Loading...
10 results
Search Results
Now showing 1 - 10 of 10
- 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.
- 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.
- 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.
- Stopping rules effect on a derivative-free filter multistart algorithm for multilocal programmingPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.Multilocal programming aims to identify all the local solutions of constrained optimization problems. The purpose of this paper is to analyze the effect of stopping rules on the performance of a particular multistart method, which relies on a derivative-free local search procedure to converge to a solution, when solving multilocal optimization problems. The method herein presented implements the approximate descent direction method combined with a filter methodology to handle the constraints by forcing the local search towards the feasible region. Two stopping rules are tested on five classical multimodal problems.
- 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.
- 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.
- Stopping rules effect on a derivative-free filter multistart algorithm for multilocal programmingPublication . Fernandes, Florbela P.; Costa, M. Fernanda P.; Fernandes, Edite M.G.P.Multilocal programming aims to identify all the local solutions of constrained optimization problems. The purpose of this paper is to analyze the effect of stopping rules on the performance of a particular multistart method, which relies on a derivative-free local search procedure to converge to a solution, when solving multilocal optimization problems. The method herein presented implements the approximate descent direction method combined with a filter methodology to handle the constraints by forcing the local search towards the feasible region. Two stopping rules are tested on five classical multimodal problems.
- 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.
- Branch and bound based coordinate search filter algorithm for nonsmooth nonconvex mixed-integer nonlinear programming problemsPublication . 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.
- 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.