Navigation in multiobjective optimization methods

Abstract

International audienceBuilding on previous work of the authors, this paper formally defines and reviews the first approach, referred to as navigation, towards a common understanding of search and decision-making strategies to identify the most preferred solution among the Pareto set for a multiobjective optimization problem. In navigation methods, the decision maker interactively learns about the problem, whereas the decision support system learns about the preferences of the decision maker. This work introduces a detailed view on navigation leading to the identification of integral components and features. A number of different existing navigation methods are reviewed and characterized. Finally, an overview of applications involving navigation is given, and promising future research direction are discussed

Interactive Optimization With Parallel Coordinates: Exploring Multidimensional Spaces for Decision Support

“…A selected number of methods are described hereafter, outlining their responses to the issues above as well as the remaining gaps. For a more extensive overview of existing approaches, we refer to Branke et al (2008), Meignan et al (2015), Allmendinger et al (2016).…”

“…Third, the interaction process promotes trust, facilitates learning, and increases the user's confidence in the solutions and thus their likelihood of actually implementing them (Hwang and Masud, 1979;Spronk, 1981;Shin and Ravindran, 1991;Liu et al, 2018). Finally, this approach avoids the need to specify any explicit a priori preference information (Hwang and Masud, 1979;Allmendinger et al, 2016).…”

“…Allmendinger et al (2016) employ the term "navigation" to encompass not only the optimization procedure, but also the efforts made on real-time exploration of optimization results. However, among the six so-called navigation methods reviewed by Allmendinger et al (2016), four are a posteriori methods (meaning solutions are precalculated), while only two are interactive (Korhonen and Wallenius, 1988;Miettinen et al, 2010). Their review further reveals that most of these methods tend to handle only five or less objectives, and do not consider problems with more objectives or highly uncertain conditions.…”

NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off

“…If h is not the last step (i.e. rs h > 1), the new point z h is not Pareto optimal and may not be even feasible for the original problem (1). However, as demonstrated in [21,31], z h is always an achievable point when rs h > 1 and this implies that, if it is not feasible, at least, there always exists a Pareto optimal objective vector which dominates it.…”

“…One appealing way of interaction is navigation. As stated in [1] regarding interactive methods, "navigation is the interactive procedure of traversing through a set of points (the navigation set) in the objective space guided by a decision maker (DM). The ultimate goal of this procedure is to identify the single most preferred Pareto optimal solution".…”