Abstract
All techniques presented in the previous chapters are dealing with pure continuous objective functions, therefore we now extend the geometric branch-andbound algorithm to mixed continuous and combinatorial optimization problems.We are not only taking continuous variables into account but also some combinatorial variables. The extended algorithm is suggested in Section 6.1 and the rate of convergence again leads to a general convergence theory as shown in Section 6.2. Next, in Section 6.3 we derive some mixed bounding operations using techniques already discussed in Chapter 3 for pure continuous problems. Moreover, we show in Section 6.4 how to find exact optimal solutions under certain conditions which is demonstrated on some facility location problems in Section 6.5. Finally, we conclude the chapter with some numerical results in Section 6.6.
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© 2012 Springer Science+Business Media, LLC
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Scholz, D. (2012). Extension for mixed combinatorial problems. In: Deterministic Global Optimization. Springer Optimization and Its Applications(), vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1951-8_6
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DOI: https://doi.org/10.1007/978-1-4614-1951-8_6
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-1950-1
Online ISBN: 978-1-4614-1951-8
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