Trapping in local solutions is the main issue in several metaheuristic techniques. To solve such drawbacks by enhancing the search agents, a modified search strategy becomes a more attractive tactic. In this paper, an innovative version of Manta Ray Foraging Optimization (MRFO) is proposed to solve its crucial drawbacks while handling global and engineering optimization problems. The proposed version presents an integrated variant of MRFO with the triangular mutation operator and orthogonal learning strategy, called MRTMO. The two approaches are considered to achieve a robust equipoise between algorithm cores and provide a reliable mechanism to guide the search agents during the optimization process. The proposed MRTMO was tested with challenging CEC2005 and CEC2017 functions and six engineering problems to show its performance. Additionally, several evaluation metrics were employed to ensure the efficiency and robustness of the proposed MRTMO. Furthermore, extensive comparisons with existing optimization algorithms were carried out to ensure the superiority of MRTMO. The numerical experiments proved the competitive performance of the proposed MRTMO in solving all tested CEC optimization and engineering problems.