Route optimization (a variant of the Traveling Salesman Problem) asks: "Given a set of
delivery stops, what is the shortest route that visits each stop exactly once and returns to
the depot?" This is NP-hard — the number of possible routes grows factorially with
stops.
📊 Algorithm Explorer
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how it works with a live animated example.
Dijkstra + NN
O(V² log V)O(V)Not Optimal
Computes the shortest-path tree from the depot using Dijkstra's
algorithm, then constructs a tour by always visiting the nearest unvisited node. The
single-source shortest paths ensure accurate distance computation even through road
networks.
🔬 Classical vs Quantum
Classical Approach
Explores solutions one-at-a-time
Heuristics trade accuracy for speed
Exact solvers limited to ~20 nodes
Gets trapped in local optima
Well-understood, mature tooling
Quantum Approach
Superposition evaluates many routes simultaneously
Interference amplifies better solutions
Quantum tunneling escapes local minima
Grover provides quadratic speedup
Hardware-limited today, massive future potential
🏭 Real-World Applications
Route optimization impacts every logistics company on earth. Amazon, FedEx, and UPS collectively
solve millions of vehicle routing problems daily. A 1% improvement in route efficiency for a
major carrier can save $50M+ annually. As quantum hardware matures,
quantum-optimized routing will become a critical competitive advantage in supply chain
management.
🧠 When To Use Each Algorithm
< 15 stops: Use Held-Karp or Branch & Bound for exact optimal solutions.
15–50 stops: Use 2-Opt or Simulated Annealing for near-optimal results in
practical time.
50–500 stops: Use Genetic Algorithm with large population sizes. Consider
QAOA for potential speedup.
500+ stops: Use Greedy NN + 2-Opt as baseline. Quantum annealing shows the
most promise at this scale.