Variable neighborhood search heuristic for nonconvex portfolio optimization

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.