With limited financial resources, decision-makers in firms and governments face the task of selecting the best portfolio of projects to invest in. As the pool of project proposals increases and more realistic constraints are considered, the problem becomes NP-hard. Thus, metaheuristics have been employed for solving large instances of the project portfolio selection problem (PPSP). However, most of the existing works do not account for uncertainty. This paper contributes to close this gap by analyzing a stochastic version of the PPSP: the goal is to maximize the expected net present value of the inversion, while considering random cash flows and discount rates in future periods, as well as a rich set of constraints including the maximum risk allowed. To solve this stochastic PPSP, a simulation-optimization algorithm is introduced. Our approach integrates a variable neighborhood search metaheuristic with Monte Carlo simulation. A series of computational experiments contribute to validate our approach and illustrate how the solutions vary as the level of uncertainty increases.

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Computational finance has become one of the emerging application fields of metaheuristic algorithms. In particular, these optimization methods are quickly becoming the solving approach alternative when dealing with realistic versions of financial problems, such as the popular portfolio optimization problem (POP). This paper reviews the scientific literature on the use of metaheuristics for solving rich versions of the POP and illustrates, with a numerical example, the capacity of these methods to provide high-quality solutions to complex POPs in short computing times, which might be a desirable property of solving methods that support real-time decision making.