A grocery chain's night-routing search stops when no swap of two nearby stops shortens the tour, and the planner files that route as the best feasible plan. A second run that starts at a different store yields a shorter tour that still hits every delivery window. What does the shorter tour demonstrate?

A search that stops when no nearby swap shortens the tour has found a local optimum. Every route one small edit away is no better, and routes outside that neighborhood were never compared. The second start reached a shorter tour that still meets every delivery window, so a better feasible solution sat beyond the first neighborhood. A local optimum can therefore be worse than another optimum the search never reached. Treating the first halt as a certified global best conflicts with that shorter feasible tour, since a local stop is not proof that every other legal tour is longer. Requiring a full listing of every route before any improvement is possible overstates the case, because a different initial store already cut the mileage without enumerating every tour. Calling the new start a different objective confuses the search path with the problem: the stops and the windows stayed the same, and only the initial route changed. Exam caveat: a local optimum can still be feasible and unbeaten inside its neighborhood, so local does not mean the route broke a window. Operational check: restart the router from several different first stores, drop any tour that misses a window, and compare mileage before you freeze the night plan.