The studies of behavioral finance show that the cognitive bias plays an important role in investors' decision-making process. In this paper, based on the robust theory and prospect theory, a robust multi-period portfolio considering investors' behavioral factors is constructed, which features the reference dependence, loss aversion and diminishing sensitivity. To solve the proposed portfolio model, an improved particle swarm optimization (PSO) algorithm is developed, which incorporates the two-stage initialization strategy, the improved stochastic ranking approach, the aging leader and the multi-frequency vibrational mutation operator. We illustrate the robust model with real market data and show its effectiveness based on the performance of the proposed algorithm. The results show that the proposed algorithm is successful in solving the constrained multi-period portfolio model and the proposed portfolio model provides an effective tool for a real multi-period investment. (C) 2015 Elsevier Ltd. All rights reserved.