A Grunwald–Letnikov based Manta ray foraging optimizer for global optimization and image segmentation

This paper presents a modified version of Manta ray foraging optimizer (MRFO) algorithm to deal with global optimization and multilevel image segmentation problems. MRFO is a meta-heuristic technique that simulates the behaviors of manta rays to find the food. MRFO established its ability to find a suitable solution for a variant of optimization problems. However, by analyzing its behaviors during the optimization process, it is observed that its exploitation ability is less than exploration ability, which makes MRFO more sensitive to attractive to a local point. Therefore, we enhanced MRFO by using the fractional-order (FO) calculus during the exploitation phase. We used the heredity and non-locality properties of the Grunwald–Letnikov fractional differ-integral operator to simulate the after effect of the previous locations of manta rays on their future movement directions. The proposed Fractional-order MRFO (FO-MRFO) quality is confirmed using a set of two experimental series. Firstly, it is applied to find the solution for CEC2017 benchmark functions with different dimensions of 10, 30, and 50. Through performing the non-parametric statistical analysis, the FO-MRFO shows its superiority in comparison with the basic MRFO. For the second series of experiments, the developed algorithm is implemented as a multilevel threshold image segmentation technique. In this experiment, a variant of natural images is used to assess FO-MFRO. According to different performance measures, the FO-MRFO outperforms the compared algorithms in the global optimization and image segmentation.