Global optimization
A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
Topographical global optimization
Recent advances in global optimization
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
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A new approach for topographical global minimization of a functionf(x), x ∈ A ⊂ R^n by using sampled points in A ispresented. The globally sampled points are firstly obtained by uniformrandom sampling or uniform sampling with threshold distances. The point withthe lowest function value is used as the nucleus atom to start a crystalgrowth process. A first triangular nucleus includes the nucleus atom and twonearest points. Sequential crystal growth is continued for which a pointnext closest to the nucleus atom is bonded to the crystal by attaching totwo nearest solidified points. A solidified point will be marked during thecrystal growth process if any of two connected points has a lower functionvalue. Upon completion of entire crystal growth process, all unmarked pointsare then used as starting points for subsequent local minimizations.Extension of the topographical algorithms to constrained problems isexercised by using penalty functions. Formulas for estimation on the numberof sampled points for problems with an assumed number of local minima areprovided. Results on three global minimization problems by two topographicalalgorithms are discussed.