Large Neighborhood Search (LNS)

An extension of LNS that dynamically selects from a portfolio of multiple destroy and repair operators based on their past performance. Instead of using a single heuristic, ALNS assigns weights to operators and updates them during the search using a roulette-wheel selection mechanism. Operators that historically lead to better solutions are chosen more frequently. This self-tuning behavior makes ALNS particularly effective for heterogeneous routing problems where no single heuristic dominates across all instances.

The combinatorial optimization challenge that LNS is most commonly applied to solve. The VRP seeks to determine the optimal set of routes for a fleet of vehicles to service a geographically dispersed set of customers. Key variants include:

• CVRP: Adds vehicle capacity constraints
• VRPTW: Enforces strict delivery time windows
• HFVRP: Handles fleets with mixed vehicle types LNS excels here because destroying and repairing large route segments can resolve tight constraint violations that local search operators miss.

A probabilistic metaheuristic that shares LNS's goal of escaping local optima but uses a fundamentally different mechanism. Simulated annealing accepts worse solutions with a probability that decreases over time, mimicking the cooling of metal. While LNS actively destroys and reconstructs parts of a solution, simulated annealing relies on random perturbations and a temperature schedule. Both are often combined: an LNS inner loop can be wrapped inside a simulated annealing acceptance criterion to create a hybrid metaheuristic with robust convergence properties.

An exact optimization method that contrasts with LNS's heuristic approach. MIP formulates routing problems using linear constraints where some decision variables—such as binary arc-traversal indicators—are restricted to integers. Solvers like Gurobi or CPLEX use branch-and-bound to guarantee optimality. However, MIP struggles with large-scale, real-time instances. A common enterprise pattern uses MIP to solve a relaxed or decomposed subproblem within an LNS repair operator, combining the optimality guarantees of MIP with the scalability of metaheuristics.

A memory-based metaheuristic that prevents the search from cycling back to previously visited solutions. Tabu search maintains a short-term memory structure (the tabu list) that records recently applied moves and forbids their reversal for a specified tenure. This forces the search into new regions of the solution space. Unlike LNS, which explores a large neighborhood in each iteration, tabu search typically examines a smaller neighborhood but uses aspiration criteria to override tabu status when a move leads to a new global best. Both methods are often benchmarked against each other on standard VRP datasets.

The real-time operational context where LNS proves its value. Dynamic re-routing adjusts a vehicle's planned path in response to live events such as traffic congestion, road closures, or newly assigned on-demand orders. LNS is well-suited here because its destroy-and-repair cycle can efficiently incorporate new orders into existing routes without rebuilding from scratch. The destroy operator removes a subset of stops near the disruption, and the repair operator reinserts them optimally—enabling sub-second response times in production logistics control towers.