Combinatorial optimization of boolean satisfiability problems

Samo Tuma (2013) Combinatorial optimization of boolean satisfiability problems. EngD thesis.

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Abstract

The purpose of this thesis is to design, implement and analyse a hybrid genetic algorithm for solving the MAX-3SAT problem. The problem is a well known NP-complete decision problem. Solving this type of problems is highly motivated by its practical use in industry. The main field of 3SAT solver application ranges from integrated circuit delay optimization to FPGA routing. See section 1.9 for details on practical applications of the MAX- 3SAT solver. The idea behind this hybrid genetic algorithm, is to see just when and how much of local search can still prove beneficial to the overall solution quality. In the results section 4.4, we have shown that this algorithm performs best when the local search is applied periodically and with our best run results (presented in section 4.6) we came very close to a similar implementation described in [14]. Our best average run time on the biggest test instances was trailing behind aforementioned article by about 30 percent. The reason, why our average running time is fairly close to the aforementioned imple- mentation, lies in exploiting parallelism. We used a simple parallelization technique of local searching, which is described in section 4.2. Moreover, our solution quality - that is the number of unsatisfied clauses, was pretty much as good as the one reported in [14]. Ours was worse by only 0,6 percent. It is important to point out that we used exactly the same test instances as used in [14].

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