## 1 Introduction  
Enhancing network revenue has consistently remained a crucial focus in the research of IUWSNs [1; 2; 3; 4]. Due to size constraints, the sensing capacity of small wireless sensors is limited. The task allocation strategy is commonly designed for IUWSNs to enhance the revenue of the network. Generating an optimum task allocation for IUWSNs with limited power sources and limited perception constraints is very useful, but the problem is NP-hard. For IUWSNs with many nodes, an exhaustive search cannot be employed to obtain the optimal task allocation results in real-time [5; 6; 7; 8; 9]. To obtain higher network revenue, many stochastic methods for task allocation have been proposed in the literature. In reference [10], [PERSON] and others of Northern Arizona University in Flagstaff, Arizona, proposed an enhanced quantum genetic algorithm (QGA) as the solution to the allocation problem. This algorithm performs well on sensor networks with a limited number of nodes. In this article, quantum genetic algorithm is used to minimize the resource consumption required to achieve goals and improve its reliability. Although the QGA has certain flexibility and advantages in solving assignment problems, it also has problems such as high computational complexity, unreasonable parameter selection, and environmental dependence. In ref. [11], [PERSON] of Hohai University and others proposed a task allocation method based on ant colony optimization. This method uses a hybrid ant colony optimization algorithm and genetic algorithm to maximize the efficiency of the network, improving the efficiency and accuracy of the solution. An ant colony optimization algorithm is used to efficiently generate initial Pheromone, multidimensional scheduling objectives, and find a more comprehensive and balanced resource allocation scheme. However, the ACO also has some problems, such as a low rate of convergence, multi-objective optimization, complex parameter selection and adjustment, etc. In ref. [12], [PERSON] of Jiangsu University and others proposed a solution of adaptive distributed artificial intelligence (ADAI) and adaptive Particle swarm optimization (APSO) in resource allocation. Due to the heterogeneity between sensor nodes and the collaborative communication between and within clusters, the overall task allocation is limited. Therefore, optimizing and coordinating task allocation has become a problem that needs to be addressed to improve network performance and efficiency. The ADAI technology and the APSO algorithm consider the heterogeneity between sensor nodes and adopt hierarchical resource allocation to optimize QoS and energy consumption, improving network performance and efficiency. However, there are real-time issues that may not be suitable for certain application scenarios with high real-time requirements. In the case of high real-time requirements, it may be necessary to consider faster resource allocation methods. At the same time, in specific network topology or application scenarios, some special situations may occur, leading to a decrease in algorithm performance. In ref. [13], [PERSON] of Yanshan University and others designed an enhanced genetic algorithm (GA) to solve the assignment problem in multi robot systems. This algorithm combines appropriate fitness functions to effectively avoid local optimization and suppress precocity. It establishes an optimization model that comprehensively considers resource consumption, task completion efficiency, and load balancing. However, this algorithm has a higher time complexity and longer code running time. In ref. [14], [PERSON] of Beihang University and others proposed an improved wolf set algorithm based on particle swarm optimization and genetic algorithm (PSO-GA-DWPA), which can quickly and effectively solve the allocation problem. Through experiments in different scenes, the PSO-GA-DWPA algorithm not only has a high Rate of convergence, but also has good search quality in high-dimensional space. It provides an effective solution to the allocation problem.