Simulated annealing cost function for TSP

Question

How does the cost function work for the TSP? Say I have a tour which has a distance of 100, and I change the tour slightly, making 4 changes to the original and it now has a distance of 50.

Would the cost function give me 4, because that's the number of changes; or 50, because of the change in distance? Or maybe I'm missing something and it's neither?

Er, neither - it would be 50, but because that's the distance, not because it's the change. You only care about the solution, not the steps you took to find it. — BlueRaja - Danny Pflughoeft, Mar 16 '13 at 05:48
Ohh sorry, so would the energy be 50 as well because that's how much the distance has changed? — Undefined, Mar 16 '13 at 18:31

score 1 · Answer 1 · answered Mar 16 '13 at 06:29

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The cost function is the total distance.

It is exactly what you want to be minimal.

answered Mar 16 '13 at 06:29

Thiago Curvelo

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Ohh sorry, so would the energy be 50 as well because that's how much the distance has changed? – Undefined Mar 16 '13 at 18:31
No. Because that's how much the salesman will walk on his tour. – Thiago Curvelo Mar 17 '13 at 15:08
So what would the energy be? I thought it was the change in cost? – Undefined Mar 19 '13 at 03:50

score 1 · Answer 2 · edited Sep 08 '17 at 06:26

The cost function is the total distance, yes, but it is also the energy parameter $E$ in Simulated Annealing. It is not the "energy" $E$ that directly determines the probability of transitioning to that state, but it is rather $\Delta{E}$ , the change in energy (the change in cost), that determines the probability $P(\Delta{E})=exp(-\Delta{E}/T)$ .

So the transition from $E=100$ to $E=50$ would be $\Delta{E}=-50$ (100% probability).

The transition from $E=100$ to $E=150$ would be $\Delta{E}=50$, and a probability of ~0.7% if the temperature were 10. $P(\Delta{E}=50)=e^{-50/10}$ .

Simulated annealing cost function for TSP

2 Answers2