Test Functions with Variable Attraction Regions for GlobalOptimization Problems

  • Authors:
  • M. Gaviano;D. Lera

  • Affiliations:
  • Mathematics Department, University of Cagliari, Cagliari, Italy (E-mail: Email: gaviano@vaxca1.unica.it, Email: lera@vaxca1.unica.it);Mathematics Department, University of Cagliari, Cagliari, Italy (E-mail: Email: gaviano@vaxca1.unica.it, Email: lera@vaxca1.unica.it)

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 1998

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Abstract

Functions with local minima and size of their ’regionof attraction‘ known a priori, are often needed for testing the performanceof algorithms that solve global optimization problems. In this paperwe investigate a technique for constructing test functions for globaloptimization problems for which we fix a priori:(i) the problem dimension,(ii) the number of local minima,(iii) the local minima points,(iv) the function values of the local minima.Further, the size of the region of attraction of each local minimum may bemade large or small.The technique consists of first constructing a convex quadratic function andthen systematically distorting selected parts of this function so as tointroduce local minima.