Ant colony optimization with horizontal and vertical crossover search: Fundamental visions for multi-threshold image segmentation

The ant colony optimization (ACO) is the most exceptionally fundamental swarm-based solver for realizing discrete problems. In order to make it also suitable for solving continuous problems, a variant of ACO (ACOR) has been proposed already. The deep-rooted ACO always stands out in the eyes of well-educated researchers as one of the best-designed metaheuristic ways for realizing the solutions to real-world problems. However, ACOR has some stochastic components that need to be further improved in terms of solution quality and convergence speed. Therefore, to effectively improve these aspects, this in-depth research introduced horizontal crossover search (HCS) and vertical crossover search (VCS) into the ACOR and improved the selection mechanism of the original ACOR to form an improved algorithm (CCACO) for the first time. In CCACO, the HCS is mainly intended to increase the convergence rate. Meanwhile, the VCS and the developed selection mechanism are mainly aimed at effectively improving the ability to avoid dwindling into local optimal (LO) and the convergence accuracy. To reach next-level strong results for image segmentation and better illustrate its effectiveness, we conducted a series of comparative experiments with 30 benchmark functions from IEEE CEC 2014. In the experiment, we compared the developed CCACO with well-known conventional algorithms and advanced ones. All experimental results also show that its convergence speed and solution quality are superior to other algorithms, and its ability to avoid dropping into local optimum (LO) is more reliable than that of its peers. Furthermore, to further illustrate its enhanced performance, we applied it to image segmentation based on multi-threshold image segmentation (MTIS) method with a non-local means 2D histogram and Kapur's entropy. In the experiment, it was compared with existing competitive algorithms at low and high threshold levels. The experimental results show that the proposed CCACO achieves excellent segmentation results at both low and high threshold levels. For any help and guidance regarding this research, readers, and industry activists can refer to the background info at http://aliasgharheidari.com/.