We introduce an unconstrained multicriteria optimization problem and discuss its relation to various well-known scalar robust optimization problems with a finite uncertainty set. Specifically, we show that a unique solution of a robust optimization problem is Pareto optimal for the unconstrained optimization problem. Furthermore, it is demonstrated that the set of weakly Pareto optimal solution...

A framework for robust optimization under uncertainty based on the use of the generalized inverse distribution function (GIDF), also called quantile function, is here proposed. Compared to more classical approaches that rely on the usage of statistical moments as deterministic attributes that define the objectives of the optimization process, the inverse cumulative distribution function allows ...

Retail energy providers (REPs) can employ different strategies such as offering demand response (DR) programs, participating in bilateral contracts, and employing self-generation distributed generation (DG) units to avoid financial losses in the volatile electricity markets. In this paper, the problem of setting dynamic retail sales price by a REP is addressed with a robust optimization techniq...

This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with gen...

in this paper, we introduce a model  to optimization of milk run system that is one of vrp problem with time window and uncertainty in inventory. this approach led to the routes with minimum cost of transportation while satisfying all inventory in a given bounded set of uncertainty .the problem is formulated as a robust optimization problem. since the resulted problem illustrates that grows up ...

Chance constraints are an important modeling tool in stochastic optimization, providing probabilistic guarantees that a solution “succeeds” in satisfying a given constraint. While they control the probability of “success,” they provide no control whatsoever in the event of a “failure.” That is, they do not distinguish between a slight overor under-shoot of the bounds, and more catastrophic viol...

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

We study the dual problems associated with the robust counterparts of uncertain convex programs. We show that while the primal robust problem corresponds to a decision maker operating under the worst possible data, the dual problem corresponds to a decision maker operating under the best possible data. © 2008 Elsevier B.V. All rights reserved.