Browsing by Author "Costa, M. Fernanda P."
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- Assessment of a hybrid approach for nonconvex constrained MINLP problemsPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.A methodology to solve nonconvex constrained mixed-integer nonlinear programming (MINLP) problems is presented. A MINLP problem is one where some of the variables must have only integer values. Since in most applications of the industrial processes, some problem variables are restricted to take discrete values only, there are real practical problems that are modeled as nonconvex constrained MINLP problems. An efficient deterministic method for solving nonconvex constrained MINLP may be obtained by using a clever extension of Branch-and-Bound (B&B) method. When solving the relaxed nonconvex nonlinear programming subproblems 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 search space. To address this issue, we propose the use of a genetic algorithm to promote convergence to a global optimum of the relaxed nonconvex NLP subproblem. We present some numerical experiments with the proposed algorithm.
- A derivative-free filter driven multistart technique for global optimizationPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.A stochastic global optimization method based on a multistart strategy and a derivative-free filter local search for general constrained optimization is presented and analyzed. In the local search procedure, approximate descent directions for the constraint violation or the objective function are used to progress towards the optimal solution. The algorithm is able to locate all the local minima, and consequently, the global minimum of a multi-modal objective function. The performance of the multistart method is analyzed with a set of benchmark problems and a comparison is made with other methods.
- A deterministic-stochastic method for nonconvex MINLP problemsPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.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.
- Improving efficiency of a multistart with interrupted hooke-and-jeeves filter search for solving MINLP problemsPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Rocha, Ana Maria A.C.; Fernandes, Edite M.G.P.This paper addresses the problem of solving mixed-integer nonlinear programming (MINLP) problems by a multistart strategy that invokes a derivative-free local search procedure based on a filter set methodology to handle nonlinear constraints. A new concept of componentwise normalized distance aiming to discard randomly generated points that are sufficiently close to other points already used to invoke the local search is analyzed. A variant of the Hooke-and-Jeeves filter algorithm for MINLP is proposed with the goal of interrupting the iterative process if the accepted iterate falls inside an ϵ-neighborhood of an already computed minimizer. Preliminary numerical results are included.
- Interior point filter method for semi-infinite programming problemsPublication . Pereira, Ana I.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.Semi-infinite programming (SIP) problems can be efficiently solved by reduction-type methods. Here, we present a new reduction method for SIP, where the multi-local optimization is carried out with a stretched simulated annealing algorithm, the reduced (finite) problem is approximately solved by a Newton’s primal–dual interior point method that uses a novel twodimensional filter line search strategy to guarantee the convergence to a KKT point that is a minimizer, and the global convergence of the overall reduction method is promoted through the implementation of a classical two-dimensional filter line search. Numerical experiments with a set of well-known problems are shown.
- Interior point filter method to solve semi-infinite programming problemsPublication . Pereira, Ana I.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.We present a new reduction-type method for solving semi-infinite programming problems, where the multi-local optimization is carried out with a sequential simulated annealing algorithm, and the finite reduced problem is solved by an interior point method combined with a line search filter strategy to ensure the global convergence. Numerical experiments with a set of well-known problems are shown.
- Interrupted searches in the BBMCSFilter context for MINLP problemsPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.The BBMCSFilter method was developed to solve mixed integer nonlinear programming problems. This kind of problems have integer and continuous variables and they appear very frequently in process engineering problems. The objective of this work is to analyze the performance of the method when the coordinate searches are interrupted in the context of the multistart strategy. From the numerical experiments, we observed a reduction on the number of function evaluations and on the CPU time.
- Multilocal programming: a derivative-free filter multistart algorithmPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.Multilocal programming aims to locate all the local solutions of an optimization problem. A stochastic method based on a multistart strategy and a derivative-free filter local search for solving general constrained optimization problems is presented. The filter methodology is integrated into a coordinate search paradigm in order to generate a set of trial approximations that might be acceptable if they improve the constraint violation or the objective function value relative to the current one. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.
- Multiple solutions of mixed variable optimization by multistart hooke and jeeves filter methodPublication . 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.
- Multistart hooke and jeeves filter method for mixed variable optimizationPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.; Rocha, Ana Maria A.C.In this study, we propose an extended version of the Hooke and Jeeves algorithm that uses a simple heuristic to handle integer and/or binary variables and a filter set methodology to handle constraints. This proposal is integrated into a multistart method as a local solver and it is repeatedly called in order to compute different optimal solutions. Then, the best of all stored optimal solutions is selected as the global optimum. The performance of the new method is tested on benchmark problems. Its effectiveness is emphasized by a comparison with other well-known stochastic solvers.