Two-Step Framework for Interactive Multi-Objective Optimization
2012 (English)Report (Other academic)
In many real-world optimization applications there are often a number of conﬂicting objective functions that are all important to optimize. The purpose of multiobjective optimization (MOO) is to give the decision maker(DM) an understanding of how these functions are conﬂicting and the possibility to choose an appropriate trade-oﬀ between them. There are multiple methods for solving MOO problems but the focus in this paper is on interactive methods. When the size and complexity of the MOO problem grows the time needed to ﬁnd a solution is too long to yield a pleasant experience for the DM. In this paper, a method to replace the original MOO problem with an approximation is suggested to speed up the process. The approximation is created and used in a two-step framework which makes it possible to investigate the Pareto frontier in real-time and that can handle nonlinear and non-convex MOO problems with m objective functions. The ﬁrst step generates a number of samples of the complete Pareto frontier which is sparse but dense enough for the approximation. The second stepis an interactive tool for the DM to use to continuously and in real-time navigate on the approximated Pareto set in both objective- and decision space. The tool is used to investigate the Pareto frontier and to ﬁnd a preferred solution. A method of decomposing the approximated set into simplices has been developed using Delaunay triangulation. This methodis able to make a good approximation for sets that are non-convex. The method is also able to handle disconnected sets and holes. This makes it possible to change the feasible region in both decision- and objective space. The framework is demonstrated on three example problems that show the functionality and performance of the implemented framework.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. , 26 p.
LiTH-ISY-R, ISSN 1400-3902 ; 3043
Multiobjective optimization, Approximating Pareto set, Interactive, Convex decomposition, Decision space navigation
IdentifiersURN: urn:nbn:se:liu:diva-97986ISRN: LiTH-ISY-R-3043OAI: oai:DiVA.org:liu-97986DiVA: diva2:650882