Improving combinatorial optimization
نویسنده
چکیده
Combinatorial Optimization is an important area of computer science that has many theoretical and practical applications. In this thesis, we present important contributions to several different areas of combinatorial optimization, including nogood learning, symmetry breaking, dominance, relaxations and parallelization. We develop a new nogood learning technique based on constraint projection that allows us to exploit subproblem dominances that arise when two different search paths lead to subproblems which are identical on the remaining unlabeled variables. On appropriate problems, this nogood learning technique provides orders of magnitude speedup compared to a base solver which does not learn nogoods. We present a new symmetry breaking technique called SBDS-1UIP, which is an extension of Symmetry Breaking During Search (SBDS). SBDS-1UIP uses symmetric versions of the 1UIP nogoods derived by Lazy Clause Generation solvers to prune symmetric parts of the search space. We show that SBDS-1UIP can exploit at least as many symmetries as SBDS, and that it is strictly more powerful on some problems, allowing us to exploit types of symmetries that no previous general symmetry breaking technique is capable of exploiting. We present two new general methods for exploiting almost symmetries (symmetries which are broken by a small number of constraints). The first is to treat almost symmetries as conditional symmetries and exploit them via conditional symmetry breaking constraints. The second is to modify SDBS-1UIP to handle almost symmetries. Both techniques are capable of producing exponential speedups on appropriate problems. We examine three reasonably well known problems: the Minimization of Open
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