SCA: A Sine Cosine Algorithm for solving optimization problems

Research output: Contribution to journalArticlepeer-review

3454 Citations (Scopus)


This paper proposes a novel population-based optimization algorithm called Sine Cosine Algorithm (SCA) for solving optimization problems. The SCA creates multiple initial random candidate solutions and requires them to fluctuate outwards or towards the best solution using a mathematical model based on sine and cosine functions. Several random and adaptive variables also are integrated to this algorithm to emphasize exploration and exploitation of the search space in different milestones of optimization. The performance of SCA is benchmarked in three test phases. Firstly, a set of well-known test cases including unimodal, multi-modal, and composite functions are employed to test exploration, exploitation, local optima avoidance, and convergence of SCA. Secondly, several performance metrics (search history, trajectory, average fitness of solutions, and the best solution during optimization) are used to qualitatively observe and confirm the performance of SCA on shifted two-dimensional test functions. Finally, the cross-section of an aircraft's wing is optimized by SCA as a real challenging case study to verify and demonstrate the performance of this algorithm in practice. The results of test functions and performance metrics prove that the algorithm proposed is able to explore different regions of a search space, avoid local optima, converge towards the global optimum, and exploit promising regions of a search space during optimization effectively. The SCA algorithm obtains a smooth shape for the airfoil with a very low drag, which demonstrates that this algorithm can highly be effective in solving real problems with constrained and unknown search spaces. Note that the source codes of the SCA algorithm are publicly available at

Original languageEnglish
Pages (from-to)120-133
Number of pages14
JournalKnowledge-Based Systems
Publication statusPublished - 15 Mar 2016
Externally publishedYes


  • Constrained optimization
  • Meta-heuristic
  • Optimization
  • Population-based algorithm
  • Stochastic optimization


Dive into the research topics of 'SCA: A Sine Cosine Algorithm for solving optimization problems'. Together they form a unique fingerprint.

Cite this