The Exploration/Exploitation Tradeoff in Whale Optimization Algorithm

The whale optimization algorithm(WOA) is a novel meta-heuristic evolutionary algorithm inspired by the behavior of whales predation. An important factor to the success of WOA is the balancing between exploration and exploitation. In the WOA, the distance control parameter <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> is the main factor to find an appropriate balance between exploration and exploitation. In the standard WOA, the distance control parameter <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> is optimized by linear control strategy (LCS), but the process of whales predation is not simply linear process. To address the issue, this paper proposed a nonlinear control strategy based on arcsine function (NCS-Arcsin) to optimize WOA. The NCS-Arcsin is applied to adjust distance control parameter <inline-formula> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula>. The NCS-Arcsin is considered to accurately describe the process of whales predation. Experiments on twelve well-known benchmark functions show the NCS-Arcsin can significantly improve the exploration and exploitation capabilities of WOA. In addition, the performance of proposed NCS-Arcsin is compared with LCS and other have been proposed NCS. The experimental results show that the optimization effect of NCS-Arcsin is stronger than that of LCS and other NCS. The NCSs based on the arcsine function is the best NCS, which can significantly improve the optimize performance of WOA.