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

Abstract

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.

Appendix A. Description of the 20 benchmark functions

• 1) $F_\mathrm{sph}$: Sphere’s Function.

• 2) $F_\mathrm{ros}$: Rosenbrock’s Function.

• 3) $F_\mathrm{ack}$: Ackley’s Function.

• 4) $F_\mathrm{grw}$: Griewank;s Function.

• 5) $F_\mathrm{ras}$: Rastrigin’s Function.

• 6) $F_\mathrm{sch}$: Generalized Schwefel’s Problem 2.26.

• 7) $F_\mathrm{sal}$: Salomon’s Function.

• 8) $F_\mathrm{wht}$: Whitely’s Function.

• 9) $F_\mathrm{pn1}$: Generalized Penalized Function 1.

• 10) $F_\mathrm{pn2}$: Generalized Penalized Function 2.

• 11) $F_{1}$: Shifted Sphere Function.

• 12) $F_{2}$: Shifted Schwefel’s Problem 1.2.

• 13) $F_{3}$: Shifted Rotated High Conditioned Elliptic Function.

• 14) $F_{4}$: Shifted Schwefel’s Problem 1.2 with Noise in Fitness.

• 15) $F_{5}$: Schwfels Problem 2.6 with global Optimum on Bounds.

• 16) $F_{6}$: Shifted Rosenbrock’s Function.

• 17) $F_{7}$: Shifted Rotated Griewank’s Function withoutBounds.

• 18) $F_{8}$: Shifted Rotated Ackley’s Function with Global Optimum on Bounds.

• 19) $F_{9}$: Shifted Rastrigin’s Function.

• 20) $F_{10}$: Shifted Rotated Rastrigin’s Function.