Influence of Lipschitz Bounds on the Speed of Global Optimization

Paulavičius, Remigijus; Žilinskas, Julius

doi:10.3846/20294913.2012.661170

Cited by 6 publications

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References 22 publications

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“…Two of these global solvers (TOMLAB/GLCCLUSTER and MCS [23,31]) are based on the DIRECT (DIviding RECTangle) algorithm [24]. The DIRECT algorithm is a modification of standard Lipschitzian approaches [10,11,19,20,22,27,[34][35][36][38][39][40]43,44] eliminating the need to specify a Lipschitz constant. Due to its simplicity, DIRECT has been used to solve many engineering optimization problems [1][2][3]6,9,17,18,28].…”

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confidence: 99%

Advantages of simplicial partitioning for Lipschitz optimization problems with linear constraints

Paulavičius

Žilinskas

2014

Optim Lett

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The well known DIRECT (DIviding RECTangles) algorithm for global optimization requires bound constraints on variables and does not naturally address additional linear or nonlinear constraints. A feasible region defined by linear constraints may be covered by simplices, therefore simplicial partitioning may tackle linear constraints in a very subtle way. In this paper we demonstrate this advantage of simplicial partitioning by applying a recently proposed deterministic simplicial partitions based DISIMPL algorithm for optimization problems defined by general linear constraints (Lc-DISIMPL). An extensive experimental investigation reveals advantages of this approach to such problems comparing with different constraint-handling methods, proposed for use with DIRECT. Furthermore the Lc-DISIMPL algorithm gives very competitive results compared to a derivative-free particle swarm algorithm (PSwarm) which was previously shown to give very promising results. Moreover, DISIMPL guarantees the convergence to the global solution, whereas the PSwarm algorithm sometimes fails to converge to the global minimum.

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