Abstract
The weapon target assignment (WTA) is a classical problem of defense-related applications which is proved to be a NP-complete problem. In this paper, a practical and available dynamic weapon target assignment (DWTA) formulation is given which incorporates two meaningful and conflicting objectives, that is, minimizing weapon costs and maximizing combat benefits. As we know, heuristic methods have some shortcomings such as slow convergence speed and local optimum in solving the nonlinear integer optimization problem. To this end, a novel DWTA algorithm based on cross-entropy (CE) method is introduced, where the resources requirement condition for targets is taken into consideration. The CE method associates an estimation problem with the DWTA optimization problem, and then, the estimation problem is transformed into a convex optimization problem. The Karush–Kuhn–Tucker conditions are applied to solve the convex optimization problem, and the iteration formulas to find the optimal solution are deducted. Furthermore, in order to verify the performance of CE method in dealing with the DWTA problem, several simulations in different combat scenarios are implemented. The results reveal that, compared with the benchmark heuristic and Monte-Carlo (MC) methods, there are some notable advantages in solving the DWTA problem based on CE method with regard to the solution quality and time consumption.
Highlights
Weapon target assignment (WTA) problem is the core content in the research of combat command aided decisionmaking, which can be categorized as a combinatorial optimization problem and nondeterministic polynomial complete problem [1], whose solution space expands exponentially with the increasing of the number of weapons and targets
E computation time of solving the different scales dynamic weapon target assignment (DWTA) problem is recorded in the four combat scenarios, and the relevant results are shown in Table 8; it is obvious that the index CT presents ascending sequence, that is, CE < GA ≈ particle swarm optimization (PSO) < MC, and the computation cost of CE method is one-order-of-magnitude lower than that of GA and PSO method; we could get that the CE method has great advantage in solving speed over GA, PSO, and MC methods
A hypothetical target is constructed to deal with the resource requirement condition, a new dynamic weapon target assignment method based on CE is introduced, and the detailed derivation process of using CE method to solve DWTA problem is given
Summary
Weapon target assignment (WTA) problem is the core content in the research of combat command aided decisionmaking, which can be categorized as a combinatorial optimization problem and nondeterministic polynomial complete problem [1], whose solution space expands exponentially with the increasing of the number of weapons and targets. In SWTA, all weapons are assigned to targets simultaneously and all information is known; in DWTA, many dynamic changes such as time window and weapon consumption should be considered; in that case, the solving algorithm for DWTA problem must have the good real-time performance. Kline et al [2] proposed a nonlinear branch and bound algorithm to solve the SWTA problem which sought to minimize the residual value of each target. Lai and Wu [4] proposed an improved simplified swarm optimization method with two novel schemes to minimize the threat value in the multistage WTA. Gao et al [11] proposed the D-NSGA-III-A algorithm with the adaptive operator selection mechanism. Both NSGAII and D-NSGA-III-A are extensions of the GA algorithm
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