Interactive learning-oriented decision support tool for nonlinear multiobjective optimization: Pareto navigator

We describe a new interactive learning-oriented method called Pareto navigatorfor nonlinear multiobjective optimization. In the method, first a polyhedral approx-imation of the Pareto optimal set is formed in the objective function space usinga relatively small set of Pareto optimal solutions representing the Pareto optimalset. Then the decision maker can navigate around the polyhedral approximationand direct the search for promising regions where the most preferred solution couldbe located. In this way, the decision maker can learn about the interdependenciesbetween the conflicting objectives and possibly adjust one’s preferences. Once aninteresting region has been identified, the polyhedral approximation can be mademore accurate in that region or the decision maker can ask for the closest counter-part in the actual Pareto optimal set. If desired, (s)he can continue with anotherinteractive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. Pareto navigator is computa-tionally efficient because most of the computations are performed in the polyhedralapproximation and for that reason function evaluations of the actual objective func-tions are not needed. Thus, the method is well suited especially for problems withcomputationally costly functions. Furthermore, thanks to the visualization tech-nique used, the method is applicable also for problems with three or more objectivefunctions, and in fact it is best suited for such problems. We illustrate the methodand the underlying ideas with an example.