Abstract
Functions with local minima and size of their ‘region of attraction’ known a priori, are often needed for testing the performance of algorithms that solve global optimization problems. In this paper we investigate a technique for constructing test functions for global optimization 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 be made large or small. The technique consists of first constructing a convex quadratic function and then systematically distorting selected parts of this function so as to introduce local minima.
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Gaviano, M., Lera, D. Test Functions with Variable Attraction Regions for Global Optimization Problems. Journal of Global Optimization 13, 207–223 (1998). https://doi.org/10.1023/A:1008225728209
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DOI: https://doi.org/10.1023/A:1008225728209