Penalty functions and two-step selection procedure based DIRECT-type algorithm for constrained global optimization

  • Linas Stripinis
  • Remigijus PaulavičiusEmail author
  • Julius Žilinskas
Research Paper


Applied optimization problems often include constraints. Although the well-known derivative-free global-search DIRECT algorithm performs well solving box-constrained global optimization problems, it does not naturally address constraints. In this article, we develop a new algorithm DIRECT-GLce for general constrained global optimization problems incorporating two-step selection procedure and penalty function approach in our recent DIRECT-GL algorithm. The proposed algorithm effectively explores hyper-rectangles with infeasible centers which are close to boundaries of feasibility and may cover feasible regions. An extensive experimental investigation revealed the potential of the proposed approach compared with other existing DIRECT-type algorithms for constrained global optimization problems, including important engineering problems.


DIRECT-type algorithm DIRECT-type constraint-handling Nonconvex optimization Derivative-free optimization 



The authors would like to thank all anonymous referees for their valuable comments and suggestions to improve the paper.

Funding information

The research work of R. Paulavičius and L. Stripinis was funded by a Grant (No. P-MIP-17-60) from the Research Council of Lithuania.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Vilnius University Institute of Data Science and Digital TechnologiesVilniusLithuania

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