Decomposition and symmetry in constraint optimization problems

This thesis presents several techniques that advance search-based algorithms for solving Constraint Optimization Problems (COPs). These techniques exploit structural features common in such problems. In particular, the thesis presents a number of innovative algorithms, and associated data structures, designed to exploit decomposition and symmetry in COPs. First, a new technique called component templating is introduced. Component templates are data structures for efficiently representing the disjoint sub-problems that are encountered during search. Information about each disjoint sub-problem can then be reused during search, increasing efficiency. A new algorithm called OR-decomposition is introduced. This algorithm obtains many of the computational benefits of decomposition without the need to resort to separate recursions. That is, the algorithm explores a standard OR tree rather than an AND-OR tree. In this way, the search algorithm gains greater freedom in its variable ordering compared to previous decomposition algorithms. Although decomposition algorithms such as OR-decomposition are effective techniques for solving COPs with low tree-width, existing decomposition algorithms offer little advantage over branch and bound search on problems with high tree-width. A new method for exploiting decomposition on problems with high tree-width is presented. This technique involves detecting and exploiting decompositions on a selected subset of the problem’s objectives. Such decompositions can then be used to more efficiently compute additional bounds that can be used by branch and bound search. The second half of the thesis explores the use of symmetries in COPs. Using component templates, it is possible to exploit dynamic symmetries that appear during search when some of the variables of a problem have been assigned a value. Symmetries have not previously been combined with decomposition in COPs. An algorithm called Set Branching is presented, which exploits almost-symmetries in the values of a variable by clustering similar values together, then branching on sets of values rather than on each single value. The decomposition and symmetry algorithms presented in this thesis increase the efficiency of constraint optimization solvers. The thesis also presents experimental results that test these algorithms on a variety of real world problems, and demonstrate performance improvements over current state-of-the-art techniques.