A new fusion of salp swarm with sine cosine for optimization of non-linear functions

  • Narinder Singh
  • Le Hoang SonEmail author
  • Francisco Chiclana
  • Jean-Pierre Magnot
Original Article


The foremost objective of this article is to develop a novel hybrid powerful meta-heuristic that integrates the salp swarm algorithm with sine cosine algorithm (called HSSASCA) for improving the convergence performance with the exploration and exploitation being superior to other comparative standard algorithms. In this method, the position of salp swarm in the search space is updated using the position equations of sine cosine; hence the best and possible optimal solutions are obtained based on the sine or cosine function. During this process, each salp adopts the information sharing strategy of sine and cosine functions to improve their exploration and exploitation ability. The inspiration behind incorporating changes in salp swarm optimizer algorithm is to assist the basic approach to avoid premature convergence and to rapidly guide the search towards the probable search space. The algorithm is validated on 22 standard mathematical optimization functions and 3 applications namely the 3-bar truss, tension/compression spring and cantilever beam design problems. The aim is to examine and confirm the valuable behaviors of HSSASCA in searching the best solutions for optimization functions. The experimental results reveal that HSSASCA algorithm achieves the highest accuracies with least runtime in comparison with the others.


Standard global optimization functions Heuristic hybridization Salp swarm algorithm Sine cosine algorithm Exploration and exploitation 



The authors are very grateful to the referees for their valuable suggestions, which helped to improve the quality of the paper significantly.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsPunjabi UniversityPatialaIndia
  2. 2.VNU Information Technology InstituteVietnam National UniversityHanoiVietnam
  3. 3.School of Computer Science and InformaticsDe Montfort UniversityThe GatewayUK
  4. 4.LAREMAUniversitéd’ AngersAngers Cedex 01France

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