E-NAUTILUS: A decision support system for complex multiobjective optimization problems based on the NAUTILUS method

Interactive multiobjective optimization methods cannot necessarily be easily used when (industrial) multiobjective optimization problems are involved. There are at least two important factors to be considered with any interactive method: computationally expensive functions and aspects of human behavior. In this paper, we propose a method based on the existing NAUTILUS method and call it the Enhanced NAUTILUS (E-NAUTILUS) method. This method borrows the motivation of NAUTILUS along with the human aspects related to avoiding trading-off and anchoring bias and extends its applicability for computationally expensive multiobjective optimization problems. In the E-NAUTILUS method, a set of Pareto optimal solutions is calculated in a pre-processing stage before the decision maker is involved. When the decision maker interacts with the solution process in the interactive decision making stage, no new optimization problem is solved, thus, avoiding the waiting time for the decision maker to obtain new solutions according to her/his preferences. In this stage, starting from the worst possible objective function values, the decision maker is shown a set of points in the objective space, from which (s)he chooses one as the preferable point. At successive iterations, (s)he always sees points which improve all the objective values achieved by the previously chosen point. In this way, the decision maker remains focused on the solution process, as there is no loss in any objective function value between successive iterations. The last post-processing stage ensures the Pareto optimality of the final solution. A real-life engineering problem is used to demonstrate how E-NAUTILUS works in practice.