A Post-Optimality Analysis Algorithm for Multi-Objective Optimization

Authors:
Vandana Venkat;Sheldon H. Jacobson;James A. Stori
Affiliations:
Department of Mechanical and Industrial Engineering, University of Illinois, 1206 W.Green Street (MC-244), Urbana, IL 61801-2906, USA;Department of Mechanical and Industrial Engineering, University of Illinois, 1206 W.Green Street (MC-244), Urbana, IL 61801-2906, USA. shj@uiuc.edu;Department of Mechanical and Industrial Engineering, University of Illinois, 1206 W.Green Street (MC-244), Urbana, IL 61801-2906, USA
Venue:
Computational Optimization and Applications
Year:
2004

Citing 4
Cited 2

Sensitivity analysis in multiobjective optimization

Journal of Optimization Theory and Applications
Stability and sensitivity analysis in convex vector optimization

SIAM Journal on Control and Optimization
Stability and sensitivity analysis in multiobjective nonlinear programming

Annals of Operations Research
Multiobjective evolutionary algorithms: classifications, analyses, and new innovations

Multiobjective evolutionary algorithms: classifications, analyses, and new innovations

Finding preferred subsets of Pareto optimal solutions

Computational Optimization and Applications
Clustering aided approach for decision making in computationally expensive multiobjective optimization

Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II

Quantified Score

Hi-index	0.00

Visualization

Abstract

Algorithms for multi-objective optimization problems are designed to generate a single Pareto optimum (non-dominated solution) or a set of Pareto optima that reflect the preferences of the decision-maker. If a set of Pareto optima are generated, then it is useful for the decision-maker to be able to obtain a small set of preferred Pareto optima using an unbiased technique of filtering solutions. This suggests the need for an efficient selection procedure to identify such a preferred subset that reflects the preferences of the decision-maker with respect to the objective functions. Selection procedures typically use a value function or a scalarizing function to express preferences among objective functions. This paper introduces and analyzes the Greedy Reduction (GR) algorithm for obtaining subsets of Pareto optima from large solution sets in multi-objective optimization. Selection of these subsets is based on maximizing a scalarizing function of the vector of percentile ordinal rankings of the Pareto optima within the larger set. A proof of optimality of the GR algorithm that relies on the non-dominated property of the vector of percentile ordinal rankings is provided. The GR algorithm executes in linear time in the worst case. The GR algorithm is illustrated on sets of Pareto optima obtained from five interactive methods for multi-objective optimization and three non-linear multi-objective test problems. These results suggest that the GR algorithm provides an efficient way to identify subsets of preferred Pareto optima from larger sets.