F. Stoican, Prodan, I., and Olaru, S., “
On the hyperplanes arrangements in mixed-integer techniques”, in
Proceedings of the 30th American Control Conference, San Francisco, California, USA, 2011, p. 1898–1903.
AbstractThis paper is concerned with the improved constraints handling in mixed-integer optimization problems. The novel element is the reduction of the number of binary variables
used for expressing the complement of a convex (polytopic) region. As a generalization, the problem of representing the complement of a possibly non-connected union of such convex sets is detailed. In order to illustrate the benefits of the proposed improvements, a practical implementation, the problem of obstacle avoidance using receding horizon optimization techniques is considered.
F. Stoican, Prodan, I., and Olaru, S., “
Enhancements on the hyperplane arrangements in mixed integer techniques”, in
Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, USA, 2011, p. 3986–3991.
AbstractThe current paper addresses the problem of optimizing a cost function over a non-convex and possibly non-connected feasible region. A classical approach for solving this type of optimization problem is based on Mixed integer technique. The exponential complexity as a function of the number of binary variables used in the problem formulation highlights the importance of reducing them. Previous work which minimize the number of binary variables is revisited and enhanced. Practical limitations of the procedure are discussed and a typical control application, the control of Multi-Agent Systems is exemplified.