Learning Value Heuristics for Constraint Programming
Search heuristics are of paramount importance for finding good solutions to optimization problems quickly. Manually designing problem specific search heuristics is a time consuming process and requires expert knowledge from the user. Thus there is great interest in developing autonomous search heuristics which work well for a wide variety of problems. Various autonomous search heuristics already exist, such as first fail, domwdeg and impact based search. However, such heuristics are often more focused on the variable selection, i.e., picking important variables to branch on to make the search tree smaller, rather than the value selection, i.e., ordering the subtrees so that the good subtrees are explored first. In this paper, we define a framework for learning value heuristics, by combining a scoring function, feature selection, and machine learning algorithm. We demonstrate that we can learn value heuristics that perform better than random value heuristics, and for some problem classes, the learned heuristics are comparable in performance to manually designed value heuristics. We also show that value heuristics using features beyond a simple score can be valuable.
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- 2.Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Proceedings of the 38th Design Automation Conference, DAC 2001, pp. 530–535. ACM, Las Vegas, June 18–22, 2001Google Scholar
- 3.Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) Proceedings of the 16th Eureopean Conference on Artificial Intelligence, ECAI 2004, Including Prestigious Applicants of Intelligent Systems, PAIS 2004, pp. 146–150. IOS Press, Valencia (2004)Google Scholar
- 9.Linderoth, J., Savelsbergh, M.: A computational study of search strategies for mixed integer programming. INFORMS Journal of Computing 11 (1999)Google Scholar
- 10.Kotthoff, L.: Algorithm selection for combinatorial search problems: A survey. CoRR abs/1210.7959 (2012)Google Scholar
- 11.Amemiya, T.: Advanced Econometrics. Harvard University Press (1985)Google Scholar
- 12.Wold, H.: Estimation of principal components and related models by iterative least squares. In: Multivariate Analysis, pp. 391–420. Academic Press (1966)Google Scholar
- 17.Miller, H., Pierskalla, W., Rath, G.: Nurse scheduling using mathematical programming. Operations Research, 857–870 (1976)Google Scholar
- 18.Dincbas, M., Simonis, H., Van Hentenryck, P.: Solving the car-sequencing problem in constraint logic programming. In: ECAI, vol. 88, pp. 290–295 (1988)Google Scholar
- 21.Savage, L.: The theory of statistical decision. Journal of the American Statistical Association 46 (1951)Google Scholar
- 22.Allouche, D., de Givry, S., Schiex, T.: Toulbar2, an open source exact cost function network solver. Technical report, INRIA (2010)Google Scholar