Penalty functions and two-step selection procedure based DIRECT-type algorithm for constrained global optimization
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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.
KeywordsDIRECT-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.
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.
- Costa MFP, Rocha AMAC, Fernandes EMGP (2017) Filter-based direct method for constrained global optimization. Journal of Global Optimization in Press. https://doi.org/10.1007/s10898-017-0596-8
- Finkel DE (2005) Global optimization with the Direct algorithm. Ph.D. thesis, North Carolina State UniversityGoogle Scholar
- Gablonsky JM (2001) Modifications of the Direct algorithm. Ph.D. thesis, North Carolina State UniversityGoogle Scholar
- Hedar A (2005) Test functions for unconstrained global optimization. http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO.htm. Online; accessed: 2017-03-22
- Jones DR (2001) The Direct global optimization algorithm. In: Floudas CA, Pardalos PM (eds) The encyclopedia of optimization. Kluwer Academic Publishers, Dordrect, pp 431–440Google Scholar
- Na J, Lim Y, Han C (2017) A modified DIRECT algorithm for hidden constraints in an LNG process optimization. Energy 126(C):488–500Google Scholar
- Stripinis L, Paulavičius R, žilinskas J (2018) Improved scheme for selection of potentially optimal hyper-rectangles in direct. Optim Lett 12(7):1699–1712. https://doi.org/10.1007/s11590-017-1228-4
- Stripinis L, Paulavičius R (2018) DIRECTLib – a library of global optimization problems for DIRECT-type methods, v1.1. https://doi.org/10.5281/zenodo.1403547
- Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. KanGAL, pp 251–256Google Scholar