A visual interactive approach for scenario-based stochastic multi-objective problems and an application

In many practical applications of stochastic programming, discretization of continuous random variables in the form of a scenario tree is required. In this paper, we deal with the randomness in scenario generation and present a visual interactive method for scenario-based stochastic multi-objective problems. The method relies on multi-variate statistical analysis of solutions obtained from a multi-objective stochastic problem to construct joint confidence regions for the objective function values. The decision maker (DM) explores desirable parts of the efficient frontier using a visual representation that depicts the trajectories of the objective function values within confidence bands. In this way, we communicate the effects of randomness inherent in the problem to the DM to help her understand the trade-offs and the levels of risk associated with each objective.