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Aiming at the shortcomings of quantum-behaved particle swarm optimization algorithm (QPSO), an improved quantum-behaved particle swarm optimization algorithm (IQPSO) is put forward, and the improved algorithm is applied in solving a kind of fuzzy portfolio selection problems. Firstly, a kind of portfolio models with fuzzy return rates and background risk is established followed by some necessary preparations of fuzzy theory. Then, in the improved algorithm, hybrid probability distribution strategy and contraction–expansion coefficient with nonlinear structure are chosen to enhance particle's exploration ability, and premature prevention mechanism is used to maintain population diversity. Furthermore, the experimental results on 16 benchmark functions show that IQPSO has better convergence and robustness than PSO with inertia weight, QPSO and QPSO with a hybrid probability distribution in most cases. Finally, when solving a fuzzy portfolio model, IQPSO provides comparable and superior results compared with the other metaheuristics. [ABSTRACT FROM AUTHOR]

To solve constrained portfolio selection model effectively, an improved quantum-behaved particle swarm optimization algorithm(LQPSO) is presented. Firstly, considering its practicality in real dealing process, a class of fuzzy portfolio models with transaction costs and background risk is established. Then in the design of improved algorithm, Lévy flight strategy and contraction–expansion coefficient with nonlinear structure are taken into account for enhancing particle's exploration ability, and premature prevention mechanism is used to increase population diversity. According to the following performance test, LQPSO demonstrates better convergence and robustness than PSO with inertia weight, QPSO and QPSO with a hybrid probability distribution in 12 benchmark functions. Furthermore, experimental results indicate that LQPSO outperforms several metaheuristics when seeking optimal solution for the fuzzy portfolio model with constraints. • A class of fuzzy portfolio models with transaction costs and background risk is developed. • Lévy flight strategy is taken into account for enhancing particle's exploration ability. • Contraction-expansion coefficient with nonlinear structure is considered to improve convergency speed. • Premature prevention mechanism is used to increase population diversity. • Compared with six metaheuristics, the improved algorithm is more robust and effective in experimental application. [ABSTRACT FROM AUTHOR]