Biobjective robust optimization over the efficient set for Pareto set reduction

This paper presents a biobjective robust optimization formulation for identifying robust solutions from a given Pareto set. The objectives consider both solution and model robustness when the exact values of the selected solution are affected by uncertainty. The problem is formulated equivalently as a model with uncertainty on the constraint parameters and objective function coefficients. Structural properties and a solution algorithm are developed for the case of multiobjective linear programs. The algorithm is based on facial decomposition; each subproblem is a biobjective linear program and is related to an efficient face of the multiobjective program. The resulting Pareto set reduction methodology allows the handling of continuous and discrete Pareto sets, and can be generalized to consider criteria other than robustness. The use of secondary criteria to further break ties among the many efficient solutions provides opportunities for additional trade-off analysis in the space of the secondary criteria. Examples illustrate the algorithm and characteristics of solutions obtained.