A 'satisfiability' based approach to integer programming

Abstract

The purpose of this work is the development of a collection of satisfiability based algorithms that can be used to solve particular instances of integer programming problems. Satisfiability based algorithms have recently obtained a strong standing within the industrial community and, although for all but a few special cases the problem is NP-complete, research has shown that other problems in this class can often be transformed into a corresponding satisfiability problem and solved more effectively using the best SAT-solvers. One of the most important uses of satisfiability based algorithms is within chip design testing, such as the floating point failure of Pentium processors which require the need of efficient satisfiability based tools to aid in the verification process. We start with the case of Pure 0-1 Integer Programming problems and show how they can be transformed into a general satisfiability problem and solved using an algorithm developed by Davis, Putnam and Loveland. The thesis then concerns itself with making the process as efficient as possible by adopting a number of approaches that include the implementation of polynomial time algorithms including 'Incremental Satisfiability', allowing flexibility to add new branching strategies and the conversion of constraints tological clauses. The programs are compiled to interact with each other fully and are tested on the 'truss design problem' found in structural engineering.

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