Cuckoo Search — Lévy Flight Metaheuristic

Both are population-based metaheuristics, but their movement mechanisms differ fundamentally. PSO moves particles according to their own velocity and attraction toward personal and global bests — a process governed by Gaussian-like perturbations. Cuckoo Search instead uses Lévy flights, which occasionally produce very large steps that help escape local optima more aggressively. Cuckoo Search also has fewer parameters to tune and the abandon step provides an explicit diversity-injection mechanism that PSO lacks.

The original paper and subsequent studies suggest a population of 15–50 nests and an alien-egg discovery probability p_a in the range 0.15–0.35. A value of 25 nests and p_a = 0.25 is a common default starting point. If the problem is high-dimensional or multimodal, a slightly larger population and a lower p_a tend to help.

The basic algorithm operates on unconstrained continuous spaces. Constraints can be handled by adding a penalty term to the objective function, by repairing infeasible solutions to the nearest feasible point, or by using a constraint-handling framework such as the epsilon-constraint or feasibility-rule approaches. These extensions require problem-specific implementation.

This depends on problem dimensionality and the required solution quality, but the algorithm is generally competitive with other swarm methods at 1,000–10,000 function evaluations for low-to-moderate dimensional problems. Because population sizes are small, each iteration is inexpensive in terms of evaluations. Always run multiple independent trials and report the distribution of results rather than a single best value.