A hybrid of the simplicial partition-based Bayesian global search with the local descent

We propose a global optimization algorithm hybridizing a version of Bayesian global search with local minimization. The implementation of Bayesian algorithm is based on the simplician partition of the feasible region. Our implementation is free from the typical computational complexity of the standard implementations of Bayesian algorithms. The local minimization counterpart improves the efficiency of search in the indicated potential basins of global minimum. The performance of the proposed algorithm is illustrated by the results of a numerical experiment.

[1]  Yaroslav D. Sergeyev,et al.  Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization , 2016, J. Optim. Theory Appl..

[2]  Robert Hooke,et al.  `` Direct Search'' Solution of Numerical and Statistical Problems , 1961, JACM.

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

[4]  Romas Baronas,et al.  Optimal design of amperometric biosensors applying multi-objective optimization and decision visualization , 2016 .

[5]  Daniel Scholz Deterministic Global Optimization: Geometric Branch-and-bound Methods and their Applications , 2011 .

[6]  Yaroslav D. Sergeyev,et al.  Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization , 2003, TOMS.

[7]  Antanas Zilinskas,et al.  Selection of a covariance function for a Gaussian random field aimed for modeling global optimization problems , 2019, Optim. Lett..

[8]  Y. D. Sergeyev,et al.  Global Optimization with Non-Convex Constraints - Sequential and Parallel Algorithms (Nonconvex Optimization and its Applications Volume 45) (Nonconvex Optimization and Its Applications) , 2000 .

[9]  Antanas Zilinskas On the worst-case optimal multi-objective global optimization , 2013, Optim. Lett..

[10]  Yaroslav D. Sergeyev,et al.  A deterministic global optimization using smooth diagonal auxiliary functions , 2015, Commun. Nonlinear Sci. Numer. Simul..

[11]  A. Zilinskas,et al.  On an Asymptotic Property of a Simplicial Statistical Model of Global Optimization , 2015 .

[12]  Antanas Zilinskas,et al.  Stochastic Global Optimization: A Review on the Occasion of 25 Years of Informatica , 2016, Informatica.

[13]  Clara Pizzuti,et al.  Local tuning and partition strategies for diagonal GO methods , 2003, Numerische Mathematik.

[14]  François Laviolette,et al.  Domain-Adversarial Training of Neural Networks , 2015, J. Mach. Learn. Res..

[15]  James M. Calvin,et al.  Bi-objective decision making in global optimization based on statistical models , 2019, J. Glob. Optim..

[16]  Antanas Žilinskas,et al.  A hybrid of Bayesian approach based global search with clustering aided local refinement , 2019, Commun. Nonlinear Sci. Numer. Simul..

[17]  Antonio Candelieri,et al.  Bayesian Optimization and Data Science , 2019, SpringerBriefs in Optimization.

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

[19]  Yaroslav D. Sergeyev,et al.  Parallel Information Algorithm with Local Tuning for Solving Multidimensional GO Problems , 1999, J. Glob. Optim..

[20]  Matthew W. Hoffman,et al.  A General Framework for Constrained Bayesian Optimization using Information-based Search , 2015, J. Mach. Learn. Res..

[21]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[22]  Rabiatul Adwiya,et al.  Perancangan Permainan Edukasi Peduli Jajanan Sehat , 2017 .

[23]  Carl Tim Kelley,et al.  Iterative methods for optimization , 1999, Frontiers in applied mathematics.

[24]  H. Kushner A versatile stochastic model of a function of unknown and time varying form , 1962 .

[25]  Antanas Zilinskas,et al.  Interval Arithmetic Based Optimization in Nonlinear Regression , 2010, Informatica.

[26]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[27]  Yaroslav D. Sergeyev,et al.  An information global minimization algorithm using the local improvement technique , 2010, J. Glob. Optim..

[28]  Julius Žilinskas,et al.  P-algorithm based on a simplicial statistical model of multimodal functions , 2010 .

[29]  A. Zilinskas,et al.  Including the derivative information into statistical models used in global optimization , 2019 .

[30]  Antanas Zilinskas,et al.  Performance of global random search algorithms for large dimensions , 2018, J. Glob. Optim..

[31]  Deterministic Global Optimization , 2012 .

[32]  James M. Calvin,et al.  On convergence rate of a rectangular partition based global optimization algorithm , 2018, J. Glob. Optim..