A novel cuckoo search algorithm under adaptive parameter control for global numerical optimization

  • Jiamin Wei
  • Yongguang YuEmail author
Methodologies and Application


Cuckoo search (CS) is a well-known population-based stochastic search technique for solving global numerical optimization problems. At each iteration process, CS searches for new solutions by Lévy flights random walk together with a local random walk (LRW). For LRW, mutation proceeds with a uniformly distributed random number in the interval [0, 1] as its mutation factor, which plays an important role in controlling the population diversity and the explorative power of the algorithm. However, this mutation factor generally results in sensitivity to the given optimization problem and thus fails to balance well these two aspects. In view of this consideration, we introduce a simple adaptive parameter control mechanism to LRW, and propose a novel adaptive cuckoo search (CSAPC) algorithm in this paper to improve the optimization performance of CS. The adaptive parameter control mechanism dynamically updates the control parameters based on a Cauchy distribution and the Lehmer mean during the iteration. To verify the performance of CSAPC, simulations and comparisons are conducted on 48 benchmark functions from two well-known test suites. In order to further test its efficacy, CSAPC is applied to solve the problem of parameter estimation of two typical uncertain fractional-order chaotic systems. The numerical, statistical and graphical analysis demonstrates the great competency of CSAPC, and hence can be regarded as an efficient and promising tool for solving the real-world complex optimization problems besides the benchmark problems.


Cuckoo search algorithm Adaptive parameter control Global numerical optimization Fractional-order chaotic systems 



This work is supported by the Fundamental Research Funds for the Central Universities (No. 2017YJS200), China Scholarship Council (No. 201807090092), the National Nature Science Foundation of China (No. 61772063) and Beijing Natural Science Foundation (Z180005).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Authors and Affiliations

  1. 1.Department of MathematicsBeijing Jiaotong UniversityBeijingPeople’s Republic of China

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