Travelling Salesman Problem(TSP) Using Heuristic Search
Heuristic Search and Traveling Salesman Problem (TSP)
Heuristic search is a problem-solving strategy that uses experience-based techniques to find solutions efficiently when exhaustive search is impractical. It evaluates possible moves based on a heuristic function, which estimates how close a given state is to the goal. This allows the algorithm to prioritize promising paths, reducing the search space and speeding up the solution process.
Traveling Salesman Problem (TSP) Using Heuristic Search
The Traveling Salesman Problem (TSP) involves finding the shortest possible route that visits each city exactly once and returns to the starting city. Because TSP is NP-hard, exact solutions for large instances are computationally expensive. Heuristic methods provide near-optimal solutions in reasonable time.
Algorithm Overview:
- Start Point Selection: Choose any city as the starting point, since the route is cyclic.
- Traversal: Move from the current city to one of its unvisited neighboring cities.
- Cost Evaluation: Calculate the travel cost for each possible move and select the city that minimizes the cumulative distance.
- Update Minimum Cost: Keep track of the minimum cost path found so far and update it whenever a better route is discovered.
- Repeat: Continue visiting unvisited cities using the heuristic evaluation until all cities have been included in the route.
- Return to Start: After visiting all cities, return to the starting city to complete the cycle.
- Output: The algorithm returns the route with the minimum estimated travel cost found during the search.
Key Points:
- Heuristic search does not guarantee the global optimum but provides a good approximation.
- It balances exploration and exploitation by using cost estimates to guide the search efficiently.
Example:
Suppose a salesman must visit cities A, B, C, and D. Using a heuristic, the algorithm may choose the nearest unvisited city at each step. The resulting route, e.g., A → B → D → C → A, may not be the absolute shortest, but it will be close and computed efficiently.
Applications:
- Route optimization for logistics and delivery systems.
- Planning efficient travel itineraries.
- Network routing and resource allocation problems.