### Further Heuristic Methods In Tsp Notes

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Lecture 10: Further Heuristic Methods in TSP
• The "One-Step Greedy" Method • One step greedy method
• The "Penalty" Method
• Penalty method
The "One-Step Greedy" Method • Method of complete enumeration
• Again, every iteration contributes one leg towards the N+1 legs in the full tour
• However, the generated partial tours may be disjointed Definitions
• Because each iteration looks for the best potential leg regardless of whether it adds • Method of Complete Enumeration (MCE) = Trying every
on to the current partial tour possible tour to find the optimal one
• "Greedy" because you want to get the most out of every iteration
• Penalty = The difference between the two best links from
• The total sum of the decisions may still not add to an optimal tour
a given point
• A short term decision in an iteration may side-track you into less optimal areas

Example of the "One-Step Greedy" Method

• Again, we should always check the reverse tour, which in this case is not so good at 53 minutes
• There are 4! = 24 possible tours
• Other methods we will examine seek to reduce the chances of getting stuck in a bad area such at
in iteration 4

• There is reduced chance of getting stuck in a relatively expensive dead-end
• Two versions of the method:
• Start from O and always build a continuous partial tour
• Start from the cheapest and use a greedy approach again
• Will generally find better tours but requires more effort
• The basic idea is at any iteration, find the cheapest double-link
○ i.e. from X→ Y→ Z then add to the tour only the first of these two links
• When faced with a tie: