Enhanced variants of the Musk Ox Optimizer for global optimization problems

This paper presents seven variants of Musk Ox Optimizer (MO), a new metaheuristic algorithm inspired by musk ox populations' social behaviour. Although the original MO shows promising performance, it may experience limitations such as premature convergence and insufficient exploration in complex optimization problems. In this work seven new variants AMOA, CMOA, OBMOA, DEMOA, HMOA-PSO, EOBMOA and QMOA are developed. The proposed algorithms are evaluated using 23 benchmark functions, 12 CEC 2022 test functions and 6 engineering design problems. Friedman and Wilcoxon tests are conducted to assess performance differences. Result shows that CMOA ranks best on unimodal problems and QMOA performs strongest on multimodal problems. HMOA-PSO achieves the most competitive results on engineering design problems. The results demonstrate that enhancement of MO's dual-phase search mechanism produces measurable improvements in convergence accuracy and solution quality across diverse problem types.