A hybrid flower pollination with β-hill climbing algorithm for global optimization

In this paper, the β-hill climbing optimizer is hybridized with the flower pollination algorithm (FPA) as a local refinement operator for global optimization problems. The proposed method is called HyFPAβ-hc. Such hybridization aims to enhance the balance between exploration and exploitation processes during the search, thus improving the quality of the outcomes. β-hill climbing optimizer is a recent trajectory-based algorithm with a powerful digging the niche to search and find the local optimum, while FPA is a recent population-based algorithm with robust mining several niches in the search space without proper concentration. The proposed HyFPAβ-hc is evaluated using 15 unimodal and multimodal test functions established in IEEE-CEC2015. The results show significant improvement in the convergence behaviour of the proposed HyFPAβ-hc over FPA using different dimensions of the test function. The comparative evaluation is also conducted against 26 state-of-the-art methods. The experiments consider three problem sizes (with dimensions 10, 30, and 50) to show the proposed HyFPAβ-hc performance against all comparative methods, where the proposed method outperformed all compared methods in optimizing 8, 7, 4 out of 15 test functions for 10, 30, 50 dimensions, respectively. Accordingly, the achieved results prove the efficiency of the proposed HyFPAβ-hc in optimizing various problem dimensions. In conclusion, the proposed hybrid metaheuristic method can search powerfully in the niches of optimization problems search space and produces very fruitful outcomes.