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Branch and bound based coordinate search filter algorithm for nonsmooth nonconvex mixed-integer nonlinear programming problems

Publication . Fernandes, Florbela P.; Costa, Fernanda P.M.; Fernandes, Edite M.G.P.

A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function. This kind of problem appears in a wide range of real applications and is very difficult to solve. The difficulties are due to the nonlinearities of the functions in the problem and the integrality restrictions on some variables. When they are nonconvex then they are the most difficult to solve above all. We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy. To solve the relaxed subproblems at each node of the branch and bound tree search, an algorithm based on a multistart strategy with a coordinate search filter methodology is implemented. The produced numerical results show the robustness of the proposed methodology.

2014Conference paper

Open access

Global asymptotic stability of nonautonomous Cohen-Grossberg neural network models with infinite delays

Publication . Esteves, Salete; Oliveira, José J.

For a general Cohen-Grossberg neural network model with potentially unbounded time varying coefficients and infinite distributed delays, we give sufficient conditions for its global asymptotic stability. The model studied is general enough to include, as subclass, the most of famous neural network models such as Cohen-Grossberg, Hopfield, and bidirectional associative memory. Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As illustrated, the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications.

2015Journal article

Restricted access

Multiple solutions of mixed variable optimization by multistart hooke and jeeves filter method

Publication . Costa, M. Fernanda P.; Fernandes, Florbela P.; Fernandes, Edite M.G.P.; Rocha, Ana Maria A.C.

In this study, we propose a multistart method based on an extended version of the Hooke and Jeeves (HJ) algorithm for computing multiple solutions of mixed variable optimization problems. The inequality and equality constraints of the problem are handled by a ﬁlter set methodology. The basic ideas present in the HJ algorithm, namely the exploratory and pattern moves, are extended to consider two objective functions and to handle continuous and integer variables simultaneously. This proposal is integrated into a multistart method as a local search procedure that is repeatedly invoked to converge to diﬀerent global and non-global optimal solutions starting from randomly generated points. To avoid repeated convergence to previously computed solutions, the concept of region of attraction of an optimizer is implemented. The performance of the new method is tested on benchmark problems. Its eﬀectiveness is emphasized by a comparison with a well-known solver.

2014Journal article

Open access