Simulated annealing–Tabu search integration for downside-risk portfolio optimization with cardinality constraints

This paper presents a hybrid metaheuristic framework for portfolio optimization with cardinality constraints, a computationally challenging problem in constrained asset allocation. The model minimizes downside risk relative to a predefined target return while incorporating realistic investment restrictions such as allocation bounds and a maximum number of selected assets. The proposed method integrates Simulated Annealing (SA) and Tabu Search (TS) within a coordinated hybrid optimization framework for mixed continuous–discrete portfolio optimization. SA performs stochastic exploration over continuous portfolio weights, while TS refines the discrete asset-selection layer through add–drop–swap neighborhood moves supported by tabu-based memory structures. The algorithm iteratively enforces feasibility, diversification, and local intensification through projection and neighborhood refinement procedures. A comprehensive computational analysis is conducted using historical data from the S&P 500 index over the period 2020–2024, including sensitivity analysis with respect to portfolio cardinality, comparative evaluation against DE, PSO, and GA metaheuristics, validation against exact mixed-integer programming benchmarks, statistical robustness analysis, and out-of-sample testing under high-volatility market conditions. The computational results indicate that the proposed SA–TS framework provides a robust and computationally effective approach for downside-risk portfolio optimization under cardinality constraints.