Integrating Approximation and Interactive Decision Making in Multicriteria Optimization

• Published in: Operations research Vol. 56; no. 1; pp. 222 - 234
• Main Authors: Klamroth, Kathrin, Miettinen, Kaisa
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.01.2008; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Approximation; Decision making; Decision theory. Utility theory; Exact sciences and technology; interactive methods; Iterative solutions; Management; Mathematical optimization; Mathematical vectors; Mathematics; Methods; multiple criteria; Multiple criteria decision making; Nadir; nonlinear; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Operations research; Optimal solutions; Optimization; Optimization techniques; Pareto efficiency; Pareto optimum; Preferences; programming; reference point; Studies; Unit ball; programming: multiple criteria; Nondominated set; Decision support system; interactive methods; Multicriteria analysis; Approximation method; Decision making; Roughness; reference point; Problem solving; nonlinear; Optimization; programming; multiple criteria
• ISSN: 0030-364X; 1526-5463; 1526-5463
• DOI: 10.1287/opre.1070.0425

We present a new interactive hybrid approach for solving multicriteria optimization problems where features of approximation methods and interactive approaches are incorporated. We produce rough approximations of the nondominated set and let the decision maker indicate with the help of reference points where to refine the approximation. In this way, (s)he iteratively directs the search toward the best nondominated solution. After the decision maker has identified the most interesting region of the nondominated set, the final solution can be fine-tuned with existing interactive methods. We suggest different ways of updating the reference point as well as discuss visualizations that can be used in comparing different nondominated solutions. The new method is computationally relatively inexpensive and easy to use for the decision maker.