RETRACTED ARTICLE: A-COA: an adaptive cuckoo optimization algorithm for continuous and combinatorial optimization

Abstract

Cuckoo optimization algorithm (COA) is inspired from the special and exotic lifestyle of a bird family called the cuckoo and her amazing and unique behavior in egg laying and breeding. Just like any other population-based swarm intelligence metaheuristic algorithms, the basic COA starts with a set of randomly generated solutions called “habitats.” Actually, the habitats can be the current locations of either the mature cuckoos or their eggs. In an iterative manner, cuckoos lay their eggs around their habitats inside the other birds’ nests by mimicking their eggs’ color, pattern, and size, and this is a kind of parasitic brooding behavior. Some hosts may discriminate the strange eggs and throw them out while the others not. The survival competition between cuckoos and their hosts, and migration of cuckoos in swarm are two main underlying motivations to introduce the COA. In this paper, an adaptive cuckoo optimization algorithm named A-COA is proposed in which three novelties in egg-laying and migration phases are applied. These modifications have made the basic algorithm more efficient with faster convergence to solve continuous and discrete optimization problems. A comprehensive comparison study of A-COA versus not only the basic COA but also some other conventional metaheuristics like GA, PSO, ABC, and TLBO has been made on a variety of unimodal and multimodal numerical benchmark functions with different characteristics, and the results show an overall 25.85% of improvement in terms of performance with a faster convergence speed compared to the basic COA, where the statistical Wilcoxon rank-sum test certifies our conclusions. In addition, a discretized version of A-COA and its application to the multiprocessor task scheduling problem as a complex combinatorial optimization problem are investigated where the proposed A-COA is very competitive with not only the strongest conventional heuristics, for example, MCP, ETF, and DLS, but also the basic COA and the newly proposed ACO-based approach.