Improving efficiency of a multistart with interrupted Hooke-and-Jeeves filter search for solving MINLP problems

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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 ϵ-neighborhood of an already computed minimizer. Preliminary numerical results are included.

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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 Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9786, pp. 345–358). Springer Verlag. https://doi.org/10.1007/978-3-319-42085-1_27

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