Browsing by Author "Fernandes, Edite M.G.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.
- 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.
- Branch-and-bound reduction type method for semi-in finite programmingPublication . Pereira, Ana I.; 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 multi-local branch-and-bound method, the reduced (finite) problem is approximately solved by an interior point method, and the global convergence is promoted through a two-dimensional filter line search. Numerical experiments with a set of well-known problems are shown.
- Caracterização da função de penalidade exponencial na resolução de problemas de programação semi-infinitaPublication . Pereira, Ana I.; Fernandes, Edite M.G.P.Os problemas de programação semi-infinita (PSI) são caracterizados por terem um conjunto finito de variáveis e um número infinito de restrições. A classe de métodos de redução é baseada na ideia que, sob certas condições, é possível substituir as infinitas restrições por um conjunto finito de restrições que, localmente, é suficiente para definir a região admissível do problema PSI. Neste trabalho é proposto um novo método de redução que combina o método simulated annealing para a optimização multilocal, e o método de penalidade para a optimização não linear com restrições.
- Comparative study of penalty simulated annealing methods for multiglobal programmingPublication . Pereira, Ana I.; Fernandes, Edite M.G.P.In a multiglobal optimization problem we aim to find all the global solutions of a constrained nonlinear programming problem where the objective function is multimodal. This class of global optimization problems is very important and frequently encountered in engineering applications, such as, process synthesis, design and control in chemical engineering. The most common method for solving this type of problems uses a local search method to refine a set of approximations, which are obtained by comparing objective function values at points of a predefined mesh. This type of method can be very expensive numerically. On the other hand, the success of local search methods depends on the starting point being at the neighbourhood of a solution. Stochastic methods are appropriate alternatives to find global solutions, in which convergence to a global solution can be guaranteed, with probability one. This is the case of the simulated annealing (SA) method. To compute the multiple solutions, a function stretching technique that transforms the objective function at each step is herein combined with SA to be able to force, step by step, convergence to each one of the required global solutions. The constraints of the problem are dealt with a penalty technique. This technique transforms the constrained problem into a sequence of unconstrained problems by penalizing the objective function when constraints are violated. Numerical experiments are shown with three penalty functions.
- Comparative study of penalty simulated annealing methods for multiglobal programmingPublication . Pereira, Ana I.; Fernandes, Edite M.G.P.In a multiglobal optimization problem we aim to find all the global solutions of a constrained nonlinear programming problem where the objective function is multimodal. This class of global optimization problems is very important and frequently encountered in engineering applications, such as, process synthesis, design and control in chemical engineering. The most common method for solving this type of problems uses a local search method to refine a set of approximations, which are obtained by comparing objective function values at points of a predefined mesh. This type of method can be very expensive numerically. On the other hand, the success of local search methods depends on the starting point being at the neighbourhood of a solution. Stochastic methods are appropriate alternatives to find global solutions, in which convergence to a global solution can be guaranteed, with probability one. This is the case of the simulated annealing (SA) method. To compute the multiple solutions, a function stretching technique that transforms the objective function at each step is herein combined with SA to be able to force, step by step, convergence to each one of the required global solutions. The constraints of the problem are dealt with a penalty technique. This technique transforms the constrained problem into a sequence of unconstrained problems by penalizing the objective function when constraints are violated. Numerical experiments are shown with three penalty functions.
- Constrained multi-global optimization using a penalty stretched simulated annealing frameworkPublication . Pereira, Ana I.; Fernandes, Edite M.G.P.This paper presents a new simulated annealing algorithm to solve constrained multi-global optimization problems. To compute all global solutions in a sequential manner, we combine the function stretching technique with the adaptive simulated annealing variant. Constraint-handling is carried out through a nondifferentiable penalty function. To benchmark our penalty stretched simulated annealing algorithm we solve a set of well-known problems. Our preliminary numerical results show that the algorithm is promising.
- 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.
- Desempenho do método de Newton truncado em optimização não linear sem restriçõesPublication . Pereira, Ana I.; Fernandes, Edite M.G.P.Newton's method for unconstrained nonlinear optimization can be a demanding iterative process. Combining Krylov iterative methods with different termination criteria for the inexact solving of the Newton system, a linear or a curvilinear search technique and monotone and nonmonotone globalization criteria, we manage to define a set of truncated Newton algorithms. Computational experiments were carried out in order to evaluate the performance of the defined algorithms. O método de Newton para a resolução de um problema de optimização não linear sem restrições pode originar um processo iterativo exigente. Combinando métodos iterativos de Krylov com diferentes critérios de terminação para a resolução inexacta do sistema Newton, uma técnica de procura que pode ser linear ou curvilínea e critérios de globalização monótonos e não monótonos, conseguimos definir um conjunto de algoritmos do método de Newton truncado. Foram realizadas experiências computacionais para avaliar o desempenho dos diferentes algoritmos.
- 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.