A trajectory-based method for mixed integer nonlinear programming problems

Terry-Leigh Oliphant () and M. Montaz Ali ()
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Terry-Leigh Oliphant: School of Computer Science and Applied Mathematics
M. Montaz Ali: School of Computer Science and Applied Mathematics

Journal of Global Optimization, 2018, vol. 70, issue 3, No 5, 623 pages

Abstract: Abstract A local trajectory-based method for solving mixed integer nonlinear programming problems is proposed. The method is based on the trajectory-based method for continuous optimization problems. The method has three phases, each of which performs continuous minimizations via the solution of systems of differential equations. A number of novel contributions, such as an adaptive step size strategy for numerical integration and a strategy for updating the penalty parameter, are introduced. We have shown that the optimal value obtained by the proposed method is at least as good as the minimizer predicted by a recent definition of a mixed integer local minimizer. Computational results are presented, showing the effectiveness of the method.

Keywords: Trajectory-based method; Mixed integer nonlinear programming; System of ordinary differential equations; Neighborhood; Local minimizer; Subproblem; Pattern search (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-017-0570-5

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