[Paper Review] Local Search Techniques for Constrained Portfolio Selection Problems

Andrea Schaerf|ArXiv.org|Apr 18, 2001

Risk and Portfolio OptimizationDecision Sciences11 references18 citations

TL;DR

This paper proposes an enhanced tabu search framework for constrained portfolio selection, integrating multiple neighborhood relations, adaptive parameter control, and randomization to improve performance on cardinality- and quantity-constrained mean-variance optimization. The approach significantly outperforms prior local search methods on public benchmarks by simplifying parameter tuning and enabling more effective exploration of the solution space.

ABSTRACT

We consider the problem of selecting a portfolio of assets that provides the investor a suitable balance of expected return and risk. With respect to the seminal mean-variance model of Markowitz, we consider additional constraints on the cardinality of the portfolio and on the quantity of individual shares. Such constraints better capture the real-world trading system, but make the problem more difficult to be solved with exact methods. We explore the use of local search techniques, mainly tabu search, for the portfolio selection problem. We compare and combine previous work on portfolio selection that makes use of the local search approach and we propose new algorithms that combine different neighborhood relations. In addition, we show how the use of randomization and of a simple form of adaptiveness simplifies the setting of a large number of critical parameters. Finally, we show how our techniques perform on public benchmarks.

Motivation & Objective

• To address the limitations of exact methods in solving cardinality- and quantity-constrained portfolio selection problems.
• To improve local search performance by combining multiple neighborhood relations and adaptive parameter control.
• To reduce the burden of manual parameter tuning through randomization and adaptive mechanisms.
• To evaluate the proposed algorithms on real-world benchmark instances from financial markets.
• To provide a reproducible and comparable evaluation framework for constrained portfolio optimization.

Proposed method

• The paper employs a tabu search framework with multiple neighborhood relations: move, insert, delete, and transfer-based moves.
• It introduces a hybrid neighborhood strategy that interleaves different move types to enhance diversification and intensification.
• Adaptive mechanisms dynamically adjust key parameters such as step size and tabu list length based on search progress.
• Randomization is applied to the step size to avoid premature convergence and improve robustness.
• A shifting penalty mechanism is used to handle constraint violations during the search process.
• The algorithm is tested on public benchmarks from the literature, using the standard mean-variance objective with cardinality and quantity constraints.

Experimental results

Research questions

• RQ1 How do different neighborhood relations impact the performance of local search in constrained portfolio selection?
• RQ2 Can adaptive parameter control and randomization reduce the need for manual tuning in tabu search for portfolio optimization?
• RQ3 How does combining multiple neighborhood types improve solution quality compared to single-neighborhood approaches?
• RQ4 What is the impact of constraint handling mechanisms such as shifting penalties on convergence and feasibility?
• RQ5 How do the proposed techniques compare to prior work in terms of solution quality and reproducibility?

Key findings

• The hybrid neighborhood strategy, combining move, insert, delete, and transfer-based moves, significantly improves solution quality over single-neighborhood approaches.
• Adaptive parameter control and randomization of the step size outperform fixed or alternating step values, especially in the constrained setting.
• The proposed tabu search framework achieves better results than prior local search methods, including those using only idR or TID neighborhoods.
• The use of a shifting penalty mechanism enhances constraint handling and improves convergence to feasible solutions.
• The benchmark results are reproducible and comparable, unlike prior work that used non-standard or non-reproducible evaluation metrics.
• The study demonstrates that tabu search, when properly enhanced with adaptive and randomized components, becomes a highly effective alternative to exact methods for constrained portfolio optimization.