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Many real-world optimization problems involving several conflicting objective functions frequently appear in current scenarios and it is expected they will remain present in the future. However, approaches combining multi-objective optimization with the incorporation of the decision maker’s (DM’s) preferences through multi-criteria ordinal classification are still scarce. In addition, preferences are rarely associated with a DM’s characteristics; the preference selection is arbitrary. This paper proposes a new hybrid multi-objective optimization algorithm called P-HMCSGA (preference hybrid multi-criteria sorting genetic algorithm) that allows the DM’s preferences to be incorporated in the optimization process’ early phases and updated into the search process. P-HMCSGA incorporates preferences using a multi-criteria ordinal classification to distinguish solutions as good and bad; its parameters are determined with a preference disaggregation method. The main feature of P-HMCSGA is the new method proposed to associate preferences with the characterization profile of a DM and its integration with ordinal classification. This increases the selective pressure towards the desired region of interest more in agreement with the DM’s preferences specified in realistic profiles. The method is illustrated by solving real-size multi-objective PPPs (project portfolio problem). The experimentation aims to answer three questions: (i) To what extent does allowing the DM to express their preferences through a characterization profile impact the quality of the solution obtained in the optimization? (ii) How sensible is the proposal to different profiles? (iii) How much does the level of robustness of a profile impact the quality of final solutions (this question is related with the knowledge level that a DM has about his/her preferences)? Concluding, the proposal fulfills several desirable characteristics of a preferences incorporation method concerning these questions.

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The problems in which there is a conflict between objectives, naturally occur in the real world, in which also intervenes the presence of a decision maker. The multi-objective problem solution has been approached through many multi-objective optimization algorithms. There are available many algorithms for solving these types of problems, mostly for two or three objectives problems, but in the real world, the number of conflicting objectives is large-scale. These algorithms provide many solutions to the decision-maker but, even though all of these are good and efficient solutions under the Pareto dominance paradigm (efficient solutions known as non-dominated), this does not solve the problem completely, because, this large number of solutions found, could overwhelm the DM at the time of selecting the one he considers best for him. There is an emerging area in multi-objective optimization, in which decision-makers preferences are incorporated, but these can be done at different times in the optimization process: a priori, a posteriori and interactively.

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