LR-NIMBUS : an interactive algorithm for uncertain multiobjective optimization with lightly robust efficient solutions

In this paper, we develop an interactive algorithm to support a decision maker to find a most preferred lightly robust efficient solution when solving uncertain multiobjective optimization problems. It extends the interactive NIMBUS method. The main idea underlying the designed algorithm, called LR-NIMBUS, is to ask the decision maker for a most acceptable (typical) scenario, find an efficient solution for this scenario satisfying the decision maker, and then apply the derived efficient solution to generate a lightly robust efficient solution. The preferences of the decision maker are incorporated through classifying the objective functions. A lightly robust efficient solution is generated by solving an augmented weighted achievement scalarizing function. We establish the tractability of the algorithm for important classes of objective functions and uncertainty sets. As an illustrative example, we model and solve a robust optimization problem in stock investment (portfolio selection).