# Retinal Vessel Segmentation Using Math-Inspired Metaheuristic Algorithms
## 1 Introduction  
In recent years, optimization problems--especially those in the area of image processing--have become increasingly complex, leading to the requirement for more effective methods for their solution. New directions of theoretical research have appeared in the literature in accordance with this requirement, involving the improvement of existing conventional or metaheuristic algorithms, hybridizing different algorithms, and proposing new metaheuristic algorithms [1]. The results presented in the literature have also proved that, due to their non-random search characteristics, conventional gradient-based approaches cannot produce results as effective as metaheuristic algorithms. Metaheuristic algorithms are usually classified into four main groups: evolutionary-based, swarm intelligence-based, physics-based, and human-inspired algorithms. Furthermore, inspired by the search strategies utilized, these algorithms can also be alternatively classified into two main groups. Simple local search and global search algorithms [2]: these search algorithms have the important disadvantages of becoming stuck inside local minima and dependence on the initial solutions. In contrast, population-based algorithms may provide higher optimization performance as a result of their global search ability, which is achieved through improving the population iteratively. In the literature, the majority of population-based algorithms have been improved in a manner inspired by swarm intelligence, physical laws, evolutionary strategies, and human behaviors. In addition to these well-established and frequently used algorithms, some novel population-based metaheuristic algorithms inspired by mathematical laws have also been proposed in recent years [1; 2; 3; 4; 5; 6]. The most recently proposed math-inspired algorithms include the Circle Search Algorithm (CSA), Tangent Search Algorithm (TSA), Arithmetic Optimization Algorithm (AOA), Generalized Normal Distribution Optimization (GNDO) Algorithm, Global Optimization Method based on Clustering and Parabolic Approximation (GOBC-PA), and Sine Cosine Algorithm (SCA). The SCA has been applied to several engineering problems in the existing literature, including the optimization of the cross-section of an aircraft wing [1], optimizing the combined economic and emission dispatch problem in power systems [7], optimizing the size and location of energy resources in radial distribution networks [8], optimizing the parameters of fractional order PID (FOPID) controller for load frequency control systems [9], designing an effective PID controller for power systems [10], designing a hybrid power generation system with minimized total annual cost and emissions [11], solving the unit commitment problem of an electric power system [12], solving the bend photonic crystal waveguides design problem [13], solving the short-term hydrothermal scheduling problem in power systems [14], tuning the FOPID/PID controller parameters for an automatic voltage regulator system [15], determining the optimal PID controller parameters for an automatic voltage regulator system [16], designing a PD-PID controller for the frequency control of a hybrid power system [17], implementation of a novel future selection approach for text categorization [18], solving the economic power-generation scheduling (EcGS) problem for thermal units [19], implementation of a parallel SCA for three communication strategies [20], implementation of an enhanced sine cosine algorithm (ESCA) to determine the threshold for use in the segmentation of color images [21], development of an optimum photovoltaic pumping system based on monitoring the maximum power point under certain meteorological conditions [22], achievement of an optimal thermal stress distribution in symmetric composite plates with non-circular holes under a uniform heat flux [23], and the implementation of an SCA-based intelligent approach for effective underwater visible light communication [24].