# Further Heuristic Methods In Tsp Notes

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Lecture 10: Further Heuristic Methods in TSP Topics

• The "One-Step Greedy" Method

• The "Penalty" Method

Key Points

• One step greedy method

• Penalty method

The "One-Step Greedy" Method

• Again, every iteration contributes one leg towards the N+1 legs in the full tour

• However, the generated partial tours may be disjointed

• Because each iteration looks for the best potential leg regardless of whether it adds on to the current partial tour

• "Greedy" because you want to get the most out of every iteration

• The total sum of the decisions may still not add to an optimal tour

• 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:

• Method of Complete Enumeration (MCE) = Trying every possible tour to find the optimal one Example of the "Two-Steps-Ahead" Method

Course Notes Page 19

• Method of complete enumeration

Definitions

• Method of Complete Enumeration (MCE) = Trying every possible tour to find the optimal one

• Penalty = The difference between the two best links from a given point

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