Robust and Stochastically Weighted Multiobjective Optimization Models and Reformulations

Abstract

We introduce and study a family of models for multi-expert multi-objective/criteria decision making. These models use a concept of weight robustness to generate a risk averse decision. In particular, the multi-expert multi-criteria robust weighted sum approach (McRow) introduced in this paper identifies a (robust) Pareto optimum decision that minimizes the worst case weighted sum of objectives over a given weight region. The corresponding objective value, called the robust-value of a decision, is shown to be increasing and concave in the weight set. Compact reformulations of the models with polyhedral and conic descriptions of the weight regions. The McRow model is developed further for stochastic multi-expert multi-criteria decision making by allowing ambiguity or randomness in the weight region as well as the objective functions. The properties of the proposed approach is illustrated with a few examples. The usefulness of the stochastic (McRow) model is demonstrated using a disaster planning example and an agriculture revenue management example.

Robust weighted expected residual minimization formulation for stochastic vector variational inequalities

“…In practice, it is very hard to determine exactly a preferable weight over others for a decision maker. Motivated by the works [13,14] on (stochastic) multiobjective optimization, we introduce a robust weighted model for VVI (2.1). That is, let us consider min…”

“…Based on the equivalent representation for SVVI, Zhao et al [33] introduced a deterministic model for SVVI, which is an extension of a series of works on ERM formulation of SVI to the vector case. In [14], Hu and Mehrotra introduced the robust weighted sum approach for multiobjective optimization problem. Hu et al [13] presented and studied two models for uncertainty/stochastic multiobjective optimization problem.…”

“…Motivated by the works [13,14] on (stochastic) multiobjective optimization, we introduce a new class of deterministic model for SVVI, called robust weighted ERM model. An approximation method based on SAA techniques is proposed for solving the robust weighted ERM problem.…”

A General Framework for Designing Approximation Schemes for Combinatorial Optimization Problems with Many Objectives Combined into One

“…The robust version of weighted multi-objective optimization problems has been studied by Hu and Mehrotra (2010) for the case when each f i is a continuous function. For discrete optimization problems, this formulation is a generalization of the robust discrete optimization model with a fixed number of scenarios (see e.g.…”

“…Consider the following robust version of a weighted multi-objective optimization problem given by Hu and Mehrotra (2010):…”