A brief review of multi-objective optimization proposals that interactively incorporate preferences.

The problems in which there is a conflict between objectives naturally occur in the real world, in which the presence of a decision maker also intervenes. The multi-objective problem solving has been approached through many multi-objective optimization algorithms. There are a large number of algorithms available for solving these types of problems, mainly for problems of two or three objectives, but in the real world, the number of conflicting objectives is large scale. These algorithms provide a large number of solutions to the decision-maker but, even though all are good and efficient solutions under the Pareto dominance paradigm (efficient solutions known as Non-dominated), this does not fully solve the problem, because this large number of solutions found can overwhelm the decision maker at the moment of selecting what he considers best for him. This is why there is an emerging area in multi-objective optimization, in which the preferences of decision-makers are incorporated, but these can be done at different times in the optimization process: a priori, a posteriori and interactively. The authors have addressed various mechanisms for the articulation of preferences, for example, statistical methods, reference points, weights, to name just a few. In the review, it is found that the use of reference points is the most used method currently. In this paper, we present a review of some outstanding works that approach the obtaining and incorporation of preferences of the decision maker in the process of multiobjective optimization, but in an interactive way. One of the of the revised algorithms and that has generated the most interest in the group of collaborators is InDM2 (Nebro et al., 2018), which combines multi-objective dynamic optimization, multicriteria decision making and interactivity using the visualization of the approximate regions of interest in optimization time; the preferences are expressed through reference points that can be changed at the disposal of the DM during the execution time. Given the limitation of the visualization of conflicting objectives, the problems solved by this metaheuristic are limited to bi-objective problems. In addition to the review of other algorithms, the proposal in which we are currently working is presented, an interactive proposal for multiobjective optimization for large-scale problems. This proposal is based on the elicitation of the preferences of the decision maker through reference sets that are transformed to parameters that are used during the search using a preferential model based on outranking. Currently, this proposal has been analyzed through the solution of the Project Portfolio Problem and the decision maker's satisfaction evaluation has been implemented through the introduction of preferential profiles, which are an emulated representation of a real decision maker. To our knowledge, since there is no general definition that associates the mechanisms of incorporation of preferences with the region of interest, it is desired to develop a procedure that can compare the degree of satisfaction of a preferential profile using some approach of incorporation of preferences in the same algorithm that is used in the literature.