Loading...
5 results
Search Results
Now showing 1 - 5 of 5
- 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.
- 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.
- 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.
- 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.
- 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.