Combining Constraint Propagation and Discrete Ellipsoid-Based Search to Solve the Exact Quadratic Knapsack Problem
We propose an extension to the discrete ellipsoid-based search (DEBS) to solve the exact quadratic knapsack problem (EQKP), an important class of optimization problem with a number of practical applications. For the first time, our extension enables DEBS to solve convex quadratically constrained problems with linear constraints. We show that adding linear constraint propagation to DEBS results in an algorithm that is able to outperform both the state-of-the-art MIP solver CPLEX and a semi-definite programming approach by about one order of magnitude on two variations of the EQKP.
Unable to display preview. Download preview PDF.
- 8.Bussieck, M.R., Vigerske, S.: MINLP solver software. Wiley Encyclopedia of Operations Research and Management Science. Wiley, Chichester (2010)Google Scholar
- 10.Krislock, N., Malick, J., Roupin, F.: Improved semidefinite bounding procedure for solving max-cut problems to optimality. Mathematical Programming, 1–26 (2012)Google Scholar
- 15.Ku, W.Y., Beck, J.C.: Combining discrete ellipsoid-based search and branch-and-cut for integer least squares problems. Submitted to IEEE Transactions on Wireless Communications (2014)Google Scholar
- 17.Krislock, N., Malick, J., Roupin, F.: BiqCrunch online solver (2012) (Retrieved: 11/06/2014). http://lipn.univ-paris13.fr/BiqCrunch/download
- 18.Achterberg, T.: Constraint Integer Programming. PhD thesis, Technische Universität Berlin (2007)Google Scholar