Solution-Based Phase Saving for CP: A Value-Selection Heuristic to Simulate Local Search Behavior in Complete Solvers

Large neighbourhood search, a meta-heuristic, has proven to be successful on a wide range of optimisation problems. The algorithm repeatedly generates and searches through a neighbourhood around the current best solution. Thus, it finds increasingly better solutions by solving a series of simplified problems, all of which are related to the current best solution. In this paper, we show that significant benefits can be obtained by simulating local-search behaviour in constraint programming by using phase saving based on the best solution found so far during the search, activity-based search (VSIDS), and nogood learning. The approach is highly effective despite its simplicity, improving the highest scoring solver, Chuffed, in the free category of the MiniZinc Challenge 2017, and can be easily integrated into modern constraint programming solvers. We validated the results on a wide range of benchmarks from the competition library, comparing against seventeen state-of-the-art solvers.

[1]  Toby Walsh,et al.  Search in a Small World , 1999, IJCAI.

[2]  Lakhdar Sais,et al.  Boosting Systematic Search by Weighting Constraints , 2004, ECAI.

[3]  Philippe Refalo,et al.  Impact-Based Search Strategies for Constraint Programming , 2004, CP.

[4]  Geoffrey Chu,et al.  Improving combinatorial optimization , 2011 .

[5]  Pierre Schaus,et al.  Cost Impact Guided LNS , 2014, CPAIOR.

[6]  J. Christopher Beck,et al.  Principles for the Design of Large Neighborhood Search , 2009, J. Math. Model. Algorithms.

[7]  Ecnica De Catalunya.  Solving hard industrial combinatorial problems with SAT , 2013 .

[8]  David Zuckerman,et al.  Optimal Speedup of Las Vegas Algorithms , 1993, Inf. Process. Lett..

[9]  Adnan Darwiche,et al.  A Lightweight Component Caching Scheme for Satisfiability Solvers , 2007, SAT.

[10]  Robert M. Haralick,et al.  Increasing Tree Search Efficiency for Constraint Satisfaction Problems , 1979, Artif. Intell..

[11]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[12]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[13]  Peter J. Stuckey,et al.  Propagation via lazy clause generation , 2009, Constraints.

[14]  Xavier Lorca,et al.  Explanation-based large neighborhood search , 2014, Constraints.

[15]  Laurent Perron,et al.  Propagation Guided Large Neighborhood Search , 2004, CP.