The weapon target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. The multi-stage weapon target assignment (MWTA) problem is the basis of the dynamic weapon target assignment (DWTA) problem which commonly exists in practice. The MWTA problem considered in this paper is formulated into a multi-objective constrained combinatorial optimization problem with two competing objectives. Apart from maximizing the damage to hostile targets, this paper follows the principle of minimizing the ammunition consumption. Decomposition and Pareto dominance both are efficient and prevailing strategies for solving multi-objective optimization problems. Three competitive multi-objective optimizers: DMOEA-epsilonC, NSGA-II, and MOEA/D are adopted to solve multi-objective MWTA problems efficiently. Then comparison studies among DMOEA-epsilonC, NSGA-II, and MOEA/D on solving three different-scaled MWTA instances are done. Three common used performance metrics are used to evaluate the performance of each algorithm. Numerical results demonstrate that NSGA-II performs best on small-scaled and medium-scaled instances compared with DMOEA-epsilonC and MOEA/D-AWA, while DMOEA-epsilonC shows advantages over other two algorithms on solving the large-scaled instance.
