Application of the non-outranked sorting genetic algorithm to public project portfolio selection

This paper proposes the application of multi-criteria analysis to the problem of allocating public funds to competing programs, projects, or policies, with a subjective approach applied to define the concept of highest portfolio social return. This portfolio corresponds to an attainable non-strictly outranked state of the social object under consideration. Its existence requires a decision-maker (DM) to establish a relational preference system of minimal consistency. As the number of feasible portfolios increases exponentially, the DM’s asymmetric preference relation should be computable to perform an exploration of the portfolio space. The complexity of many real situations requires evolutionary algorithms, but, in presence of many objectives, evolutionary algorithms are inefficient. We overcome this problem by using the extended non-outranked sorting genetic algorithm (NOSGA-II), which handles multi-criteria preferences through a robust model based on a binary fuzzy outranking relation expressing the truth value of the predicate “portfolio x is at least as good as portfolio y”. The DM is assumed to be capable of assigning the parameters for constructing the outranking relation. In case of collective decision-making, we first assume that the possible differing values of the group members are not strongly conflicting, so that a consensus can be achieved on the model’s parameters. Otherwise, we propose a method in which each member of the heterogeneous group gets his/her own best portfolio. These individual solutions are then aggregated in a group’s best acceptable portfolio, which maximizes a measure of group satisfaction and minimizes regret. The proposal is examined through two real size problems, in which good solutions are reached; the first example is useful to illustrate the case of social-action program selection; the second illustrates the case of basic research project portfolios.