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A decomposition-based solution method for stochastic mixed integer nonlinear programs

4OR 2006年第4期4卷 343-346页

作者： Bruni, Maria Elena Dipartimento di Elettronica Informatica e Sistemistica Università degli Studi della Calabria 87030 Rende (CS) Italy

This is a summary of the main results presented in the author's PhD thesis, supervised by D. Conforti and P. Beraldi and defended on March 2005. The thesis, written in English, is available from the author upon request. It describes one of the very few existing implementations of a method for solving stochastic mixed integer nonlinear programming problems based on deterministic global optimization. In order to face the computational challenge involved in the solution of such multi-scenario nonconvex problems, a branch and bound approach is proposed that exploits the peculiar structure of stochastic programming problem. © Springer-Verlag 2006.

关键词： Cutting and packing mixed integer nonlinear problems Stochastic programming

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mixed integer programming for a special logic constrained optimal control problem

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MATHEMATICAL PROGRAMMING 2005年第2期103卷 309-333页

作者： Preda, D Noailles, J IRIT ENSEEIHT F-31071 Toulouse France

Integrating logical constraints into optimal control problems is not an easy task. In fact, optimal control problems are usually continuous while logical constraints are naturally expressed by integer (binary) variables. In this article we are interested is a particular form of an LQR optimal control problem: the energy (control L-2 norm) is to be minimized, system dynamic is linear and logical constraints on the control use are to be fulfilled. Even if the starting continuous problem is not a complicated one, difficulties arise when integrating the additional logical constraints. First, we will present two different ways of modeling the problem, both of them leading us to mixed integer problems. Furthermore, algorithms (Generalized Outer Approximation, Benders Decomposition and Branch and Cut) are applied on each model and results analyzed. We also present a Benders Decomposition algorithm variant that is adapted to our problem (taking into account its particular form) and we will conclude by looking at the optimal solutions obtained in an interesting physical example: the harmonic spring.

关键词： mixed integer Quadratic problems mixed integer nonlinear problems optimal control logical constraints decision variables

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