Discrete Sine-Cosine Algorithm (DSCA) with Local Search for Solving Traveling Salesman Problem

  • Mohamed A. Tawhid
  • Poonam SavsaniEmail author
Research Article - Computer Engineering and Computer Science


One of the new population-based optimization algorithms, named sine-cosine algorithm (SCA), is introduced to solve continuous optimization problems. SCA utilizes the sine and cosine functions to recast a set of potential solutions to balance between exploration and exploitation in the search space. Many researchers have developed and introduced a modified version of SCA to solve engineering problems, multi-objective version of SCA to solve multi-objective engineering design problems, and a binary version of SCA to deal with datasets. Our goal from this work to propose discrete SCA (DSCA) to solve the traveling salesman problem (TSP). The TSP is one of the typical NP-hard problems. DSCA works on the basic concepts of exploration and exploitation. To balance the exploration and exploitation in DSCA, it uses two different mathematical expressions to update the solutions in each generation. DSCA is combined with 2-opt local search method to improve exploitation. To enhance the exploration heuristic crossover, it is united with the proposed DSCA. A benchmarks problem selected from TSPLIB is used to test the algorithm, and the results show that the DSCA algorithm proposed in this article is comparable with the other state-of-the-art algorithms over a wide range of TSP.


Traveling salesman problems Discrete sine-cosine algorithm NP-hard combinatorial optimization problem Metaheuristic 


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We would like to thank the reviewers for their thoughtful comments and efforts toward improving our manuscript. Also, we are grateful to Marium Tawhid for editing this paper. The research of the Mohamed A. Tawhid is supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC). NSERC also supports the postdoctoral fellowship of the Poonam Savsani by NSERC.


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Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Faculty of ScienceThompson Rivers UniversityKamloopsCanada
  2. 2.Department of Industrial EngineeringPandit Deendayal Petroleum UniversityGandhinagarIndia

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