This chapter introduces readers to the world of continuous global optimization problems.We start with detailed definitions of the search space, admissible domain and objective function. The most conventional problem, which consists of finding all admissible points in which the objective function has its global extreme, is the basis of further considerations. The next problems concern finding local extremes. We also consider the approximate problems that allow finite accuracy of data representation. Much space is devoted to the definition of the basins of attraction of local isolated extremes and the problem of their approximate recognition. Next we introduce the scheme of population-oriented stochastic global optimization search. Two important instances: random walk and Pure Random Search are defined. We have focused on a more formal definition of populations (random samples) and the mathematical operations on them. Moreover, definitions that classify search possibilities and some kind of convergence are formulated and commented on. The chapter contains several computation examples, which show the potential skill of various genetic global optimization strategies by solving difficult continuous engineering problems.
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© 2007 Springer-Verlag Berlin Heidelberg
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Schaefer, R. (2007). Global optimization problems. In: Foundations of Global Genetic Optimization. Studies in Computational Intelligence, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73192-4_2
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DOI: https://doi.org/10.1007/978-3-540-73192-4_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73191-7
Online ISBN: 978-3-540-73192-4
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