Expected improvement of penalty-based boundary intersection for expensive multiobjective optimization

Nobuo Namura, Koji Shimoyama, Shigeru Obayashi

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


Computationally expensive multiobjective optimization problems are difficult to solve using solely evolutionary algorithms (EAs) and require surrogate models, such as the Kriging model. To solve such problems efficiently, we propose infill criteria for appropriately selecting multiple additional sample points for updating the Kriging model. These criteria correspond to the expected improvement of the penalty-based boundary intersection (PBI) and the inverted PBI. These PBI-based measures are increasingly applied to EAs due to their ability to explore better nondominated solutions than those that are obtained by the Tchebycheff function. In order to add sample points uniformly in the multiobjective space, we assign territories and niche counts to uniformly distributed weight vectors for evaluating the proposed criteria. We investigate these criteria in various test problems and compare them with established infill criteria for multiobjective surrogate-based optimization. Both proposed criteria yield better diversity and convergence than those obtained with other criteria for most of the test problems.

Original languageEnglish
Pages (from-to)898-913
Number of pages16
JournalIEEE Transactions on Evolutionary Computation
Issue number6
Publication statusPublished - 2017 Dec


  • Efficient global optimization (EGO)
  • Expected improvement (EI)
  • Expensive optimization
  • Multiobjective optimization
  • Penalty-based boundary intersection (PBI)


Dive into the research topics of 'Expected improvement of penalty-based boundary intersection for expensive multiobjective optimization'. Together they form a unique fingerprint.

Cite this