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A trajectory-based method for mixed integer nonlinear programming problems. (English) Zbl 1393.90075
Summary: 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.
Reviewer: Reviewer (Berlin)
MSC:
90C11 Mixed integer programming
Software:
AlphaECP; OPTIMA
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