Abstract: A swarm intelligence optimization algorithm is an effective method to rapidly solve large-scale complex optimization problems. The JAYA algorithm is a new swarm intelligence evolutionary optimization algorithm, which was proposed in 2016. Compared with other active evolutionary algorithms, the JAYA algorithm has several advantages, such as a clear mechanism, concise structure, and ease of implementation. Further, it has guiding characteristics, obtains the best solution, and avoids the worst solution. The JAYA algorithm has an excellent optimization effect on many problems, and it is one of the most influential algorithms in the field of swarm intelligence. However, when dealing with the CEC test suite, which contains and combines shifted, rotation, hybrid, combination, and other composite characteristics, and the complex engineering constrained optimization problems with considerable difficulty and challenges, the JAYA algorithm has some flaws, that is, it easily falls into the local extremum, its optimization accuracy is sometimes low, and its solution is unstable. To better solve complex function optimization and engineering constrained optimization problems and further enhance the optimization capability of the JAYA algorithm, a global optimization-oriented hybrid evolutionary JAYA algorithm is proposed. First, opposition-based learning is introduced to calculate the current best and worst individuals, which improves the possibility of the best and worst individuals jumping out of the local extremum region. Second, the sine–cosine operator and differential disturbance mechanism are introduced and integrated into individual position updating, which not only improves the diversity of the population but also better balances and meets the different requirements of the algorithm for exploration and mining in different iteration periods. Finally, in the algorithm structure, the hybrid evolution strategy with different parity states is adopted and the advantages of different evolution mechanisms are effectively used, which further improves the convergence and accuracy of the algorithm. Then, the pseudocode of the improved algorithm is given, and the theoretical analysis proves that the time complexity of the improved algorithm is consistent with the basic JAYA algorithm. Through the simulation experiment of function extremum optimization of six representative algorithms on multiple dimensions of the CEC2017 test suite, which contains and combines 30 benchmark functions and the optimal solution of six challenging engineering design problems, such as tension/compression spring, corrugated bulkhead, tubular column, reinforced concrete beam, welded beam, and car side impact. The optimal solution of the test results shows that the improved algorithm has significantly improved the optimization accuracy, convergence performance, and solution stability, and it has obvious advantages in solving CEC complex functions and engineering constrained optimization problems.