Solving the uncertain multi-objective multi-stage weapon target assignment problem via MOEA/D-AWA

The weapon target assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. And the multi-stage weapon target assignment (MWTA) problem is the basis of dynamic weapon target assignment (DWTA) problems which commonly exist in practice. The MWTA problem considered in this paper is with uncertainties, namely the uncertain MWTA (UMWTA) problem, and is formulated into a multi-objective constrained combinatorial optimization problem with two competing objectives. Apart from maximizing damage to hostile targets, this paper follows the principle of minimizing ammunition consumption under the assumption that each element of the kill probability matrix follows four different probability distributions. In order to tackle the two challenges, i.e., multi-objective and the uncertainty, the multi-objective evolutionary algorithm based on decomposition with adaptive weight adjustment (MOEA/D-AWA) and the Max-Min robust operator are adopted to solve the problem efficiently. Then comparison studies between the MOEA/D-AWA and a single objective solver used for a relaxed formulation on solving both certain and uncertain instances of two different scaled MWTA problems which include four uncertain scenarios are conducted. Numerical results show that MOEA/D-AWA outperforms the single objective solver on solving both certain and uncertain multi-objective MWTA problems discussed in this paper. Comparisons between the results of the certain and uncertain formulation also indicate the necessity of the robust formulation of practical problems.