Bi-level programming modeling and hierarchical hybrid algorithm for antimissile dynamic firepower allocation problem with uncertain environment

Aiming at the shortcomings of antimissile dynamic firepower allocation (ADFA) researches under uncertain environment, the fuzzy chance-constrained bi-level programming model with complex constraints is proposed by introducing the uncertain programming theory. Firstly, maximization cost-effectiveness ratio and earliest interception time as the upper and the lower objective functions of the model, respectively, are used. In order to close to the battlefield environment, the model constraint includes interception time window, effective damage lower bound and intercept strategy, etc. Secondly, a particle coding scheme and repairing scheme are given with hierarchical structure for multi-constrained bi-level ADFA problem. Furthermore, the improved variable neighborhood PSO algorithm with convergence criterions and the PSO algorithm with doubt and repulsion factor (PSO-DR) are effectively combined. On these bases, the hierarchical hybrid fuzzy particle swarm optimization algorithm is presented with fuzzy simulation technique. Finally, the results of comparison show the proposed algorithm has stronger global searching ability and faster convergence speed, which can effectively solve large-scale ADFA problem and adapt to the requirements of real-time decision.