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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]