Multi-objective Basic Variable Neighborhood Search for Portfolio Selection

The Portfolio Selection Problem looks for a set of assets with the best trade-off between return and risk, that is, with the maximum expected return and the minimum risk (e.g., the variance of returns). As these objectives are conflicting, it is a difficult multi-objective problem. Different models and algorithms have been proposed to obtain the (optimal) Pareto front. However, exact approaches take days for a large set of points to the Pareto front. Within this perspective, we develop a basic variable neighborhood search heuristic to solve the bi-objective portfolio selection problem. The proposed heuristic considers ten neighborhood structures that are mainly based on swap moves and has a local improvement based on averaging the proportions that are invested in consecutive assets. The proposed heuristic was experimentally compared with the Mean-Variance model of Markowitz, using benchmark instances from the OR-Library. The number of assets in these instances ranges from 31 to 225. According to the experimental results, the proposed heuristic performed well in the construction of different Pareto fronts.

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