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Derivative-free Methods for Mixed-Integer Constrained Optimization Problems

G. Liuzzi(giampaolo.liuzzi***at***iasi.cnr.it)
S. Lucidi(lucidi***at***dis.uniroma1.it)
F. Rinaldi(rinaldi***at***math.unipd.it)

Abstract: Methods which do not use any derivative information are becoming popular among researchers, since they allow to solve many real-world engineering problems. Such problems are frequently characterized by the presence of discrete variables which can further complicate the optimization process. In this paper, we propose derivative-free algorithms for solving continuously differentiable Mixed Integer NonLinear Programming problems with general nonlinear constraints and explicit handling of bound constraints on the problem variables. We use an exterior penalty approach to handle the general nonlinear constraints and a local search approach to take into account the presence of discrete variables. We show that the proposed algorithms globally converge to points satisfying different necessary optimality conditions. We report a computational experience and a comparison with a well-known derivative-free optimization software package, i.e., NOMAD, on a set of test problems. Furthermore, we employ the proposed methods and NOMAD to solve a real problem concerning the optimal design of an industrial electric motor. This allows to show that the method converging to the better extended stationary points obtains the best solution also from an applicative point of view

Keywords: Mixed-integer nonlinear programming; derivative-free optimization; nonlinear constrained optimization

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Applications -- OR and Management Sciences


Download: [Postscript][PDF]

Entry Submitted: 03/07/2014
Entry Accepted: 03/07/2014
Entry Last Modified: 03/07/2014

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