A sampling-based method for generating nondominated solutions in stochastic multi-objective mathematical programming problems

This paper presents a method for generating nondominated solutions for stochastic multiobjective mathematical programming problems which is applicable to both continuous and zero–one variables. The method is based on the assumption that the objective function coefficients are random variables with probability distributions that are known or can be approximated. The method results in solutions that are nondominated in terms of the expected value of each objective and the probability that each objective meets or exceeds a specified target value. A method for generating a set of such solutions is presented and illustrated with examples. The paper also discusses computational matters.