Splitting heuristics for disjunctive numerical constraints

Abstract

Numerical constraint solving techniques operate in a branch& prune fashion, using consistency enforcement techniques to prune the search space and splitting operations to explore it. Extensions address disjunctions of constraints as well, but usually in a restrictive case and not tting well the branch&prune scheme. On the other hand, Ratschan has recently proposed a general framework for rst-order formulas whose atoms are numerical constraints. It extends the notion of consistency to logical terms, but little is done with respect to the splitting operation. In this paper, we explore the potential of splitting heuristics that exploit the logical structure of disjunctive numerical constraint problems in order to simplify the problem along the search. First experiments on CNF formulas show that interesting solving time gains can be achieved by choosing the right splitting points.

Efficient Solution of a Class of Quantified Constraints with Quantifier Prefix Exists-Forall

“…Since splitting heuristics for classical interval branch-and-bound (or branchand-prune) algorithms are well-studied [6,9,20] we assume that in Step 6 the algorithm already arrived at an interval linear system of inequalities. We will try to come up with splits that bring the next linear program closer to solvability.…”