## Nonlinear pseudo-Boolean optimization: relaxation or propagation?

Please always quote using this URN: urn:nbn:de:0297-zib-11232
• Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.

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Author: Timo Berthold, Stefan Heinz, Marc E. Pfetsch ZIB-Report Pseudo-Boolean; constraint integer programming; domain propagation; linear relaxation; separation algorithm 65-XX NUMERICAL ANALYSIS / 65Kxx Mathematical programming, optimization and variational techniques / 65K05 Mathematical programming methods [See also 90Cxx] 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C09 Boolean programming 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming 2009/03/29 ZIB-Report (09-11) 1438-0064 Appeared in: O. Kullmann (Ed.), Theory and Applications of Satisfiability Testing -- SAT 2009; Lecture Notes in Computer Science 5584, pp. 441-446, 2009

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