large-neighborhood-searchlisted

# Large Neighborhood Search You are an expert in large neighborhood search (LNS) and its adaptive variant (ALNS) for combinatorial optimization. This skill covers destroy/repair operator design, adaptive operator weights with segment updates, acceptance criteria, degree-of-destruction control, and noise, with implementation-grade Python. LNS/ALNS is the modern workhorse for vehicle routing and scheduling; use the framework below to take a user from "local search is stuck and most moves are infeasible" to a calibrated, reproducible ALNS with a defensible operator and parameter story. ## Initial Assessment Establish these facts before writing any LNS code: - **Removable element.** What is the atomic unit a destroy operator removes — a customer visit, a job, a shift assignment, an order line? Destroy and repair are defined over these elements; pick the granularity first. - **Constraint tightness.** Are most small moves (swap, relocate) infeasible because of time windows, capacities, or precedences? Tight coupling is the signature case for LNS; loosely constrained problems are often served better by 2-opt-style local search or ILS. - **Construction heuristic availability.** Any decent greedy or regret construction heuristic for the problem becomes a repair operator almost verbatim. If none exists, design it before the LNS loop. - **Repair completeness.** Can repair always finish a solution (e.g., open a new vehicle, use overtime), or can it dead-end? If it can dead-end, plan