Algorithm 829

Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization. A procedure for generating non-differentiable, continuously differentiable, and twice continuously differentiable classes of test functions for multiextremal multidimensional box-constrained global optimization is presented. Each test class consists of 100 functions. Test functions are generated by defining a convex quadratic function systematically distorted by polynomials in order to introduce local minima. To determine a class, the user defines the following parameters: (i) problem dimension, (ii) number of local minima, (iii) value of the global minimum, (iv) radius of the attraction region of the global minimizer, (v) distance from the global minimizer to the vertex of the quadratic function. Then, all other necessary parameters are generated randomly for all 100 functions of the class. Full information about each test function including locations and values of all local minima is supplied to the user. Partial derivatives are also generated where possible. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 38 articles , 1 standard article )

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  1. Žilinskas, Antanas; Gimbutienė, Gražina: A hybrid of Bayesian approach based global search with clustering aided local refinement (2019)
  2. Gimbutas, Albertas; Žilinskas, Antanas: An algorithm of simplicial Lipschitz optimization with the bi-criteria selection of simplices for the bi-section (2018)
  3. Kvasov, Dmitri E.; Mukhametzhanov, Marat S.: Metaheuristic vs. deterministic global optimization algorithms: the univariate case (2018)
  4. Larson, Jeffrey; Wild, Stefan M.: Asynchronously parallel optimization solver for finding multiple minima (2018)
  5. Lera, Daniela; Sergeyev, Yaroslav D.: GOSH: derivative-free global optimization using multi-dimensional space-filling curves (2018)
  6. Beiranvand, Vahid; Hare, Warren; Lucet, Yves: Best practices for comparing optimization algorithms (2017)
  7. Fok, Ricky; An, Aijun; Wang, Xiaogong: Geodesic and contour optimization using conformal mapping (2017)
  8. Liu, Qunfeng; Yang, Guang; Zhang, Zhongzhi; Zeng, Jinping: Improving the convergence rate of the DIRECT global optimization algorithm (2017)
  9. Long, Qiang; Wu, Changzhi; Wang, Xiangyu; Wu, Zhiyou: A modified quasisecant method for global optimization (2017)
  10. Larson, Jeffrey; Wild, Stefan M.: A batch, derivative-free algorithm for finding multiple local minima (2016)
  11. Lampariello, F.; Liuzzi, G.: A filling function method for unconstrained global optimization (2015)
  12. Liu, Haitao; Xu, Shengli; Ma, Ying; Wang, Xiaofang: Global optimization of expensive black box functions using potential Lipschitz constants and response surfaces (2015)
  13. Liu, Qunfeng; Zeng, Jinping; Yang, Gang: MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems (2015)
  14. Sergeyev, Yaroslav D.; Kvasov, Dmitri E.: A deterministic global optimization using smooth diagonal auxiliary functions (2015)
  15. Paulavičius, Remigijus; Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Žilinskas, Julius: Globally-biased disimpl algorithm for expensive global optimization (2014)
  16. Kvasov, D. E.; Sergeyev, Ya. D.: Lipschitz global optimization methods in control problems (2013)
  17. Pintér, János D.; Kampas, Frank J.: Benchmarking nonlinear optimization software in technical computing environments (2013)
  18. Aguiar e Oliveira, Hime jun.; Ingber, Lester; Petraglia, Antonio; Rembold Petraglia, Mariane; Soares Machado, Maria Augusta: Stochastic global optimization and its applications with fuzzy adaptive simulated annealing (2012)
  19. Kvasov, Dmitri E.; Sergeyev, Yaroslav D.: Lipschitz gradients for global optimization in a one-point-based partitioning scheme (2012)
  20. Rönkkönen, Jani; Li, Xiaodong; Kyrki, Ville; Lampinen, Jouni: A framework for generating tunable test functions for multimodal optimization (2011) ioport

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