Cuckoo search

In operations research, cuckoo search is an optimization algorithm developed by Xin-She Yang and Suash Deb in 2009.

[1][2] It has been shown to be a special case of the well-known (μ + λ)-evolution strategy.

Some host birds can engage direct conflict with the intruding cuckoos.

Some cuckoo species such as the New World brood-parasitic Tapera have evolved in such a way that female parasitic cuckoos are often very specialized in the mimicry in colors and pattern of the eggs of a few chosen host species.

[4] Cuckoo search idealized such breeding behavior, and thus can be applied for various optimization problems.

The algorithm can be extended to more complicated cases in which each nest has multiple eggs representing a set of solutions.

CS is based on three idealized rules: In addition, Yang and Deb discovered that the random-walk style search is better performed by Lévy flights rather than simple random walk.

In fact, comparing with other population- or agent-based metaheuristic algorithms such as particle swarm optimization and harmony search, there is essentially only a single parameter

An important issue is the applications of Lévy flights and random walks in the generic equation for generating new solutions where

is drawn from a standard normal distribution with zero mean and unity standard deviation for random walks, or drawn from Lévy distribution for Lévy flights.

The generation of Lévy step size is often tricky, and a comparison of three algorithms (including Mantegna's[5]) was performed by Leccardi[6] who found an implementation of Chambers et al.'s approach[7] to be the most computationally efficient due to the low number of random numbers required.

So a proper step size is important to maintain the search as efficient as possible.

Though the exact derivation may require detailed analysis of the behaviour of Lévy flights.

[9] Algorithm and convergence analysis will be fruitful, because there are many open problems related to metaheuristics[10] As significant efforts, theoretical analyses are required to improve performances of CS-base algorithms:[11] Convergence of Cuckoo Search algorithm can be substantially improved by genetically replacing abandoned nests (instead of using the random replacements from the original method).

[12] Modifications to the algorithm have also been made by additional interbreeding of best (high quality) nests [13] and this approach has been successfully applied to a range of industrial optimisation problems.