###### Abstract
The initialization strategy played an important role [24]. Chaos initialization improves population diversity due to its ergodic and random nature, and the chaotic particle algorithm was demonstrated to successfully reduce the PSLL of sparse sensor arrays [25]. With the development of intelligent algorithms, more chaotic initialization algorithms, including the chaotic invasive weed optimization algorithm [26], chaotic cuckoo search algorithm [27], and chaotic sparrow search algorithm [28], have been applied to sparse array design for improving global search capability. These success examples lead us to believe that WOA embedded with chaotic initialization will improve the performance of large-scale array design. In the next step, search strategy optimization can be achieved by introducing adaptive weights [29] and search path planning [30]. WOA with adaptive weights had a good global search capability [31,32]. Search path planning is another effective method. Levy flight strategy, as a random search path strategy with global search capability, was introduced to WOA [33]. Although the method has not been widely applied to array design within WOA, it has been successful within other swarm algorithms for linear and circular array design, including the differential evolutionary algorithm [34], CS algorithm [27], InvasiveWeed Optimization [35], and biogeography-based optimization approach [36]. Unfortunately, the Levy flight strategy destroys the original whale spiral search, which causes the convergence speed to slow down; hence, a new search strategy should be introduced to maintain the speed. In the third step to produce a new population, it was found that opposition-based learning (OBL) can also improve the search accuracy of WOA [37]. The combined strategy of adaptive weights with OBL was applied to high-dimensional global optimization problems [38]. However, it is easy to fall into the inverse local optimum, since the search range of the inverse solution is limited. A new learning algorithm should be developed to jump out of local minima. In short, the existing methods still have some shortcomings in the large-scale array design, particularly for the insufficient global search capability. To tackle this issue, GEWOA with a three-step enhanced global search strategy is introduced in this paper. Additionally, the sparse sensor array design is a discrete problem, while the WOA is suitable for the solution of continuous variables. Therefore, WOA needs to be customized for discrete problems. Continuous variables discretization is generally achieved by transfer functions. If the discrete array element is on an integral multiple of the half wavelength, then this is an on-grid problem, otherwise it is an off-grid problem. The former is a discrete optimization problem with popular S-shaped and V-shaped transfer functions [39; 40]. The latter uses binary discrete continuous variables with the ability to achieve lower PSLL [41; 42]. Considering the physical limit of the array element size, the array design needs to constrain the minimum spacing between adjacent array elements while minimizing the PSLL. A novel approach based on GEWOA for sparse sensor array design is proposed to reduce PSLL. A three-step enhanced global search strategy is introduced in GEWOA to improve the global search capability. In the initial stage, chaotic initialization is embedded in GEWOA, which enhances the ergodicity of the algorithm. In the search stage, the conventional spiral strategy is replaced by the Archimedean spiral strategy (ASS) to avoid premature algorithm results. In the offspring selection stage, refraction learning (RL) is used to obtain the inverse solution of the offspring, which avoids falling into local optima.