Enhancement of Sandwich Algorithms for Approximating Higher-Dimensional Convex Pareto Sets

Authors:
Gijs Rennen;Edwin R. van Dam;Dick den Hertog
Affiliations:
Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands;Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands;Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands
Venue:
INFORMS Journal on Computing
Year:
2011

Citing 8
Cited 1

&egr;-optimality for bicriteria programs and its application to minimum cost flows

Computing
The quickhull algorithm for convex hulls

ACM Transactions on Mathematical Software (TOMS)
An Outer Approximation Algorithm for Generating AllEfficient Extreme Points in the Outcome Set of a Multiple ObjectiveLinear Programming Problem

Journal of Global Optimization
Multicriteria Optimization

Multicriteria Optimization
Multiobjective Optimization: Interactive and Evolutionary Approaches

Multiobjective Optimization: Interactive and Evolutionary Approaches
Integrating Approximation and Interactive Decision Making in Multicriteria Optimization

Operations Research
Generating a Representative Subset of the Nondominated Frontier in Multiple Criteria Decision Making

Operations Research
Performance assessment of multiobjective optimizers: an analysis and review

IEEE Transactions on Evolutionary Computation

An Algorithm for Approximating Convex Pareto Surfaces Based on Dual Techniques

INFORMS Journal on Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In many fields, we come across problems where we want to optimize several conflicting objectives simultaneously. To find a good solution for such multiobjective optimization problems, an approximation of the Pareto set is often generated. In this paper, we consider the approximation of higher-dimensional convex Pareto sets using sandwich algorithms. We extend higher-dimensional sandwich algorithms in three different ways. First, we introduce the new concept of adding dummy points to the inner approximation of a Pareto set. By using these dummy points, we can determine accurate inner and outer approximations more efficiently, i.e., using less time-consuming optimizations. Second, we introduce a new method for the calculation of an error measure that is easy to interpret. Third, we show how transforming certain objective functions can improve the results of sandwich algorithms and extend their applicability to certain nonconvex problems. To show the effect of these enhancements, we make a numerical comparison using four test cases, including a four-dimensional case from the field of intensity-modulated radiation therapy. The results of the different cases show that we can achieve an accurate approximation using significantly fewer optimizations by using the enhancements.