One Benders cut to rule all schedules in the neighbourhood
Ioannis Avgerinos, Ioannis Mourtos, Stavros Vatikiotis, Georgios Zois

TL;DR
This paper introduces a novel Benders cut based on local search neighborhoods to efficiently eliminate large sets of suboptimal solutions in resource-constrained scheduling problems, improving convergence speed.
Contribution
It proposes integrating local branching cuts as Benders cuts within Branch-and-Check to eliminate entire neighborhoods of solutions, reducing computational overload and enhancing convergence.
Findings
Significant reduction in optimality gaps for tested scheduling problems
Faster convergence to optimal solutions compared to traditional methods
Method is transferable to other sequencing optimization problems
Abstract
Logic-Based Benders Decomposition (LBBD) and its Branch-and-Cut variant, namely Branch-and-Check, enjoy an extensive applicability on a broad variety of problems, including scheduling. Although LBBD offers problem-specific cuts to impose tighter dual bounds, its application to resource-constrained scheduling remains less explored. Given a position-based Mixed-Integer Linear Programming (MILP) formulation for scheduling on unrelated parallel machines, we notice that certain OPT neighbourhoods could implicitly be explored by regular local search operators, thus allowing us to integrate Local Branching into Branch-and-Check schemes. After enumerating such neighbourhoods and obtaining their local optima - hence, proving that they are suboptimal - a local branching cut (applied as a Benders cut) eliminates all their solutions at once, thus avoiding an overload of the master problem with…
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Taxonomy
TopicsScheduling and Optimization Algorithms · Constraint Satisfaction and Optimization · Formal Methods in Verification
