Abstract
This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are sufficiently close to other points already used to invoke the local search is analyzed. A variant of the Hooke-and-Jeeves filter algorithm for MINLP is proposed with the goal of interrupting the iterative process if the accepted iterate falls inside an \(\epsilon \)-neighborhood of an already computed minimizer. Preliminary numerical results are included.
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Acknowledgments
The authors wish to thank two anonymous referees for their comments and suggestions. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundação para a Ciência e Tecnologia, within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.
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Fernandes, F.P., Costa, M.F.P., Rocha, A.M.A.C., Fernandes, E.M.G.P. (2016). Improving Efficiency of a Multistart with Interrupted Hooke-and-Jeeves Filter Search for Solving MINLP Problems. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2016. ICCSA 2016. Lecture Notes in Computer Science(), vol 9786. Springer, Cham. https://doi.org/10.1007/978-3-319-42085-1_27
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DOI: https://doi.org/10.1007/978-3-319-42085-1_27
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