A global optimization algorithm for simulation-based problems via the extended DIRECT scheme

This article presents a global optimization algorithm via the extension of the DIviding RECTangles (DIRECT) scheme to handle problems with computationally expensive simulations efficiently. The new optimization strategy improves the regular partition scheme of DIRECT to a flexible irregular partition scheme in order to utilize information from irregular points. The metamodelling technique is introduced to work with the flexible partition scheme to speed up the convergence, which is meaningful for simulation-based problems. Comparative results on eight representative benchmark problems and an engineering application with some existing global optimization algorithms indicate that the proposed global optimization strategy is promising for simulation-based problems in terms of efficiency and accuracy.

[1]  C. T. Kelley,et al.  A Locally-Biased form of the DIRECT Algorithm , 2001, J. Glob. Optim..

[2]  Kenneth Holmström,et al.  Global Optimization Using the DIRECT Algorithm in Matlab , 1999 .

[3]  Erik Kjeang,et al.  Modification of DIRECT for high-dimensional design problems , 2014 .

[4]  G. G. Wang,et al.  Design Space Reduction for Multi-Objective Optimization and Robust Design Optimization Problems , 2004 .

[5]  B. Shubert.  A Sequential Method Seeking the Global Maximum of a Function , 1972 .

[6]  G. Venter,et al.  An algorithm for fast optimal Latin hypercube design of experiments , 2010 .

[7]  Arnold Neumaier,et al.  Global Optimization by Multilevel Coordinate Search , 1999, J. Glob. Optim..

[8]  Andrew D. Back,et al.  Radial Basis Functions , 2001 .

[9]  S. Filizadeh,et al.  A surrogate-model based multi-modal optimization algorithm , 2011 .

[10]  Zuomin Dong,et al.  Trends, features, and tests of common and recently introduced global optimization methods , 2010 .

[11]  E. S. Siah,et al.  Fast parameter optimization of large-scale electromagnetic objects using DIRECT with Kriging metamodeling , 2004, IEEE Transactions on Microwave Theory and Techniques.

[12]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[13]  T. Simpson,et al.  Fuzzy clustering based hierarchical metamodeling for design space reduction and optimization , 2004 .

[14]  R. Grandhi,et al.  A global structural optimization technique using an interval method , 2001 .

[15]  Daniel E. Finkel,et al.  Global optimization with the direct algorithm , 2005 .

[16]  Ernesto P. Adorio,et al.  MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization , 2005 .

[17]  Shapour Azarm,et al.  An accumulative error based adaptive design of experiments for offline metamodeling , 2009 .

[18]  G. Gary Wang,et al.  Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions , 2010 .

[19]  Yaroslav D. Sergeyev,et al.  Global Search Based on Efficient Diagonal Partitions and a Set of Lipschitz Constants , 2006, SIAM J. Optim..

[20]  G. Gary Wang,et al.  Review of Metamodeling Techniques in Support of Engineering Design Optimization , 2007, DAC 2006.

[21]  Yaroslav D. Sergeyev,et al.  A univariate global search working with a set of Lipschitz constants for the first derivative , 2009, Optim. Lett..

[22]  Haitao Liu,et al.  A Robust Error-Pursuing Sequential Sampling Approach for Global Metamodeling Based on Voronoi Diagram and Cross Validation , 2014 .

[23]  Christine A. Shoemaker,et al.  Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions , 2005, J. Glob. Optim..

[24]  Z. Dong,et al.  Metamodelling and search using space exploration and unimodal region elimination for design optimization , 2010 .

[25]  Zuomin Dong,et al.  Hybrid and adaptive meta-model-based global optimization , 2012 .

[26]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[27]  G. G. Wang,et al.  Mode-pursuing sampling method for global optimization on expensive black-box functions , 2004 .