Algorithm 829: Software for generation of classes of test functions with known local and global minima for global optimization

  • Authors:

  • Marco Gaviano;Dmitri E. Kvasov;Daniela Lera;Yaroslav D. Sergeyev

  • Affiliations:

  • Università di Cagliari, Cagliari, Italy;Università di Roma "La Sapienza" and University of Nizhni Novgorod, Italy;Università di Cagliari, Cagliari, Italy;Università della Calabria and University of Nizhni Novgorod, Italy

  • Venue:
  • ACM Transactions on Mathematical Software (TOMS)
  • Year:
  • 2003

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Abstract

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.