A logistics company must generate delivery routes every night for nearly 5 000 vehicles under tight time-window and driver-hours constraints. An exact mixed-integer linear programming (MILP) model failed to prove optimality after six hours of computation. The data science team replaced it with an Adaptive Large Neighborhood Search (ALNS) heuristic that reliably produces solutions within about 2 % of the best known bound in under 10 minutes. Which characteristic of heuristic optimisation methods best justifies choosing ALNS over the exact solver in this situation?
They rely on duality gaps from linear programming to prove that the solution returned is mathematically optimal.
They deterministically enumerate every feasible solution to ensure the optimal one is always found.
They can be applied only when the objective function is linear and convex so that gradients exist.
They deliberately trade the guarantee of global optimality for much faster runtime when solving very large, complex search spaces.
Heuristic algorithms are designed to explore only the most promising regions of an enormous search space, giving up the mathematical guarantee of a globally optimal answer so they can return a high-quality solution in a practical amount of time. This trade-off is exactly what allows ALNS to satisfy the 15-minute SLA on a very large vehicle-routing instance. Heuristics do not require linear, convex objectives, they do not enumerate every feasible solution, and they do not compute duality gaps to certify optimality; those properties belong to exact or mathematical-programming approaches.
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