Stochastic Planning and Scheduling with Logic-Based Benders Decomposition
Ozgun Elci, J. N. Hooker

TL;DR
This paper demonstrates that logic-based Benders decomposition significantly outperforms the integer L-shaped method in solving two-stage stochastic planning and scheduling problems, enabling larger instances to be tackled efficiently.
Contribution
It introduces the first application of LBBD to stochastic optimization with scheduling second-stage problems and compares its performance to the integer L-shaped method.
Findings
LBBD is computationally superior to the integer L-shaped method.
A branch-and-check LBBD variant is several orders of magnitude faster.
LBBD enables solving larger stochastic scheduling instances.
Abstract
We apply logic-based Benders decomposition (LBBD) to two-stage stochastic planning and scheduling problems in which the second-stage is a scheduling task. We solve the master problem with mixed integer/linear programming and the subproblem with constraint programming. As Benders cuts, we use simple nogood cuts as well as analytical logic-based cuts we develop for this application. We find that LBBD is computationally superior to the integer L-shaped method, with a branch-and-check variant of LBBD faster by several orders of magnitude, allowing significantly larger instances to be solved. This is due primarily to computational overhead incurred by the integer L-shaped method while generating classical Benders cuts from a continuous relaxation of an integer programming subproblem. To our knowledge, this is the first application of LBBD to two-stage stochastic optimization with a…
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Taxonomy
TopicsConstraint Satisfaction and Optimization · Bayesian Modeling and Causal Inference · Logic, Reasoning, and Knowledge
