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• In this article, we present a three-phased framework to aid the multi-criteria decision analysis of portfolios in an online and interactive fashion. • This approach is based on the idea of enriching a classical mathematical technique (e.g. goal programming, ?-constraint, or compromise programming) by incorporating some concepts based on fuzzy relations taken from the European School of MCDA (Multi-Criteria Decision Analysis). • Experimental evidence on synthetic and real-world instances shows that our model computes quickly enough to be interactive and it is even capable of improving high quality solutions. • The contribution of this paper is in providing a guideline to build compromise programming models that follow the principles of ELECTRE III to prevent incomparability during the analysis. It aids the DM in identifying strictly preferred solutions. • In practical terms, the chief contribution of this approach is the level of confidence that the DM can feel in the final prescription. This paper introduces an interactive approach to support multi-criteria decision analysis of project portfolios. In high-scale strategic decision domains, scientific studies suggest that the Decision Maker (DM) can find help by using many-objective optimisation methods, which are supposed to provide values in the decision variables that generate high-quality solutions. Even so, DMs usually wish to explore the possibility of reaching some levels of benefits in some objectives. Consequently, they should repeatedly run the optimisation method. However, this approach cannot perform well – in an interactive way – for large instances under the presence of many objective functions. We present a mathematical model that is based on compromise programming and fuzzy outranking to aid DMs in analysing multi-criteria project portfolios on the fly. This approach allows relaxing the problem of rapidly optimising portfolios while preserving the beneficial properties of the DM's preferences expressed by outranking relations. Our model supports the decision analysis on two instance benchmarks: for the first one, a better compromise solution was generated 84% of the runs; for the second one, this ranged from 93% to 97%. Our model was also applied to a real-world problem involving social projects, obtaining satisfactory results. [ABSTRACT FROM AUTHOR]

Organisations often face portfolio optimisation problems. In many practical cases, the decision is not only to select a subset of applicant projects but also to assign a number of resources to the favoured proposals within the projects’ feasibilities. In the scientific literature, multi-objective optimisation algorithms have addressed this issue by means of generating redundant dummy projects for each proposal that is likely to be partially funded. However, unfortunately, if there are many projects that can be supported in a wide variety of ways, this approximation results in a large overload for the optimisation methods, which provokes poor algorithmic performance. To alleviate these problems, we propose the Non-Outranked Ant Colony Optimisation II method, which incorporates a fuzzy outranking preference model for optimising portfolio problems with partial-support features. The advantages offered by this novel approach are supported by a series of experiments that provide evidence of its capacity for solving those real-world problems in which the level of resources allocated to the selected proposals has a proportional impact on the projects’ expected benefits. [ABSTRACT FROM AUTHOR]