Matthew Kitching

IJCAI Conference 2009 Conference Paper

• Matthew Kitching
• Fahiem Bacchus

Branch and bound is an effective technique for solving constraint optimization problems (COP’s). However, its search space expands very rapidly as the domain sizes of the problem variables grow. In this paper, we present an algorithm that clusters the values of a variable’s domain into sets. Branch and bound can then branch on these sets of values rather than on individual values, thereby reducing the branching factor of its search space. The aim of our clustering algorithm is to construct a collection of sets such that branching on these sets will still allow effective bounding. In conjunction with the reduced branching factor, the size of the explored search space is thus significantly reduced. We test our method and show empirically that it can yield significant performance gains over existing stateof-the-art techniques.

IJCAI Conference 2009 Conference Paper

• Matthew Kitching
• Fahiem Bacchus

Decomposition is an effective technique for solving discrete Constraint Optimization Problems (COPs) with low tree-width. On problems with high treewidth, however, existing decomposition algorithms offer little advantage over branch and bound search (B&B). In this paper we propose a method for exploiting decomposition on problems with high treewidth. Our technique involves modifying B&B to detect and exploit decomposition on a selected subset of the problem’s objectives. Decompositions over this subset, generated during search, are exploited to compute tighter bounds allowing B&B to prune more of its search space. We present a heuristic for selecting an appropriate subset of objectives—one that readily decomposes during search and yet can still provide good bounds. We demonstrate empirically that our approach can significantly improve B&B’s performance and outperform standard decomposition algorithms on a variety of high tree-width problems.

IJCAI Conference 2007 Conference Paper

• Matthew Kitching
• Fahiem Bacchus

Caching, symmetries, and search with decomposition are powerful techniques for pruning the search space of constraint problems. In this paper we present an innovative way of efficiently combining these techniques with branch and bound for solving certain types of constraint optimization problems (COPs). Our new method significantly reduces the overhead of performing decomposition during search when dynamic variable orderings are employed. In addition, it supports the exploitation of dynamic symmetries that appear only during search. Symmetries have not previously been combined with decomposition. Finally, we achieve a superior integration of decomposition and caching with branch and bound than previous approaches. We test our methods on the Maximum Density Still Life problem and show that each of our ideas yields a significant gain in search performance.