Using box indices in supporting comparison in multiobjective optimization

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2008.05.013 Byline: Kaisa Miettinen (a), Julian Molina (b), Mercedes Gonzalez (b), Alfredo Hernandez-Diaz (c), Rafael Caballero (b) Keywords: Multiple criteria programming; MCDM; Preference information; Pareto optimality; Visualization; Interactive methods Abstract: Because of the conflicting nature of criteria or objectives, solving a multiobjective optimization problem typically requires interaction with a decision maker who can specify preference information related to the objectives in the problem in question. Due to the difficulties of dealing with multiple objectives, the way information is presented plays a very important role. Questions posed to the decision maker must be simple enough and information shown must be easy to understand. For this purpose, visualization and graphical representations can be useful and constitute one of the main tools used in the literature. In this paper, we propose to use box indices to represent information related to different solution alternatives of multiobjective optimization problems involving at least three objectives. Box indices are an intelligible and easy to handle way to represent data. They are based on evaluating the solutions in a natural and rough enough scale in order to let the decision maker easily recognize the main characteristics of a solution at a glance and to facilitate comparison of two or more solutions in an easily understandable way. Author Affiliation: (a) Department of Mathematical Information Technology, P.O. Box 35 (Agora), FI-40014, University of Jyvaskyla, Finland (b) University of Malaga, Malaga, Spain (c) Pablo de Olavide University, Seville, Spain Article History: Received 23 April 2007; Accepted 17 May 2008