| Name: | Description: | Size: | Format: | |
|---|---|---|---|---|
| 162.56 KB | Adobe PDF |
Advisor(s)
Abstract(s)
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.
Description
Keywords
Mixed-Integer programming Branch-and-bound Stochastic method
Citation
Fernandes, Florbela P.; Fernandes, Edite M. G. P.; Costa, Maria F.P. (2010). A deterministic-stochastic method for nonconvex MINLP problems. In Proceedings of 2nd International Conference on Engineering Optimization. Lisboa, Portugal. ISBN: 978‐989‐96264‐ 3‐0.