用GA解决TSP：距离矩阵是否应加快运行时间？

Question

I am trying to write a GA in Python to solve TSP. I would like to speed it up. Because right now, it takes 24 seconds to run 200 generations with a population size of 200 .

I am using a map with 29 cities . Each city has an id and (x,y) coordinates.

I tried implementing a distance matrix, which calculates all the distances once and stores it in a list. So instead of calculating the distance using the sqrt() function 1M+ times, it only uses the function 406 times. Every time a distance between two cities is required, it is just retrieved from the matrix using the id of the two cities as the index.

But even with this, it takes just as much time. I thought sqrt() would be more expensive than just indexing a list. Is it not? Would a dictionary make it faster?

Answer 1

The short answer:

Yes. Dictionary would make it faster.

The long answer:

Lets say, you pre-processing and calculates all distances once - Great! Now, lets say I want to find the distance between A and B. So, all I have to do now is to find that distance where I put it - it is in the list!

What is the time complexity to find something in the list? Thats right - O(n)

And how may times I'm going to use it? My guess according to your question: 1M+ times

Now, that is a huge problem. I suggest you to use a dictionary so you could search in the pre-calculated distace between any two cities in O(1).