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The manta ray foraging optimization algorithm (MRFO) is a recently proposed meta-heuristic algorithm that mimics the foraging process of manta rays. It has yielded good outcomes in solving some optimization problems because its mechanism is clear, no additional parameters need to be set, and the balance between global and local search is good. Nonetheless, while dealing with high-dimensional global optimization and complex engineering optimization problems, there are also issues such as premature convergence, low optimization-seeking accuracy, or unstable solutions. To this end, this article proposes an efficient manta ray foraging optimization algorithm (NIFMRFO) by incorporating individual information interaction and fractional derivative mutation. First, to prevent premature convergence of the algorithm, a nonlinear cosine adjustment parameter is presented, which is intended to make the demand relationship between global exploration and local development more reasonable. Then, an information interaction strategy among random individuals is employed to expedite the rate at which the algorithm converges. Finally, a fractional derivative mutation strategy is utilized to continually enhance individuals' quality in each iteration, which not only increases the population diversity but also helps to improve the precision and stability of the search results. Theoretical analysis indicates that the improved NIFMRFO algorithm and basic MRFO algorithm have the same time complexity. In simulation experiments, the CEC2017 suite is used to conduct comparison tests with six superior-performance representative comparison algorithms in several dimensions. In terms of the optimization-seeking accuracy, convergence curve, violin plot, and Friedman average ranking, the analysis of these graphs and data shows that the NIFMRFO algorithm's ameliorated strategy improves superiority-seeking power, convergence speed, and steadiness. Meanwhile, the Wilcoxon rank-sum test result illustrates significant differences between NIFMRFO and other compared algorithms. Finally, these algorithms are utilized to tackle seven realistic engineering design optimization problems. The result makes it clear that NIFMRFO is distinctly superior to the other six algorithms, showing that its solving ability is superior and has broad application prospects. • A novel manta ray foraging optimization NIFMRFO with three improved strategies is proposed. • The execution efficiency of NIFMRFO is demonstrated by time complexity analysis. • The performance of NIFMRFO is verified by the CEC2017 test suite. • Multiple statistical analysis and chart analysis methods are used. • NIFMRFO's application capability is evaluated by seven engineering constraint problems. [ABSTRACT FROM AUTHOR]