Competition-Driven Multimodal Multiobjective Optimization and Its Application to Feature Selection for Credit Card Fraud Detection

Shoufei Han, Kun Zhu, Mengchu Zhou, Xinye Cai

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Feature selection has been considered as an effective method to solve imbalanced classification problems. It can be formulated as a multiobjective optimization problem (MOP) aiming to find a small feature subset while achieving a high classification accuracy. With traditional MOP, the focus is on deriving an optimal solution (i.e., a feature subset), while ignoring the diversity in solution space (e.g., there could exist multiple feature subsets achieving the same accuracy). Providing more options for feature selection would be beneficial since some features can be more difficult to obtain than others. In this work, we treat feature selection as a multimodal MOP (MMOP) whose goals are to find an excellent Pareto front in objective space and as many equivalent Pareto optimal solutions (feature subsets) as possible in feature space. Note that though several multimodal multiobjective evolutionary algorithms (MMEAs) have been proposed, their use of a convergence-first selection criterion could cause the loss of solution diversity in an objective and feature space. To address the issue, a novel competition-driven mechanism is designed to assist the existing multimodal MMEAs in locating more equivalent feature subsets and a desired Pareto front. The effectiveness of the proposed mechanism is first verified on all 22 MMOPs from CEC2019. Then, the proposed method is applied to feature selection in imbalanced classification problems and a real-world application, i.e., credit card fraud detection. Experimental results show that the proposed mechanism can not only provide more equivalent feature subsets but also improve classification accuracy.

Original languageEnglish (US)
Pages (from-to)7845-7857
Number of pages13
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number12
StatePublished - Dec 1 2022

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Competition mechanism (CM)
  • credit card fraud detection
  • feature selection
  • imbalanced classification
  • machine learning
  • multimodal MOPs (MMOPs)
  • multimodal multiobjective evolutionary algorithms (MMEAs)


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