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In nature-inspired metaheuristic algorithms, two key components are local intensification and global diversification, and their interaction can significantly affect the efficiency of a metaheuristic algorithm. However, there is no rule for how to balance these important components. In this paper, we provide a first attempt to give some theoretical basis for the optimal balance of exploitation and exploration for 2D multimodal objective functions. Then, we use it for choosing algorithm-dependent parameters. Finally, we use the recently developed eagle strategy and cuckoo search to solve two benchmarks so as to confirm if the optimal balance can be achieved in higher dimensions. For multimodal problems, computational effort should focus on the global explorative search, rather than intensive local search. We also briefly discuss the implications for further research.

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