Incorporating preferential weights as a benchmark into a Sequential Reference Point Method

In multi-objective optimization models, it is common that the decision maker expresses the relative importance of objectives through a weighting scheme. However, many solving techniques do not assure that the corresponding solution fits the preferential weights. It could be the case that an objective with a very low weight achieves a good value, whereas another with a high weight yields a very poor achievement. In order to overcome the aforementioned drawback, this paper proposes a new resolution method based on the well-known Reference Point Method. The methodology consists in generating a sequence of Reference Point Method models which share the same reference point fixed at the vector of preferential weights. In the iterative process, the projection direction on the Pareto frontier changes in each iteration according to the deviations between the preferential weights and the current normalised objective values. In this way, a sequence of Pareto-efficient solutions is generated which converges towards a solution that best fits the decision maker's preferential weights. The proposed method is illustrated by means of a numerical example. In order to show its feasibility and usefulness, the methodology is applied to a portfolio selection problem where the corporate sustainability performance of each firm is taken into account.