On the quality of discrete representations in multiple objective programming

Abstract

Within the past ten years, emphasis has been placed on generating discrete representations of the nondominated set which are truly representative of the nondominated set as a whole. This paper reviews measures for assessing the quality of discrete representations as well as exact solution methods that attempt to produce representations satisfying certain quality criteria. The measures are classified according to the aspect of the representation which they assess: cardinality, coverage, or spacing. The proposed solution methods are categorized according to whether a measure is integrated into the procedure a priori (before generation of solution points), a posteriori (after the generation of solution points), or not at all. The paper concludes with a comparative discussion of these three approaches and directions for future research.

Discrete representation of non-dominated sets in multi-objective linear programming

“…Therefore most methods work without the knowledge of X E . A recent survey of methods for computing discrete representations in multi-objective optimisation can be found in Faulkenberg and Wiecek (2010). In the following, we focus on methods that are related to the concepts of the global shooting and the normal boundary intersection methods.…”

Simulation-based process windows simultaneously considering two and three conflicting criteria in injection molding

“…In light of the limitations faced by several multiple criteria optimization representations, (Faulkenberg, & Wiecek, 2009) and the incompletely solved challenge of selecting among several efficient solutions, Sayarshad and Marler (2009) developed an approach that incorporates preferences in an evolutionary algorithm. This algorithm is then combined with Pareto-optimality conditions (Mateo, P.M., & Alberto, I., 2012) to arrive to a final decision.…”

Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes

“…It is therefore impractical for a decision maker to examine all non-dominated points. Instead, a practical approach is to obtain a discrete representation of the non-dominated set satisfying some quality requirements (Sayın 2000;Faulkenberg and Wiecek 2010). Many methods that follow this approach have been proposed in the last two decades, as the paper by Faulkenberg and Wiecek (2010) shows.…”

“…Instead, a practical approach is to obtain a discrete representation of the non-dominated set satisfying some quality requirements (Sayın 2000;Faulkenberg and Wiecek 2010). Many methods that follow this approach have been proposed in the last two decades, as the paper by Faulkenberg and Wiecek (2010) shows. Given this representative non-dominated set, the decision maker can navigate through the non-dominated points and decide on the most preferred point.…”