Quantum annealing for traveling salesman problem executed in R language. You can also operate it on the browser.
The Traveling Salesman Problem (TSP) is a combination of a set of cities and a distance between each two cities to find the one with the smallest total distance traveled by a tour traveling around all cities just once and returning to the departure place It is an optimization problem. This problem belongs to the class of NP difficulties in computational complexity theory.
Quantum annealing is a metaheuristic for finding the global minimum of a given objective function over a given set of candidate solutions, by a process using quantum fluctuations.
The qatsp package simulates quantum annealing in the R language and can approximate the traveling salesman problem. Quantum Monte Carlo method is used for simulation of quantum annealing.
I refer to "Combinatorial optimization with quantum annealing" implemented with python.
You can install from R console.
If devtools is not installed on your PC, install devtools with Internet connection.
install.packages("devtools")
Install from GitHub using devtools.
library(devtools)
install_github("ToshihiroIguchi/qatsp")
Load the qatsp package and attach it.
library(qatsp)
Installation may fail if running under proxy environment.
In that case, you may be able to install using the httr package.
If you do not install the qatsp package, you can perform quantum annealing even if you copy the code and data and paste it into the R console.
For reproducibility of results, we set random seeds.
set.seed(123)
Designate city coordinates for x and y to solve the traveling salesman problem. The length of x and y must be the same. We will explain by way of example about traveling municipalities in Akita prefecture of Japan.
There are 25 points in this latitude and longitude data.
It seems that it takes 359 days if supercomputer K calculates the shortest route with brute force.
The latitude is stored in Akita [, 1]. Longitude is stored in Akita [, 2].
Perform quantum annealing with qatsp function.
result <- qatsp(x = Akita[,1], y= Akita[,2])
By default, trace = TRUE, and the transition of the shortest distance during calculation is displayed on the graph.
Optionally, by setting route = TRUE, the shortest route is displayed every time the shortest route is updated during calculation.
Other parameters of the qatsp function are
beta = 50, trotter = 10, ann_para = 1, ann_step = 500, mc_step = 5000, and reduc = 0.99 by default.
summary function can display summary.
summary(result)
The shortest path, the shortest distance, the parameters used for calculation, and the calculation time are displayed.
The transition of the shortest distance is displayed by the plot function.
plot(result)
The shortest path obtained by the route function is displayed.
route(result)
Combinatorial optimization with quantum annealing
Akita Prefecture - Geographical Survey Institute
Astonishing quantum computers - suddenly commercialized dream machines
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Copyright (c) 2017 Toshihiro Iguchi
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Toshihiro Iguchi