How does a 2-Opt swap work to improve a route?

Conditions

• Requires an existing valid TSP route.
• Involves selecting two distinct edges.
• The reconnection must produce a single valid cycle.

Reasoning, step by step

1. Identify two edges in the current route that can be swapped.
2. Remove the two selected edges.
3. Reconnect the four endpoints of the removed edges in a different configuration.
4. Verify that the new configuration forms a valid single cycle.
5. Calculate the new total distance to confirm improvement.

Example

The video shows a 2-Opt swap being applied to a self-crossing greedy route, successfully eliminating the intersection and reducing the total distance from 8969 km to 8570 km.

Common misconceptions

• Believing that a 2-Opt swap can only be applied to routes generated by the Greedy Algorithm.
• Assuming that any random reconnection of two edges will always improve the route.

Watch the explanation

Explore next

• What is the process of Local Search optimization and what is its main limitation?
• Why does the Greedy Algorithm fail to find the optimal solution for TSP?
• What is a 2-opt swap in the context of TSP?