This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms.

本文通过集成两种基于种群的算法：鲸鱼优化算法 (WOA) 和花授粉算法 (FPA)，提出了一种新的混合算法，以解决复杂的非线性系统和无约束优化问题。WOFPA 表示建议的算法，即混合鲸鱼优化算法和花授粉算法。非线性系统可以转化为无约束优化问题，称为评价函数，其中评价函数的最优解等价于非线性系统的解。WOFPA 旨在减少 WOA 和 FPA 的执行时间和复杂性。WOFPA具有WOA和FPA的优点；WOFPA 是一种解决非线性系统和无约束优化问题的高质量算法。例如，FPA 可能会在局部最优中过早收敛，而WOFPA则弥补了FPA的劣势。14个基准非线性系统和30个CEC 2014基准的各种维度无约束优化函数的数值实验被用来测试WOFPA的性能。为了进一步研究 WOFPA 的性能，将 WOFPA 与 WOA、FPA 和其他现有的文献算法进行了比较。本研究进行了两个非参数统计检验，Wilcoxon 统计检验和 Friedman 检验，以检查所提出的算法和其他比较算法的性能以及我们结果的显着性。