traveling-salesman | C Implementation of Traveling Salesman Problem | Learning library
kandi X-RAY | traveling-salesman Summary
kandi X-RAY | traveling-salesman Summary
The problem: Given a set of cities and known distances between each pair of cities, find a tour in which each city is visited exactly once and the distance travelled is minimized. Implementation: Uses Christofides’ algorithm to construct a tour and the 2-opt algorithm to improve it.
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QUESTION
I am still learning pyomo, and so far i have made some progress:
This link! gives an example of tsp in pyomo. I reproduced the code as below. And everything is working just fine. However, I am not able to print the optimal route, could someone help or give me a fair idea of how to print and plot the optimal route?
The code:
...ANSWER
Answered 2019-Apr-30 at 00:22First you have to think about what form the solution takes. If we look at this imlementation, we see that we have the matrix x with dimensions NxN and the domain binary (0 or 1). Think about what it means for an element x[j][k] to be equal to 1. And what does it mean if j < k or j > k?
To extract the values for x, a simple way might be
QUESTION
I just want some clarification/reassurance, looking at the code on this GitHub here, would the Big O notation for the time complexity by On2, as it is directly proportional to the amount of vertices/cities in the problem?
...ANSWER
Answered 2019-Apr-04 at 17:56The code relies on a distance matrix of cities:
QUESTION
I am trying to solve a Traveling-salesman problem with a flight fares, so main idea is to start from one Airport and visit all Airports only once and return to origin.
So for example: Starting from LAX Visit LV, CA, NY End LAX.
This is a classic graph problem where we can represent an Airport as Node and Route as Edge with a price as edge weights.
So this is the easiest part, what is really confusing me is the dates that user wish to travel. For example I want to give user option to chose a dates that he/she wish to travel, say starting at 01 and finish 15. So I want to find a cheapest way how to do that. For example Output will be something like that:
01 - LAX - LV;
04 - LV - CA;
08 - CA - NY;
15 - NY - LAX
So I understand that I can put extra attributes on edges, but the question is how the algorithm will distinguish how to travers a graph, for example not choosing a edge with a least weight that is already in past.
So you can see that I have a two edges coming out from CA (Note edges format is DD - price, 01 - 20 means 1st of the date and cost 20), and how to deal with this type of situation when multiple edges to same node present.
It also can be viewed as three dimension graph where third dimension is the date that user travels. So the main question is how to deal with those dates?
Hope I got to the point, any suggestions appreciated
Thanks with advance.
...ANSWER
Answered 2018-Feb-05 at 16:40The way I understood your problem, you need the cheapest path which arrives before an specific time. If that's the case, one possible answer can be that you still solve it only based on the prices of the flights, and at the same time for each possible answer in the queue (I am assuming a method like Dijkstra) you keep that how much time has passed (for comparing with deadline).
Whenever you want to add the neighbors of a possible answer you can check that if it is before the deadline and if it is not you ignore that instance.
In summery you are still finding all possible paths from cheapest to the most expensive in order and you choose the first one which does not contradicts with your deadline.
QUESTION
I want to compare Gurobi and Scipy's linear programming tools, such as linprog. Scipy requires to specify problems in a matrix-list-vector-form while Gurobi works like here such that
...ANSWER
Answered 2017-Jun-05 at 11:07That sounds like a lot of work to show the obvious:
- Commercial solvers like Gurobi are much faster and much more robust than non-commercial ones
- There are also high-quality benchmarks showing this by H. Mittelmann (CLP and GLPK beeing the most popular non-commercial ones)
- While scipy's linprog is ok, it's much worse than the open-source competition including CBC/CLP, GLPK, lpSolve...
- Speed and robustness!
- Also: scipy's linprog really seems unmaintained open issues
There are some ways you could do that:
- A) Use linprog's way of problem-definition and convert this to Gurobi-style
- very easy to convert-matrix form to Gurobi's modelling
- B) Use cvxpy as modelling-tool, grab the standard-form and write a wrapper for Gurobi (actually: there is one) and linprog (again easy). This would allow a very powerful modelling-language to be used by both
- Disadvantage: Intransparent transformations according to the problem (e.g.
abs(some_vector)might introduce auxiliary variables)
- Disadvantage: Intransparent transformations according to the problem (e.g.
- C) Write some MPS-reader / or take one from other tools to model you problems within Gurobi, output these and read & solve within linprog
- Candidate tools: cvxopt's mps-reader (well-hidden in the docs), some GLPK-interface or even some CBC-interface
- (Maybe hidden transformations)
No matter what you do, solution-process analysis will be a big part of your code as linprog might fail a lot. It's also not able to handle big sparse models.
Remarks based on your gurobi-example
- Your example (TSP) is a MIP, not an LP
- For MIP, everything said above get's worse (especially performance differences between commerical and open-source)
- There is no MIP-solver within scipy!
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