Emphasizing the importance of shift invariance in metaheuristics by using whale optimization algorithm as a test bed.

To solve global optimization problems, nature-inspired metaheuristics have emerged as the best option in many cases. The researchers have mimicked or mapped the optimal behaviors of living organisms, natural phenomena and human behaviors to solve optimization problems. Whenever a new algorithm is proposed, its exploration, exploitation and convergence capabilities are tested; however, in this study, it is highlighted that a metaheuristic should also exhibit invariance to function translation/shifting. Whale optimization algorithm (WOA) is a well-reputed and highly referred algorithm in the literature; however, we find that its performance is strongly affected under certain circumstances involving function shifting. Our analysis reveals that WOA performs really well when the global optimum is situated at the origin ( 0 , 0 , ... , 0 ); on the contrary, the performance amazingly degrades whenever the global optimum is situated away from the origin. Moreover, in most cases, our findings reveal that the performance degradation is directly proportional to the distance of the global optimum from the origin. Furthermore, the root cause of the problem is discovered and discussed. Finally, it is suggested how WOA can be made shift-invariant. [ABSTRACT FROM AUTHOR]