In recent times, the progress of Intelligent Unmanned Wireless Sensor Networks (IUWSNs) has inspired scientists to develop inventive task allocation algorithms. These efficient techniques serve as robust stochastic optimization methods, aimed at maximizing revenue for the network’s objectives. However, with the increase in sensor numbers, the computation time for addressing the challenge grows exponentially. To tackle the task allocation issue in IUWSNs, this paper introduces a novel approach: the Chaotic Elite Adaptive Genetic Algorithm (CEAGA). The optimization problem is formulated as an NP-complete integer programming challenge. Innovative elite and chaotic operators have been devised to expedite convergence and unveil the overall optimal solution. By merging the strengths of genetic algorithms with these new elite and chaotic operators, the CEAGA optimizes task allocation in IUWSNs. Through simulation experiments, we compare the CEAGA with other methods—Hybrid Genetic Algorithm (HGA), Multi-objective Binary Particle Swarm Optimization (MBPSO), and Improved Simulated Annealing (ISA)—in terms of task allocation performance. The results compellingly demonstrate that the CEAGA outperforms the other approaches in network revenue terms.