Open AccessA GLOBAL OPTIMIZATION METHOD BASED ON THE REDUCED SIMPLICIAL STATISTICAL MODEL
Author(s) -
Antanas Žilinskas,
Julius Žilinskas
Publication year - 2011
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2011.602988
Subject(s) - simplex , subdivision , mathematics , simplex algorithm , mathematical optimization , function (biology) , algorithm , cover (algebra) , statistical model , global optimization , point (geometry) , computer science , linear programming , combinatorics , statistics , mechanical engineering , geometry , archaeology , evolutionary biology , biology , engineering , history
A simplicial statistical model of multimodal functions is used to construct a global optimization algorithm. The search for the global minimum in the multidimensional space is reduced to the search over the edges of simplices covering the feasible region combined with the refinement of the cover. The refinement is performed by subdivision of selected simplices taking into account the point where the objective function value has been computed at the current iteration. For the search over the edges the one-dimensional P-algorithm based on the statistical smooth function model is adapted. Differently from the recently proposed algorithm here the statistical model is used for modelling the behaviour of the objective function not over the whole simplex but only over its edges. Testing results of the proposed algorithm are included.