An efficient surrogate-assisted quasi-affine transformation evolutionary algorithm for expensive optimization problems

Nengxian Liu, Jeng Shyang Pan, Chaoli Sun, Shu Chuan Chu

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)


Many real-world engineering optimization problems usually need a lot of time for function evaluations or have massive decision variables. It is still a big challenge to address these problems effectively. Recently, surrogate-assisted meta-heuristic algorithms have drawn increasing attention, and have shown their potential to deal with such expensive complex optimization problems. In this study, a surrogate-assisted quasi-affine transformation evolutionary (SA-QUATRE) algorithm is proposed to further enhance the optimization efficiency and effectiveness. In SA-QUATRE, the global and the local surrogate models are effectively combined for fitness estimation. The global surrogate model is built based on all data in the database for global exploration. While, the local surrogate model is constructed with a predefined number of top best samples for local exploitation. Meanwhile, both the generation- and individual-based evolution controls as well as a top best restart strategy are incorporated in the global and the local searches. To enhance the exploration and the exploitation capabilities, the global search uses the mean of the population to be evaluated with the expensive real fitness function, while the local search chooses the individual with the best fitness according to the surrogate for real evaluation. The proposed SA-QUATRE is compared with five state-of-the-art optimization approaches over seven commonly used benchmark functions with dimensions varying from 10 to 100. Moreover, the proposed SA-QUATRE is also applied to solve the tension/compression spring design problem. The experimental results show that SA-QUATRE is promising for optimizing computationally expensive problems.

Original languageEnglish
Article number106418
Number of pages12
JournalKnowledge-Based Systems
Publication statusPublished - 17 Dec 2020
Externally publishedYes


  • Expensive problems
  • Global surrogate
  • Local surrogate
  • Surrogate-assisted


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