RLT-POS: Reformulation-Linearization Technique-based optimization software for solving polynomial programming problems
- 319 Downloads
In this paper, we introduce a Reformulation-Linearization Technique-based open-source optimization software for solving polynomial programming problems (RLT-POS). We present algorithms and mechanisms that form the backbone of RLT-POS, including constraint filtering techniques, reduced RLT representations, and semidefinite cuts. When implemented individually, each model enhancement has been shown in previous papers to significantly improve the performance of the standard RLT procedure. However, the coordination between different model enhancement techniques becomes critical for an improved overall performance since special structures in the original formulation that work in favor of a particular technique might be lost after implementing some other model enhancement. More specifically, we discuss the coordination between (1) constraint elimination via filtering techniques and reduced RLT representations, and (2) semidefinite cuts for sparse problems. We present computational results using instances from the literature as well as randomly generated problems to demonstrate the improvement over a standard RLT implementation and to compare the performances of the software packages BARON, COUENNE, and SparsePOP with RLT-POS.
KeywordsReformulation-Linearization Technique (RLT) Open-source code Constraint filtering strategies Valid inequalities Reduced RLT representations Polynomial programming
Mathematics Subject Classification65K05 90-08 90C26 90C57
The authors gratefully acknowledge Nick Sahinidis at Carnegie Mellon University for permitting the use of the BARON solver.
- 4.Balas, E., Ceria, S., Cornuejols, G.: Mixed 0–1 programming by lift-and-project in a branch-and-cut framework (1996)Google Scholar
- 7.Cafieri, S., Hansen, P., Létocart, L., Liberti, L., Messine, F.: Compact relaxations for polynomial programming problems. In: Klasing, R. (ed.) Experimental Algorithms, Lecture Notes in Computer Science, vol. 7276, pp. 75–86. Springer, Berlin (2012)Google Scholar
- 11.Ibm, ILOG CPLEX Optimization Studio. http://www.ilog.com/products/cplex
- 17.MATLAB: version 7.12.0 (R2011a). The MathWorks Inc., Natick, Massachusetts (2011)Google Scholar