Exploring the Impact of Early Decisions in Variable Ordering for Constraint Satisfaction Problems

Abstract

When solving constraint satisfaction problems (CSPs), it is a common practice to rely on heuristics to decide which variable should be instantiated at each stage of the search. But, this ordering influences the search cost. Even so, and to the best of our knowledge, no earlier work has dealt with how first variable orderings affect the overall cost. In this paper, we explore the cost of finding high-quality orderings of variables within constraint satisfaction problems. We also study differences among the orderings produced by some commonly used heuristics and the way bad first decisions affect the search cost. One of the most important findings of this work confirms the paramount importance of first decisions. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. Another one is the evidence that many of the existing variable ordering heuristics fail to appropriately select the first variable to instantiate. We propose a simple method to improve early decisions of heuristics. By using it, performance of heuristics increases.

Online learning of variable ordering heuristics for constraint optimisation problems

“…Sixth, use of the score from the DHSF might be improved by adding exploration and exploitation attributes. For instance, one could add a discount factor to give more weight to earlier choices adhering to the principle of making good early decisions [12].…”

“…A cutoff bound restarts search after a specified number of failures. A new first variable is selected after each restart, in order to gain maximal data at the top of the search tree [12].…”

Racing Control Variable Genetic Programming for Symbolic Regression

“…The choice of variables is an important topic in AI, including variable ordering in decision diagrams (Cappart et al 2022), variable selection in tree search (Song et al 2022a), variable elimination in probabilistic inference (Dechter 2019;Derkinderen et al 2020) and backtracking search in constraint satisfaction problems (Ortiz-Bayliss et al 2018;Li, Feng, and Yin 2020;Song et al 2022b). Our method is one variant of variable ordering in symbolic regression.…”