Solving bi-objective uncertain stochastic resource allocation problems by the CVaR-based risk measure and decomposition-based multi-objective evolutionary algorithms

This paper investigates the uncertain stochastic resource allocation problem in which the results of a given allocation of resources are described as probabilities and these 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 redundancy allocation problem (RAP) and the multi-stage weapon-target assignment (MWTA) problem are special cases of stochastic resource allocation problems. Bi-objective models for the uncertain RAP and MWTA problem in which the conditional value-at-risk measure is used to control the risk brought by uncertainties are presented in this paper. The bi-objective formulation covers the objectives of minimizing the risk of failure of completing activities and the resulting cost of resources. With the aim of determining referenced Pareto fronts, a linearized formulation and an approximated linear formulation are put forward for RAPs and MWTA problems based on problem-specific characteristics, respectively. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (i.e., MOEA/D-AWA and DMOEA- $$\varepsilon \hbox {C}$$ ε C ) are used to solve the formulated bi-objective problem. In view of differences between MOEA/D-AWA and DMOEA- $$\varepsilon \hbox {C}$$ ε C , two matching schemes inspired by DMOEA- $$\varepsilon \hbox {C}$$ ε C are proposed and embedded in MOEA/D-AWA. Numerical experiments have been performed on a set of uncertain RAP and MWTA instances. Experimental results demonstrate that DMOEA- $$\varepsilon \hbox {C}$$ ε C outperforms MOEA/D-AWA on the majority of test instances and the superiority of DMOEA- $$\varepsilon \hbox {C}$$ ε C can be ascribed to the $$\varepsilon $$ ε -constraint framework.