Cardinality-constrained portfolio selection based on collaborative neurodynamic optimization

Man Fai Leung, Jun Wang

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


Portfolio optimization is one of the most important investment strategies in financial markets. It is practically desirable for investors, especially high-frequency traders, to consider cardinality constraints in portfolio selection, to avoid odd lots and excessive costs such as transaction fees. In this paper, a collaborative neurodynamic optimization approach is presented for cardinality-constrained portfolio selection. The expected return and investment risk in the Markowitz framework are scalarized as a weighted Chebyshev function and the cardinality constraints are equivalently represented using introduced binary variables as an upper bound. Then cardinality-constrained portfolio selection is formulated as a mixed-integer optimization problem and solved by means of collaborative neurodynamic optimization with multiple recurrent neural networks repeatedly repositioned using a particle swarm optimization rule. The distribution of resulting Pareto-optimal solutions is also iteratively perfected by optimizing the weights in the scalarized objective functions based on particle swarm optimization. Experimental results with stock data from four major world markets are discussed to substantiate the superior performance of the collaborative neurodynamic approach to several exact and metaheuristic methods.

Original languageEnglish
Pages (from-to)68-79
Number of pages12
JournalNeural Networks
Publication statusPublished - Jan 2022
Externally publishedYes


  • Cardinality constraint
  • Mixed-integer programming
  • Neurodynamic optimization
  • Portfolio selection


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