Learning a Stopping Criterion for Local Search
Local search is a very effective technique to tackle combinatorial problems in multiple areas ranging from telecommunications to transportations, and VLSI circuit design. A local search algorithm typically explores the space of solutions until a given stopping criterion is met. Ideally, the algorithm is executed until a target solution is reached (e.g., optimal or near-optimal). However, in many real-world problems such a target is unknown. In this work, our objective is to study the application of machine learning techniques to carefully craft a stopping criterion. More precisely, we exploit instance features to predict the expected quality of the solution for a given algorithm to solve a given problem instance, we then run the local search algorithm until the expected quality is reached. Our experiments indicate that the suggested method is able to reduce the average runtime up to 80% for real-world instances and up to 97% for randomly generated instances with a minor impact in the quality of the solutions.
KeywordsLocal Search Problem Instance Travel Salesman Problem Local Search Algorithm Average Runtime
This work was supported by DISCUS (FP7 Grant Agreement 318137) and Science Foundation Ireland (SFI) Grant No. 10/CE/I1853. The Insight Centre for Data Analytics is also supported by SFI under Grant Number SFI/12/RC/2289.
- 2.Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: Constraint-based local search for the distance- and capacity-bounded network design problem. In: ICTAI 2014, Limassol, Cyprus, November 10–12, 2014, pp. 178–185 (2014)Google Scholar
- 3.Arbelaez, A., Mehta, D., O’Sullivan, B., Quesada, L.: Constraint-based local search for edge disjoint rooted distance-constrainted minimum spanning tree problem. In: CPAIOR 2015, pp. 31–46 (2015)Google Scholar
- 4.Arbelaez, A., Mehta, D., O’Sullivan, B.: Constraint-based local search for finding node-disjoint bounded-paths in optical access networks. In: CP 2015, pp. 499–507 (2015)Google Scholar
- 7.Hoos, H., Stütze, T.: Stochastic Local Search: Foundations and Applications. Morgan Kaufmann, New York (2005)Google Scholar
- 8.Larochelle, H., Bengio, Y.: Classification using Discriminative Restricted Boltzmann Machines. In: ICML 2008, Helsinki, Finland, ACM 536–543., June 2008Google Scholar
- 10.Gelly, S., Silver, D.: Combining Online and Offline Knowledge in UCT. In: ICML 2007. vol. 227, pp. 273–280. ACM, Corvalis, Oregon, USA, June 2007Google Scholar
- 12.Kotthoff, L.: Algorithm selection for combinatorial search problems: a survey. AI Mag. 35(3), 48–60 (2014)Google Scholar
- 16.Kahavi, R.: A study of cross-validation and bootstrap for accuracy estimation and model selection. In: IJCAI 1995, pp. 1137–1145 (1995)Google Scholar