The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. Given a set of cities and the distances between them, the task is to find the shortest possible route that visits each city exactly once and returns to the starting point. Despite its simple formulation, TSP is NP-hard,and understanding how algorithms search for optimal solutions can be difficult for students encountering the problem for the first time. NP-hard To make this process more tangible, I built a web-based Traveling Salesman Problem solver designed primarily for educational use. web-based Traveling Salesman Problem solver The project recently received a Proof of Usefulness (PoU) score of 21 in HackerNoon’s Proof of Usefulness contest. Proof of Usefulness (PoU) score of 21 The Problem Many resources explain the Traveling Salesman Problem theoretically, but fewer allow students to experiment with it interactively. experiment with it interactively Common challenges include: Optimization algorithms are often presented abstractly
Many implementations are command-line tools
Visualizing how routes are constructed can be difficult Optimization algorithms are often presented abstractly Many implementations are command-line tools Visualizing how routes are constructed can be difficult For teaching combinatorial optimization, having a tool where students can create graphs and immediately see optimal paths can make the concept much easier to grasp. create graphs and immediately see optimal paths The Solution: An Interactive Web-Based TSP Solver I developed a web application that allows users to construct Traveling Salesman instances and compute optimal routes directly in the browser. The solver currently supports: Up to 30 nodes
Full or partial connectivity between nodes
Interactive experimentation with graph structures
Immediate visualization of the computed optimal path Up to 30 nodes Up to 30 nodes Full or partial connectivity between nodes Full or partial connectivity between nodes Interactive experimentation with graph structures Interactive experimentation with graph structures Immediate visualization of the computed optimal path Immediate visualization of the computed optimal path The project is deployed online and accessible through a public demo. The goal is to provide an accessible environment where students and instructors can explore how optimal routing emerges from combinatorial search. explore how optimal routing emerges from combinatorial search. How The Solver Works The application accepts a set of nodes representing cities and computes an optimal tour that visits each node exactly once. Choose the number of nodes from the selector.


Choose the level of connectivity (from 0.1 connectivity to full 1.0 connectivity)


Press Run Simulation.


The Solver displays the graph using your selected requirements. Choose the number of nodes from the selector. Choose the number of nodes from the selector. Choose the level of connectivity (from 0.1 connectivity to full 1.0 connectivity) Choose the level of connectivity (from 0.1 connectivity to full 1.0 connectivity) Press Run Simulation. Press Run Simulation. Run Simulation. The Solver displays the graph using your selected requirements. The Solver displays the graph using your selected requirements. If Full Connectivity was chosen, then the Results section will show Hamiltonian Path Found, followed by the optimal route. If Full Connectivity was chosen, then the Results section will show Hamiltonian Path Found, followed by the optimal route. Full Connectivity Results Hamiltonian Path Found If there is no Hamiltonian path is present or Partial Connectivity was chosen, the Solver shows a message of No Hamiltonian Cycle Found. Showing Multiple Partial Traversals.


This shows the longest, optimal path of maximum connected nodes from origin, followed by smaller optimal routes of the remaining nodes--- in decreasing order. If there is no Hamiltonian path is present or Partial Connectivity was chosen, the Solver shows a message of No Hamiltonian Cycle Found. Showing Multiple Partial Traversals. If there is no Hamiltonian path is present or Partial Connectivity was chosen, the Solver shows a message of No Hamiltonian Cycle Found. Showing Multiple Partial Traversals. No Hamiltonian Cycle Found. Showing Multiple Partial Traversals. This shows the longest, optimal path of maximum connected nodes from origin, followed by smaller optimal routes of the remaining nodes--- in decreasing order. This shows the longest, optimal path of maximum connected nodes from origin, followed by smaller optimal routes of the remaining nodes--- in decreasing order. The Solver also shows the animation of the route traversal---including the partial routes. The Solver also shows the animation of the route traversal---including the partial routes. Example Classroom Use Case An instructor teaching algorithms could use the solver to demonstrate how optimal routes change as nodes are added or connectivity constraints are modified. Students can experiment with small graph instances and immediately see how the optimal tour adapts. This makes abstract concepts in combinatorial optimization easier to visualize. Live Demo The solver is deployed online and can be accessed here: TSP Solver Render Link TSP Solver Render Link TSP Solver Render Link Users can input node coordinates or use example graphs, run the solver, and visualize the resulting route. Proof of Usefulness Score As part of HackerNoon’s Proof of Usefulness contest, the project received the following evaluation: Proof of Usefulness contest Final Score: 21 Final Score: 21 Score breakdown: Real World Utility: +10.00
Audience Reach Impact: +0.50
Technical Innovation: +3.00
Evidence of Traction: +0.63
Market Timing Relevance: +3.00
Functional Completeness: +4.00 Real World Utility: +10.00 Audience Reach Impact: +0.50 Technical Innovation: +3.00 Evidence of Traction: +0.63 Market Timing Relevance: +3.00 Functional Completeness: +4.00 Subtotal: 21.13Usefulness Multiplier: ×0.98 Final Score: 21 21 This places the project in the category of working MVPs demonstrating real-world usefulness, though still early in terms of audience reach and adoption. working MVPs demonstrating real-world usefulness Early Validation The solver is currently in the pre-launch validation stage. pre-launch validation stage Early demos with a small number of testers confirmed that the interface and visualization approach help make TSP behavior easier to understand. The next step is expanding validation with students and instructors in algorithms or operations research courses. students and instructors in algorithms or operations research courses Potential Applications While the current focus is educational, the Traveling Salesman Problem has well-known real-world applications in: Delivery routing
Logistics optimization
Manufacturing processes
Circuit board drilling optimization Delivery routing Logistics optimization Manufacturing processes Circuit board drilling optimization Future versions of the project may integrate established solvers such as Concorde to support larger problem sizes and practical routing scenarios for small logistics teams. larger problem sizes and practical routing scenarios for small logistics teams. Future Development Planned improvements include: Expanded visualization tools for algorithm exploration
Larger graph support using high-performance solvers
Classroom-oriented datasets and tutorials
Public usage analytics to track solver runs Expanded visualization tools for algorithm exploration Larger graph support using high-performance solvers Classroom-oriented datasets and tutorials Public usage analytics to track solver runs These features would help bridge the gap between educational experimentation and practical optimization applications. educational experimentation and practical optimization applications. Conclusion Optimization problems like the Traveling Salesman Problem are often introduced through theory. Tools that allow users to experiment with these problems interactively can make the underlying ideas much clearer. This project aims to provide a simple, accessible platform for exploring TSP solutions in practice, while serving as a foundation for more advanced optimization experiments in the future. simple, accessible platform for exploring TSP solutions in practice

Building a Web-Based Traveling Salesman Solver That Earned a 21 Proof of Usefulness Score

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