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Adaptive evolutionary algorithms for portfolio selection problems

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Abstract

In this contribution we propose to solve complex portfolio selection problems via Evolutionary Algorithms (EAs) that resort to adaptive parameter control to manage the Exploration versus Exploitation balance and to find (near)-optimal solutions. This strategy modifies the algorithm’s parameters during execution, and relies on continuous feedbacks provided to the EA with respect to some user-defined criteria. In particular, our study aims to understand whether a standard EA can benefit from a robust method that iteratively selects the crossover operator out of a predefined set, in the context of optimised portfolio choices. We apply this approach to large-scale optimization problems, by tackling a number of NP-hard mixed-integer programming problems. Our results show that generic EAs equipped with single crossover operator do not perform homogeneously across problem instances, whereas the adaptive policy leads to robust (and improved) solutions, by alternating exploration and exploitation on the basis of the features of the current search space.

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Notes

  1. Metaheuristics may be partitioned in trajectory-based and population-based ones: in the former case, the search can be represented as a trajectory in the search space; in the latter, the search can be seen as an evolution of a discrete set of points (solutions). Also hybrid approaches that combine the two paradigms exist: please refer to Blum and Roli (2003) for more details.

  2. A stock market sector is a group of public companies that share similar business activities, outputs or characteristics. The U.S. stock market is partitioned into eleven sectors, according to the Global Industry Classification Standard (GICS).

  3. For practical purposes, from now on we focus our attention on genetic algorithms, hence in this section we review crossover methods specifically for GAs: nonetheless, note that our adaptive approach is flexible enough to manage a broad range of evolutionary algorithms.

  4. Please notice that, in the literature about Meta-Heuristics, the term ‘objective function’ and ‘cost function’ have different meanings: the former corresponds to the target function to be optimized, whereas the latter represents the function guiding the search algorithm in the search space (di Tollo and Roli 2008).

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Authors and Affiliations

  1. Department of Economics, Ca’ Foscari University of Venice, Sestiere Cannaregio 873, 30121, Venezia, Italy

    Gianni Filograsso

  2. Dipartimento di Diritto, Economia, Management e Metodi Quantitativi, University of Sannio, Via delle Puglie 82, 82100, Benevento, Italy

    Giacomo di Tollo

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Filograsso, G., di Tollo, G. Adaptive evolutionary algorithms for portfolio selection problems. Comput Manag Sci 20, 7 (2023). https://doi.org/10.1007/s10287-023-00441-7

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