Decision Tree Learning-Inspired Dynamic Variable Ordering for the Weighted CSP

The weighted constraint satisfaction problem (WCSP) is a powerful mathematical framework for combinatorial optimization. The branch-and-bound search paradigm is very successful in solving the WCSP but critically depends on the ordering in which variables are instantiated. In this paper, we introduce a new framework for dynamic variable ordering for solving the WCSP. This framework is inspired by regression decision tree learning. Variables are ordered dynamically based on samples of random assignments of values to variables as well as their corresponding total weights. Within this framework, we propose four variable ordering heuristics (sdr, inv-sdr, rr and inv-rr). We compare them with many state-of-the-art dynamic variable ordering heuristics, and show that sdr and rr outperform them on many real-world and random benchmark instances.