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Portfolio optimization is an essential issue in quantitative investing, which aims to find the best set of portfolios by allocating the proportion of assets. One of the most widely studied portfolio optimization models is the cardinality constrained mean–variance model, which incorporates real-world constraints on the number of selected assets and lower and upper bounds on the proportion of each asset. This paper presents a novel metaheuristic algorithm based on the Mayfly algorithm to solve the cardinality constrained mean–variance portfolio optimization problem. To better adapt to this problem, we design and introduce some new features to the proposed algorithm, including (1) a new cardinality constraint handling strategy; (2) a new local search strategy; and (3) changes to the crossover operator. We have designed comparison experiments for the proposed metaheuristic and evaluated its performance using five commonly used performance metrics. The experimental results show that the proposed approach achieves competitive performance on datasets of different sizes. The results also demonstrate the feasibility of this approach in solving the cardinality constrained mean–variance portfolio optimization problem. • The proposed algorithm is used for Cardinality Constrained Portfolio Optimization. • A fast cardinality constraint handling strategy. • A nuptial dance and bi-direction-based local search strategy. • Excellent comparison experimental results on benchmark from OR-Lib. [ABSTRACT FROM AUTHOR]

This paper presents a novel bio-inspired algorithm inspired by starlings' behaviors during their stunning murmuration named starling murmuration optimizer (SMO) to solve complex and engineering optimization problems as the most appropriate application of metaheuristic algorithms. The SMO introduces a dynamic multi-flock construction and three new search strategies, separating, diving, and whirling. The separating search strategy aims to enhance the population diversity and local optima avoidance using a new separating operator based on the quantum harmonic oscillator. The diving search strategy aims to explore the search space sufficiently by a new quantum random dive operator, whereas the whirling search strategy exploits the vicinity of promising regions using a new operator called cohesion force. The SMO strikes a balance between exploration and exploitation by selecting either a diving strategy or a whirling strategy based on the flocks' quality. The SMO was tested using various benchmark functions with dimensions 30, 50, 100. The experimental results prove that the SMO is more competitive than other state-of-the-art algorithms regarding solution quality and convergence rate. Then, the SMO is applied to solve several mechanical engineering problems in which results demonstrate that it can provide more accurate solutions. A statistical analysis shows that SMO is superior to the other contenders. • Proposing a novel, bio-inspired algorithm named starling murmuration optimizer (SMO). • Introducing a diving strategy and a quantum random dives operator for exploration. • Introducing a whirling strategy and a cohesion operator for exploitation. • Introducing a strategy using quantum harmonic oscillator to enhance diversity. • SMO is superior to other tested algorithms on benchmarks and engineering problems. [ABSTRACT FROM AUTHOR]