Semidefinite Programming Relaxations in Timetabling
نویسندگان
چکیده
This paper extends semidefinite programming relaxations of graph colouring to bounded graph colouring and extensions encountered in timetabling, where room sizes, room features, room stability, and pre-allocated assignments are considered. A matrix-free implementation of an augmented Lagrangian method is presented. Encouraging computational results are reported for conflict graphs from all three tracks of the International Timetabling Competition 2007, the Toronto benchmark, random, Knesser and “forbidden intersection” graphs.
منابع مشابه
Semidefinite relaxations of the quadratic assignment problem in a Lagrangian framework
In this paper, we consider partial Lagrangian relaxations of continuous quadratic formulations of the Quadratic Assignment Problem (QAP) where the assignment constraints are not relaxed. These relaxations are a theoretical limit for semidefinite relaxations of the QAP using any linearized quadratic equalities made from the assignment constraints. Using this framework, we survey and compare stan...
متن کاملSecond-Order Cone Relaxations for Binary Quadratic Polynomial Programs
Several types of relaxations for binary quadratic polynomial programs can be obtained using linear, secondorder cone, or semidefinite techniques. In this paper, we propose a general framework to construct conic relaxations for binary quadratic polynomial programs based on polynomial programming. Using our framework, we re-derive previous relaxation schemes and provide new ones. In particular, w...
متن کاملSemidefinite relaxation for dominating set
‎It is a well-known fact that finding a minimum dominating set and consequently the domination number of a general graph is an NP-complete problem‎. ‎In this paper‎, ‎we first model it as a nonlinear binary optimization problem and then extract two closely related semidefinite relaxations‎. ‎For each of these relaxations‎, ‎different rounding algorithm is exp...
متن کاملOn Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming
We analyze two popular semidefinite programming relaxations for quadratically constrained quadratic programs with matrix variables. These relaxations are based on vector lifting and on matrix lifting; they are of different size and expense. We prove, under mild assumptions, that these two relaxations provide equivalent bounds. Thus, our results provide a theoretical guideline for how to choose ...
متن کاملExact SDP relaxations for classes of nonlinear semidefinite programming problems
An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...
متن کامل