Optimizing multi-objective uncertain multi-stage weapon target assignment problems with the risk measure CVaR

This paper investigates the multi-objective uncertain multi-stage weapon target assignment (UMWTA) problem in which weapons' kill probabilities are considered to be uncertain from practical aspects. Here uncertainties are introduced by assuming that these probabilities depend on random parameters which are impacted by various factors. The multi-objective formulation of UMWTA problems covers the objectives of minimizing the risk of missing hostile targets measured by the conditional value-at-risk (CVaR) measure and minimizing the ammunition consumption. With the aim of determining referenced Pareto fronts, an approximated linear formulation of the UMWTA problem is put forward based on problem-specific characteristics. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (DMOEAs), i.e., MOEA/D-AWA and DMOEA -ϵC are used to solve the formulated problem. In view of the inefficiency of the standard comparison mechanism in DMOEAs, a hierarchical comparison strategy which takes into account Pareto dominance relationships and aggregated objective values simultaneously is proposed and embedded in MOEA/D-AWA and DMOEA-ϵC. MOEA/D-AWA and DMOEA-ϵC with the hierarchical comparison strategy are denoted as MOEA/D-AWA-H and DMOEA-ϵC-H, respectively. Numerical experiments have been performed on two sets of UMWTA instances. Experimental results confirm the effectiveness of the proposed hierarchical comparison strategy and demonstrate the superiority of DMOEA-ϵC-H over MOEA/D-AWA-H on the majority of test instances.