Empirical methods for artificial intelligence
Empirical methods for artificial intelligence
Constraint-Based Scheduling
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Algorithms for Hybrid MILP/CP Models for a Class of Optimization Problems
INFORMS Journal on Computing
A Hybrid Method for the Planning and Scheduling
Constraints
Computers and Operations Research
Solving a location-allocation problem with logic-based Benders' decomposition
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Reconsidering mixed integer programming and MIP-Based hybrids for scheduling
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
INFORMS Journal on Computing
Scheduling a dynamic aircraft repair shop with limited repair resources
Journal of Artificial Intelligence Research
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Branch-and-Check, introduced ten years ago, is a generalization of logic-based Benders decomposition. The key extension is to solve the Benders sub-problems at each feasible solution of the master problem rather than only at an optimal solution. We perform the first systematic empirical comparison of logic-based Benders decomposition and branchand-check. On four problem types the results indicate that either Benders or branch-and-check may perform best, depending on the relative difficulty of solving the master problem and the sub-problems. We identify a characteristic of the logic-based Benders decomposition runs, the proportion of run-time spent solving the master problem, that is valuable in predicting the performance of branch-and-check. We also introduce a variation of branch-and-check to address difficult sub-problems. Empirical results show that this variation leads to more robust performance than both logic-based Benders decomposition and branch-and-check on the problems investigated.