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In this article, a new variant of a recent optimization algorithm namely Runge Kutta optimizer (RUN) is proposed to solve the partial shading condition in photovoltaic systems and global optimization. The RUN’s improvement is mainly to mitigate the lack of the solutions quality, the imbalance between the exploitation and exploration phases, and premature convergence of the RUN algorithm. The mRUN, in which the standard RUN is incorporated with a promising strategy namely Orthogonal learning (OL) strategy to address out the original RUN’s drawbacks. To estimate the proposed algorithm’s efficiency, two experimental series were performed. In the first experiment, the mRUN was compared with other state-of-art metaheuristics on IEEE CEC’2020 test suite. Moreover, the quantitative and qualitative approved the robustness of the suggested algorithm. As a second experimental series, the proposed approach is …