Minimum-risk decision for the uncertain multiobjective cooperative task assignment problem of heterogeneous unmanned aerial vehicles

The uncertain cooperative task assignment (CTA) problem based on uncertainty theory is a complex combinatorial optimization problem that cannot be effectively addressed using probability theory due to insufficient samples. In light of this limitation, this paper initially proposes an uncertain multiobjective CTA (UMCTA) problem, taking into account the uncertainties present in the battlefield environment. Consequently, the expected-value standard-deviation UMCTA model ( E σ -UMCTA) model, which emphasize the minimization of expected returns and stability of the objective functions, is developed. Nonetheless, this approach may yield suboptimal assignment schemes under predetermined risk levels. To address this issue, a minimum-risk model for the UMCTA problem is introduced by maximizing the belief degree that the objective functions do not exceed the predefined risk levels, and the concept of the minimum-risk efficient assignment scheme is delineated. Given the challenges in solving the minimum-risk model due to uncertain variables, two scenarios for addressing these uncertainties in the UMCTA problem are contemplated, and the minimum-risk model is transformed into a deterministic multiobjective programming problem. Subsequently, recognizing the combinational nature and complexity of the resulting deterministic multiobjective programming problem, an enhanced discrete particle swarm optimization (PSO) algorithm with non-dominated sorting is devised, where the crossover and mutation operators are employed to sustain diversity and avert premature convergence. Finally, a simulation study is conducted to substantiate the practicability of the proposed model and assess the efficacy of the designed algorithm.