Browsing by Author "Costa, Maria F.P."
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- A deterministic-stochastic method for nonconvex MINLP problemsPublication . Fernandes, Florbela P.; Fernandes, Edite M.G.P.; Costa, Maria F.P.A mixed-integer programming problem is one where some of the variables must have only integer values. Although some real practical problems can be solved with mixed-integer linear methods, there are problems occurring in the engineering area that are modelled as mixed-integer nonlinear programming (MINLP) problems. When they contain nonconvex functions then they are the most difficult of all since they combine all the difficulties arising from the two sub-classes: mixed-integer linear programming and nonconvex nonlinear programming (NLP). Efficient deterministic methods for solving MINLP are clever combinations of Branch-and-Bound (B&B) and Outer-Approximations classes. When solving nonconvex NLP relaxation problems that arise in the nodes of a tree in a B&B algorithm, using local search methods, only convergence to local optimal solutions is guaranteed. Pruning criteria cannot be used to avoid an exhaustive search in the solution space. To address this issue, we propose the use of a simulated annealing algorithm to guarantee convergence, at least with probability one, to a global optimum of the nonconvex NLP relaxation problem. We present some preliminary tests with our algorithm.
- Multistart coupled with a derivative-free filter local search for locating multiple solutionsPublication . Fernandes, Florbela P.; Pereira, Ana I.; Costa, Maria F.P.; Fernandes, Edite M.G.P.A multistart technique coupled with a derivative-free lter local search algorithm for locating all the optimal solutions of a nonconvex constrained optimization is presented. To reach a fast convergence to the optimal solutions, the local search procedure is based on descent directions. The lter-set concept is introduced to handle the constraints of the problem. The generated direction vector is descent for the objective function if the sample point is feasible; otherwise, it is descent for the constraint violation. Numerical experiments with benchmark problems are reported and a comparison with other stochastic methods is included.
- Numerical experiments with nonconvex MINLP problemsPublication . Fernandes, Florbela P.; Costa, Maria F.P.; Fernandes, Edite M.G.P.We present a methodology to solve nonconvex Mixed-Integer Nonlinear Programming problems, that combines the Branch-and-Bound and simulated annealing type methods, which was implemented in MATLAB. A set of benchmark functions with simple bounds and different dimensions was used to analyze its practical behaviour. We exhibit computational results showing the good performance of the method.
- Overview on mixed integer nonlinear programming problemsPublication . Fernandes, Florbela P.; Costa, Maria F.P.; Fernandes, Edite M.G.P.Many optimization problems involve integer and continuous variables that can be modeled as mixed integer nonlinear programming (MINLP) problems. This has led to a wide range of applications, in particular in some engineering areas. Here, we provide a brief overview on MINLP, and present a simple idea for a future nonconvex MINLP solution technique.
- Reduction method with multistart technique for semi-infinite programming problemsPublication . Pereira, Ana I.; Fernandes, Florbela P.; Costa, Maria F.P.; Fernandes, Edite M.G.P.Semi-infinite programming problems can be efficiently solved by reduction type methods. In this work a new global reduction method for semi-infinite programming is presented. The multilocal optimization is carried out with a multistart technique and the reduced problem is approximately solved by a primal-dual interior point method combined with a two-dimensional filter line search strategy. The filter strategy is used to promote the global convergence of the algorithm. Numerical experiments with a set of well-known problems are shown and comparisons with other methods are presented.