Multi-UAV Target Allocation via Matrix Game Reduction and Eigen-Crossover Differential Evolution

Abstract

To address the challenge of dynamic target allocation in multi-unmanned aerial vehicle (UAV) aerial games, this paper proposes a hierarchical solution method that combines matrix game dimensionality reduction with the Eigen-Crossover Differential Evolution (ECDE) algorithm. Assuming that both parties’ UAV platforms are identical, we first model the aerial game as a two-player zero-sum mixed-strategy matrix game, and introduce target value factors and mutual-confrontation cross term to characterize the coupling between target value and antagonism. Second, by performing fast dimensionality reduction on the utility matrix through convex hull vertex enumeration, we effectively compress the strategy space while preserving the strategic information relevant to the original game equilibrium. Finally, we designed ECDE to find the Nash equilibrium in a dimensionality-reduction game. This algorithm uses elite covariance eigendecomposition to rotate the crossover operation into the natural coordinates of the fitness landscape, and combines parameter adaptation with population size reduction strategies to balance search efficiency and convergence stability. Experimental results show that in the CEC2022 test suite, ECDE achieved the top overall ranking among 13 compared algorithms for both D=10 and D=20; in the 3v2 adversarial scenario, it achieved an average decision time of only 0.026 s and a Nash equilibrium solution accuracy of the 10−15 order of magnitude, while maintaining efficient solution capabilities across matrices of varying sizes. The proposed method meets real-time decision-making requirements while ensuring solution accuracy, demonstrating engineering value.