Robust optimization for multiobjective programming problems with imprecise information

TL;DR: Two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty are developed and a label setting algorithm is developed to solve the multi- objective uncertain shortest path problem.

TL;DR: The concept of regret is extended from the single-objective case to the multiobjective setting and a proper definition of multivariate (robust) (relative) regret is introduced and this approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases.

TL;DR: In this paper, the min-ordering and the max-ordering methods are used to find min-max robust efficient solutions for multi-objective uncertain combinatorial optimization problems with special uncertainty sets.

TL;DR: An approach for comparing sets of robust efficient solutions and their outcomes under the nominal scenario and in the worst case using the upper set-less order from set-valued optimization is developed.

TL;DR: In this paper, the authors propose an approach that attempts to make this trade-off more attractive by flexibly adjusting the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations.

TL;DR: An approach is proposed that flexibly adjust the level of conservatism of the robust solutions in terms of probabilistic bounds of constraint violations, and an attractive aspect of this method is that the new robust formulation is also a linear optimization problem, so it naturally extend to discrete optimization problems in a tractable way.

TL;DR: Mathematical Background Topics from Linear Algebra Single Objective Linear Programming Determining all Alternative Optima Comments about Objective Row Parametric Programming Utility Functions, Nondominated Criterion Vectors and Efficient Points Point Estimate Weighted-sums Approach.

TL;DR: This note formulates a convex mathematical programming problem in which the usual definition of the feasible region is replaced by a significantly different strategy via set containment.