Anonymous
9 hours ago
Outline the procedure of the Clark and Wright heuristic technique for solving the traveling salesman problem.
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ChatGPT
9 hours ago
1. Calculate the savings matrix: For each pair of nodes i and j, calculate the savings in distance that would result from combining the routes from i to the depot and from the depot to j into a single route from i to j. The savings are calculated as the sum of the distances from i to the depot, from the depot to j, minus the distance from i to j.
2. Sort the savings matrix in descending order: Sort the savings matrix in descending order based on the calculated savings.
3. Initialize the routes: Start with each node as a separate route.
4. Merge routes: Starting from the top of the sorted savings matrix, merge the routes of the corresponding nodes i and j if merging them results in a feasible route (i.e., the resulting route does not violate any constraints such as capacity or time limits).
5. Repeat step 4 until all nodes are visited: Continue merging routes based on the sorted savings matrix until all nodes are visited.
6. Optimize the routes: After merging all nodes into a single route, optimize the route by rearranging the order of nodes to minimize the total distance traveled.
7. Output the optimized route: Output the optimized route as the solution to the traveling salesman problem.
2. Sort the savings matrix in descending order: Sort the savings matrix in descending order based on the calculated savings.
3. Initialize the routes: Start with each node as a separate route.
4. Merge routes: Starting from the top of the sorted savings matrix, merge the routes of the corresponding nodes i and j if merging them results in a feasible route (i.e., the resulting route does not violate any constraints such as capacity or time limits).
5. Repeat step 4 until all nodes are visited: Continue merging routes based on the sorted savings matrix until all nodes are visited.
6. Optimize the routes: After merging all nodes into a single route, optimize the route by rearranging the order of nodes to minimize the total distance traveled.
7. Output the optimized route: Output the optimized route as the solution to the traveling salesman problem.
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Google Gemini AI
9 hours ago
Clark and Wright Heuristic Technique for Traveling Salesman Problem
1. Initialization
- Construct a complete graph with the cities as nodes and distances as edge weights.
- Select a starting city.
2. Savings Calculation
- For each pair of unvisited cities (i, j), calculate the savings:
- Savings(i, j) = Distance(start, i) + Distance(j, start) - Distance(i, j)
3. Edge Selection
- Sort the savings values in descending order.
- Select the savings edge with the highest value that does not create a cycle.
- Add the selected edge to the route.
4. Route Construction
- Repeat Step 3 until all cities are visited.
- When a city is visited twice, a sub-tour is completed.
5. Sub-tour Linking
- Identify the sub-tours in the route.
- Select the cheapest edge between two different sub-tours to link them.
- Repeat until only one sub-tour remains.
6. Optimization
- Perform 2-opt or 3-opt local search to further improve the route.
7. Output
- The resulting route represents a feasible solution to the traveling salesman problem.
1. Initialization
- Construct a complete graph with the cities as nodes and distances as edge weights.
- Select a starting city.
2. Savings Calculation
- For each pair of unvisited cities (i, j), calculate the savings:
- Savings(i, j) = Distance(start, i) + Distance(j, start) - Distance(i, j)
3. Edge Selection
- Sort the savings values in descending order.
- Select the savings edge with the highest value that does not create a cycle.
- Add the selected edge to the route.
4. Route Construction
- Repeat Step 3 until all cities are visited.
- When a city is visited twice, a sub-tour is completed.
5. Sub-tour Linking
- Identify the sub-tours in the route.
- Select the cheapest edge between two different sub-tours to link them.
- Repeat until only one sub-tour remains.
6. Optimization
- Perform 2-opt or 3-opt local search to further improve the route.
7. Output
- The resulting route represents a feasible solution to the traveling salesman problem.
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