## 1 Introduction  
With the rapid development of multi-unmanned systems, these systems are increasingly being utilized to replace human involvement when performing tasks that are difficult and entail high degrees of risk. For example, multi-unmanned systems are deployed to specific areas for search [1], rescue [2], and reconnaissance tasks [3]. To enhance the efficiency of task execution in multi-unmanned systems, researchers have developed various task allocation algorithms to address the task allocation challenges encountered by such systems. Task allocation algorithms require the integration of task information and the capabilities of multi-unmanned systems to effectively distribute tasks among unmanned systems. The fundamental objective of task allocation algorithms is to maximize benefits while minimizing costs [4]. To further enhance the cost efficiency of tasks executed by multi-unmanned systems and augment the associated benefits, researchers have introduced numerous refinements for cooperative task allocation methods in multi-unmanned systems [5]. Throughout the task allocation process, multiple unmanned systems engage in interaction and information sharing via a communication network, gathering task requirements and system status information. By utilizing this comprehensive information, they formulate precise task allocation decisions. Via this effective information exchange strategy, the multiple unmanned systems can collaborate effectively, mitigating conflicts and eliminating redundant task execution steps, thereby enhancing the overall efficiency of the task completion process. The research task discussed in this text is centered on collaborative coverage and search missions, which include a few relatively large task areas and a multitude of heterogeneous unmanned surface vessels (USVs). The focus is on how to allocate tasks to these USVs to achieve high mission execution efficiency. The specific details of the task background are introduced in Section 3. Currently, two main types of cooperative task allocation methods are used for multi-unmanned systems: centralized and distributed approaches. Centralized systems can be uniformly controlled, but their disadvantage is that they have poor scalability. On the other hand, distributed systems have strong scalability, but they require a higher standard for communication systems [1; 6]. The mainstream cooperative task allocation methods for centralized multi-unmanned systems can be roughly divided into three categories: mathematical programming, market auction, and intelligent optimization algorithms. However, with the expansion of the scale of unmanned systems, mathematical programming and market auction methods face limitations when addressing large-scale unmanned systems. For cases with large-scale systems, a market auction method consumes considerable time and communication resources; mathematical programming makes it difficult to establish and solve complex cooperative work constraint models in a short period. In contrast, intelligent optimization algorithms are suitable for large-scale systems due to their high adjustability and flexibility levels. Therefore, using intelligent optimization algorithms to solve the cooperative task allocation problem encountered by large-scale unmanned systems has become a mainstream method. Currently, the classic intelligent algorithms include the genetic algorithm (GA), ant colony optimization (ACO), particle swarm optimization (PSO), the wolf pack algorithm (WPA), the black widow algorithm (BWO), and the sheep flock optimization algorithm (SFOA) [7; 8; 9; 10; 11]. The GA has good global optimization capabilities, but the parameters selected for this algorithm have a significant impact on its performance. The WPA simulates the process of wolf predation, fully embodying the ideas of cooperation and division of labour in a wolf pack. A \"survival of the fittest\" elimination mechanism is also included in the wolf pack, which gives the algorithm good optimization performance.