In cooperative autonomous attack missions with multiple UAVs, cooperative target assignment (CTA) is critical to operational effectiveness. This paper formulates a multi-objective model considering target damage value, formation loss cost, and task execution time, and proposes an improved grey wolf optimization (GWO) algorithm with piecewise chaotic initialization, population diversity measurement via position variance, and softmax-weighted leader updates. Simulations under two scenarios (4 UAVs/6 targets and 6 UAVs/8 targets) show that the improvements significantly enhance convergence speed (82.9% and 24.7% fewer iterations), reduce final fitness (10.0% and 6.0%), increase expected damage (12.9% and 5.3%), and shorten average path length (15.0% and 13.7%). These results demonstrate substantial gains in damage effectiveness, timeliness, and survivability, offering a lightweight decision-making framework for contested environments.