TSP Route Optimizer
Find the shortest route visiting all locations and returning to the depot. Uses heuristic algorithms (Nearest Neighbor, Clarke-Wright Savings) to solve the…
Uses heuristic algorithms (Nearest Neighbor, Clarke-Wright Savings) to solve the Traveling Salesman Problem. Enter location coordinates to find an optimized route.
What is the Traveling Salesman Problem (TSP)?
The Traveling Salesman Problem (TSP) asks: given a set of locations and distances between them, what is the shortest possible route that visits each location exactly once and returns to the starting point? It is one of the most studied problems in combinatorial optimization.
TSP is NP-hard, meaning no known algorithm can solve large instances optimally in polynomial time. For n locations, there are (n-1)!/2 possible routes — 10 stops yield 181,440 routes; 20 stops yield 10^16. Practical solutions rely on heuristics: Nearest Neighbor (fast, ~25% above optimal), Clarke-Wright Savings (better quality), and metaheuristics like 2-opt, simulated annealing, or genetic algorithms.
TSP has direct applications in last-mile delivery routing, field service scheduling, PCB drilling, and warehouse pick path optimization. Even a 10-15% route improvement translates into significant fuel and time savings for fleet operations.
Formula: Objective: minimize Σ d(route[i], route[i+1]) for i = 0..n Nearest Neighbor: greedily visit the closest unvisited location Savings: s(i,j) = d(depot,i) + d(depot,j) − d(i,j) Merge routes by largest saving first
Example Calculation
Depot at (0,0), 4 stops at (3,4), (6,1), (8,5), (2,7). Nearest Neighbor from depot: visit (3,4) d=5.0, then (2,7) d=3.2, then (8,5) d=6.3, then (6,1) d=4.5, return d=6.1. Total = 25.1. Clarke-Wright might find a shorter route of 23.4 by merging the most beneficial pairs first.
When to Use This Calculator
- A delivery dispatcher planning a daily route for a single driver visiting 10-30 customer locations
- A field service manager optimizing technician routes to minimize travel time between service calls
- A warehouse engineer designing an optimal pick path through multiple aisle locations
- A sales representative planning a multi-city trip to visit clients with minimal driving distance
Common Mistakes to Avoid
- Assuming the nearest-neighbor solution is optimal — it is a greedy heuristic that can be 20-25% above the optimal route; always try multiple algorithms and compare
- Using straight-line (Euclidean) distances for road-based routing — actual driving distances can be 20-40% longer due to road networks; for road routing, use actual distances if available
- Forgetting to include the return trip to the depot — TSP requires returning to the starting point; omitting the return underestimates total route distance
- Applying TSP to problems that are really VRP — if you have capacity constraints, time windows, or multiple vehicles, use the VRP tool instead for better results
How to Interpret Results
- Compare Nearest Neighbor and Clarke-Wright results: if they differ significantly, the problem has room for further optimization with more advanced methods
- Computation time in milliseconds helps assess whether real-time re-routing is feasible for your problem size
- The route map visualization helps identify obvious inefficiencies like crossing routes or unnecessary backtracking that heuristics may produce
Related Standards & References
- Nearest Neighbor and Clarke-Wright savings (1964) — the constructive heuristics benchmarked in this tool
- Lin-Kernighan local search — the de facto reference heuristic for high-quality TSP tours
- TSPLIB — the standard public benchmark library used to compare TSP solver quality
Frequently Asked Questions
Which algorithm should I use for my routing problem?
For < 15 stops, Nearest Neighbor gives quick results within 20-25% of optimal. For 15-50 stops, Clarke-Wright Savings followed by 2-opt improvement typically achieves within 5-10% of optimal. For 50+ stops, use metaheuristics (genetic algorithm, simulated annealing) or commercial solvers like Google OR-Tools.
How is TSP different from real-world delivery routing?
Real routing adds time windows, vehicle capacity, driver hours, traffic, one-way streets, and multiple vehicles (making it VRP). TSP is the foundation, but practical routing software layers these constraints on top. Still, TSP solutions provide the distance lower bound for benchmarking.