Introduction to Multiobjective Optimization: Interactive Approaches

Abstract

Abstract. We give an overview of interactive methods developed for solving nonlinear multiobjective optimization problems. In interactive methods, a decision maker plays an important part and the idea is to support her/him in the search for the most preferred solution. In interactive methods, steps of an iterative solution algorithm are repeated and the decision maker progressively provides preference information so that the most preferred solution can be found. We identify three types of specifying preference information in interactive methods and give some examples of methods representing each type. The types are methods based on trade-off information, reference points and classification of objective functions. IntroductionSolving multiobjective optimization problems typically means helping a human decision maker (DM) in finding the most preferred solution as the final one. By the most preferred solution we refer to a Pareto optimal solution which the DM is convinced to be her/his best option. Naturally, finding the most preferred solution necessitates the participation of the DM who is supposed to have insight into the problem and be able to specify preference information related to the objectives considered and different solution alternatives, as discussed in Chapter 1. There we presented four classes for multiobjective optimization methods according to the role of the DM in the solution process.

Data-Based Forest Management with Uncertainties and Multiple Objectives

“…Miettinen, 1999, Miettinen et al 2008, the final Pareto optimal solution, to be called the most preferred solution, is identified by iterating the steps of re-defining the preferences and producing a solution fulfilling these preferences as well as possible, until the DM is satisfied. The idea is that in this way the DM learns about what kind of preferences are attainable and what kind of solutions are achievable.…”

A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

“…Therefore, most of multiobjective optimization methods use preference information provided by the DM. In this paper, we concentrate on interactive methods for they are believed to be most promising methods of multiobjective optimization because of numerous advantages [25]. An important advantage of interactive methods is the possibility for the DM to learn about the problem during the solution process, which makes him/her more confident in the final choice [1].…”

NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization

“…Because of their desirable properties, many interactive methods have been proposed in the literature (see, e.g., Luque et al (2011);Miettinen (1999); Miettinen et al (2008) and references therein). They differ from each other, for example, by the type of preference information utilized, the way of incorporating the preference information in the solution process and the information that is given to the decision maker.…”