Project portfolio selection is addressed here as a multi-objective optimization problem. This work introduces an interval-based method that takes into consideration imperfect knowledge of the contribution of projects to a portfolio, the project requirements, available resources and preference parameters in the model. The multi-objective optimization problem is solved using an evolutionary algorithm that is adapted to handle intervals. To direct the search toward the region of interest of the Pareto frontier, the preferences of the decision maker (DM) are incorporated using an interval-based outranking approach. This allows to address problems with many objective functions; intransitive preferences and incomparability situations can also be handled using this approach. In terms of analyzing robustness, the DM can obtain different solutions according to his/her level of conservatism. The effectiveness of this proposal was tested both on an example from the related literature and another example of a public project portfolio with nine objective functions and large number of applicant projects.

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Characterizing the preferences of a decision maker in a multicriteria decision is a complex task that becomes even harder if the information available is limited. This paper addresses a particular case of project portfolio selection; in this case, the measures of project impacts are not assumed, and the available information is only projects' ranking and costs. Usually, resource allocation follows the ranking priorities until they are depleted. This action leads to a feasible solution, but not necessarily to a good portfolio. In this paper, a good portfolio is found by solving a multiobjective problem. To effectively address such dimensionality, the decision maker's preferences in the form of a fuzzy relational system are incorporated in an ant-colony algorithm. The Region of Interest is approached by solving a surrogate triobjective problem. The results show that the reduction of the dimensionality supports the decision maker in choosing the best portfolio.