Temporal Data Stream Mining Using Incrementally Optimized Very Fast Decision Forest (iOVFDF), Grant No. MYRG2015-00128-FST, offered by the University of Macau, FST, and RDAO.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Suash Deb
    • 1
  • Simon Fong
    • 2
    Email author
  • Zhonghuan Tian
    • 2
  • Raymond K. Wong
    • 3
  • Sabah Mohammed
    • 4
  • Jinan Fiaidhi
    • 4
  1. 1.IT and Educational ConsultantJharkhandIndia
  2. 2.Department of Computer and Information ScienceUniversity of MacauMacau SARChina
  3. 3.School of Computer Science and EngineeringUniversity of New South WalesSydneyAustralia
  4. 4.Department of Computer ScienceLakehead UniversityThunder BayCanada

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