Derivative-Free Methods for Mixed-Integer Constrained Optimization Problems

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 NonLinearProgrammingproblemswith 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 comparisonwith awell-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. G. Liuzzi (B) Istituto di Analisi dei Sistemi ed Informatica (IASI) “A.Ruberti”, CNR, Viale Manzoni 30, 00185 Rome, Italy e-mail: [email protected] S. Lucidi Dipartimento di Informatica e Sistemistica “A. Ruberti”, “Sapienza” Università di Roma, Via Ariosto 25, 00185 Rome, Italy e-mail: [email protected] F. Rinaldi Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padua, Italy e-mail: [email protected]