mirror of
https://github.com/fverdugo/XM_40017.git
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Merge branch 'main' of github.com:fverdugo/XM_40017 into main
This commit is contained in:
Francesc Verdugo
commit
d8f8564236
163
notebooks/LEQ.ipynb
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163
notebooks/LEQ.ipynb
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@ -0,0 +1,163 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "599913a3",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Solving Linear Equations\n",
|
||||
"\n",
|
||||
"## Serial Algorithm\n",
|
||||
"First, we construct a linear equations system $Ax=b$."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "fe3b5b02",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"n = 5\n",
|
||||
"A = rand(-10.0:10.0, (n, n))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "57c912fb",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"x = rand(-10.0:10.0, n)\n",
|
||||
"b = A * x"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "4baa0681",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The code in the following cell converts the problem $Ax=b$ to the upper triangular equation system $Ux=y$. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "11d255e0",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"function convert_to_upper_triangular(A,b)\n",
|
||||
" # Upper Triangularization: convert Ax=b to Ux=y\n",
|
||||
" for k in 1:n\n",
|
||||
" for j in k+1:n\n",
|
||||
" # Divide by pivot\n",
|
||||
" A[k,j] = A[k,j] / A[k,k]\n",
|
||||
" end\n",
|
||||
" b[k] = b[k] / A[k,k]\n",
|
||||
" A[k,k] = 1\n",
|
||||
" # Substract lower rows\n",
|
||||
" for i in k+1:n \n",
|
||||
" for j in k+1:n\n",
|
||||
" A[i,j]=A[i,j] - A[i,k] * A[k,j]\n",
|
||||
" end\n",
|
||||
" b[i] = b[i] - A[i,k] * b[k]\n",
|
||||
" A[i,k] = 0\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" return A, b #U,y\n",
|
||||
"end\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "02c47593",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"The function in the following cell solves the upper triangular equation system using backwards substitution. "
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "3c19497c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"function solve_upper_triangular(U,y)\n",
|
||||
" n = size(U,1)\n",
|
||||
" for step in reverse(1:n)\n",
|
||||
" if U[step,step] == 0\n",
|
||||
" if y[step] != 0\n",
|
||||
" return \"No solution\"\n",
|
||||
" else\n",
|
||||
" return \"Infinity solutions\"\n",
|
||||
" end\n",
|
||||
" else\n",
|
||||
" # Backwards substitution\n",
|
||||
" y[step] = y[step] / U[step,step]\n",
|
||||
" end\n",
|
||||
" for row in reverse(1:step-1)\n",
|
||||
" y[row] -= U[row,step] * y[step]\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" return y \n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "2c24d85e",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"U,y = convert_to_upper_triangular(A,b)\n",
|
||||
"sol = solve_upper_triangular(U,y)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "1c356b5a",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"We can test if the obtained solution is correct using `@test`:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "5c71828d",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"using Test\n",
|
||||
"@test sol ≈ x"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "fe3c5374",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
}
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.1",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
"language_info": {
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
"nbformat_minor": 5
|
||||
}
|
||||
@ -31,7 +31,7 @@
|
||||
"id": "ade31d26",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## The all pairs of shortest paths (ASP) problem\n",
|
||||
"## The All Pairs of Shortest Paths (ASP) problem\n",
|
||||
"\n",
|
||||
"Let us start by presenting the all pairs of shortest paths (ASP) problem and its solution with the [Floyd–Warshall algorithm](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm).\n",
|
||||
"\n",
|
||||
@ -70,10 +70,21 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 1,
|
||||
"id": "4fe447c5",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"floyd! (generic function with 1 method)"
|
||||
]
|
||||
},
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"function floyd!(C)\n",
|
||||
" n = size(C,1)\n",
|
||||
@ -99,10 +110,25 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"execution_count": 2,
|
||||
"id": "860e537c",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"4×4 Matrix{Int64}:\n",
|
||||
" 0 9 6 1\n",
|
||||
" 2 0 8 3\n",
|
||||
" 5 3 0 6\n",
|
||||
" 10 8 5 0"
|
||||
]
|
||||
},
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"inf = 1000\n",
|
||||
"C = [\n",
|
||||
@ -296,7 +322,7 @@
|
||||
"id": "db9a3294",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"TODO explain this part"
|
||||
"At each iteration, the processor needs the input values `C[i,j]`, `C[i,k]` and `C[k,j]`. Since we split the data row-wise, the process already has values `C[i,j]` and `C[i,k]`. However, `C[k,j]` may be stored in a different process. "
|
||||
]
|
||||
},
|
||||
{
|
||||
@ -314,6 +340,14 @@
|
||||
"</div>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "a01872ef",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"As we iterate over columns $j$, the process needs input from all values of row $k$. Therefore, at the start of iteration $k$, the whole row $k$ needs to be communicated."
|
||||
]
|
||||
},
|
||||
{
|
||||
"attachments": {
|
||||
"g12957.png": {
|
||||
@ -634,7 +668,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.0",
|
||||
"display_name": "Julia 1.9.1",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
@ -642,7 +676,7 @@
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.0"
|
||||
"version": "1.9.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
@ -291,6 +291,194 @@
|
||||
"rmprocs(workers())"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "19641daf",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## TSP Exercise: Measure search overhead"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "f00557a0",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"## TSP serial \n",
|
||||
"function tsp_serial(connections,city)\n",
|
||||
" num_cities = length(connections)\n",
|
||||
" path=zeros(Int,num_cities)\n",
|
||||
" hops = 1\n",
|
||||
" path[hops] = city\n",
|
||||
" min_path = zeros(Int, num_cities)\n",
|
||||
" current_distance = 0\n",
|
||||
" min_distance = typemax(Int)\n",
|
||||
" # Collect search time \n",
|
||||
" search_time = @elapsed min_path, min_distance = tsp_serial_impl(connections,hops,path,current_distance, min_path, min_distance)\n",
|
||||
" (;path=min_path,distance=min_distance, search_time)\n",
|
||||
"end"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "30784da2",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"## TSP distributed\n",
|
||||
"@everywhere function tsp_dist_impl(wait_time, connections,hops,path,current_distance,min_dist_chnl, max_hops,jobs_chnl,ftr_result)\n",
|
||||
" num_cities = length(connections)\n",
|
||||
" if hops == num_cities\n",
|
||||
" min_distance = fetch(min_dist_chnl)\n",
|
||||
" if current_distance < min_distance\n",
|
||||
" take!(min_dist_chnl)\n",
|
||||
" # Collect wait time to substract from overall search time \n",
|
||||
" if ftr_result !== nothing\n",
|
||||
" wait_time += @elapsed @spawnat 1 begin\n",
|
||||
" result = fetch(ftr_result)\n",
|
||||
" result.path .= path\n",
|
||||
" result.min_distance_ref[] = current_distance\n",
|
||||
" end |> wait\n",
|
||||
" end\n",
|
||||
" put!(min_dist_chnl, current_distance)\n",
|
||||
" end\n",
|
||||
" elseif hops <= max_hops\n",
|
||||
" current_city = path[hops]\n",
|
||||
" next_hops = hops + 1\n",
|
||||
" for (next_city,distance_increment) in connections[current_city]\n",
|
||||
" if !visited(next_city,hops,path)\n",
|
||||
" path[next_hops] = next_city\n",
|
||||
" next_distance = current_distance + distance_increment\n",
|
||||
" # Collect wait time because fetch may block\n",
|
||||
" wait_time += @elapsed min_distance = fetch(min_dist_chnl)\n",
|
||||
" if next_distance < min_distance\n",
|
||||
" tsp_dist_impl(wait_time, connections,next_hops,path,next_distance,min_dist_chnl,max_hops,jobs_chnl,ftr_result)\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" end \n",
|
||||
" else\n",
|
||||
" # Collect communication time and add to wait time\n",
|
||||
" wait_time += @elapsed if jobs_chnl !== nothing \n",
|
||||
" path_copy = copy(path) \n",
|
||||
" put!(jobs_chnl,(;hops,path=path_copy,current_distance))\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" # Return wait time\n",
|
||||
" wait_time\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"function tsp_dist(connections,city)\n",
|
||||
" max_hops = 2\n",
|
||||
" num_cities = length(connections)\n",
|
||||
" path=zeros(Int,num_cities)\n",
|
||||
" result_path=zeros(Int, num_cities)\n",
|
||||
" wait_time = 0\n",
|
||||
" search_time = 0\n",
|
||||
" hops = 1\n",
|
||||
" path[hops] = city\n",
|
||||
" current_distance = 0\n",
|
||||
" min_distance = typemax(Int)\n",
|
||||
" jobs_chnl = RemoteChannel(()->Channel{Any}(10))\n",
|
||||
" min_dist_chnl = RemoteChannel(()->Channel{Int}(1))\n",
|
||||
" put!(min_dist_chnl, min_distance)\n",
|
||||
" ftr_result = @spawnat 1 (;path=result_path,min_distance_ref=Ref(min_distance))\n",
|
||||
" @async begin\n",
|
||||
" # Collect search time from master process\n",
|
||||
" search_time += @elapsed wait_time += tsp_dist_impl(wait_time,connections,hops,path,current_distance,min_dist_chnl,max_hops,jobs_chnl,nothing)\n",
|
||||
" for w in workers()\n",
|
||||
" put!(jobs_chnl,nothing)\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" @sync for w in workers()\n",
|
||||
" @spawnat w begin\n",
|
||||
" path = zeros(Int, num_cities)\n",
|
||||
" max_hops = typemax(Int)\n",
|
||||
" while true\n",
|
||||
" job = take!(jobs_chnl)\n",
|
||||
" if job == nothing\n",
|
||||
" break\n",
|
||||
" end\n",
|
||||
" hops = job.hops\n",
|
||||
" path = job.path \n",
|
||||
" current_distance = job.current_distance\n",
|
||||
" min_distance = fetch(min_dist_chnl)\n",
|
||||
" if current_distance < min_distance\n",
|
||||
" # Collect search time from worker processes \n",
|
||||
" search_time += @elapsed wait_time += tsp_dist_impl(wait_time,connections,hops,path,current_distance,min_dist_chnl,max_hops,nothing,ftr_result)\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" end \n",
|
||||
" result = fetch(ftr_result)\n",
|
||||
" (;path = result.path, distance = result.min_distance_ref[], search_time, wait_time)\n",
|
||||
"end\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "694de934",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"using Distributed\n",
|
||||
"using RandomMatrix\n",
|
||||
"using Plots\n",
|
||||
"\n",
|
||||
"function generate_rand_connections(city_range, distance_range)\n",
|
||||
" # generate random connections matrix \n",
|
||||
" n_cities = rand(city_range)\n",
|
||||
" matrix = randTriangular(distance_range, n_cities; Diag=false)\n",
|
||||
"\n",
|
||||
" connections = Array{Array{Tuple{Int64,Int64},1},1}(undef, n_cities)\n",
|
||||
" for i in 1:n_cities\n",
|
||||
" connections[i] = Array{Tuple{Int64,Int64},1}(undef, n_cities)\n",
|
||||
" end\n",
|
||||
" for i in 1:n_cities\n",
|
||||
" for j in i:n_cities\n",
|
||||
" distance = matrix[i,j]\n",
|
||||
" connections[i][j] = (j,distance)\n",
|
||||
" connections[j][i] = (i,distance)\n",
|
||||
" end\n",
|
||||
" end\n",
|
||||
" return connections\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"# Run once so compile times are not measured\n",
|
||||
"distance_range = 1:100\n",
|
||||
"connections = generate_rand_connections(4:4, distance_range)\n",
|
||||
"tsp_dist(connections,1)\n",
|
||||
"tsp_serial(connections,1)\n",
|
||||
"\n",
|
||||
"# Measure runtimes of serial and parallel algorithm\n",
|
||||
"n_it = 5\n",
|
||||
"city_ranges = [4:4, 6:6, 8:8, 10:10]\n",
|
||||
"search_overhead = zeros(Float64, length(city_ranges), n_it )\n",
|
||||
"for (i, n) in enumerate(city_ranges)\n",
|
||||
" for k in 1:n_it\n",
|
||||
" connections = generate_rand_connections(n, distance_range)\n",
|
||||
" @show n, k\n",
|
||||
" path_dist, distance_dist, search_time_dist, wait_time_dist = tsp_dist(connections,1)\n",
|
||||
" path_serial, distance_serial, search_time_serial = tsp_serial(connections,1)\n",
|
||||
" # Compute search overhead as difference between distributed program and serial program\n",
|
||||
" # (without time spent communicating or waiting)\n",
|
||||
" search_overhead[i, k] = search_time_dist - wait_time_dist - search_time_serial\n",
|
||||
" end\n",
|
||||
"end\n",
|
||||
"\n",
|
||||
"min_search_oh = minimum(search_overhead, dims=2)\n",
|
||||
"city_sizes = [4,6,8,10]\n",
|
||||
"plot(city_sizes, min_search_oh, yaxis=:log, seriestype=:scatter,legend=false)\n",
|
||||
"plot!(city_sizes, min_search_oh, yaxis=:log, legend=false)\n",
|
||||
"\n",
|
||||
"xlabel!(\"Number of cities\")\n",
|
||||
"ylabel!(\"Search overhead (s)\")\n",
|
||||
"title!(\"Minimum search overhead for different problem sizes\")"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "47d88e7a",
|
||||
@ -314,7 +502,7 @@
|
||||
],
|
||||
"metadata": {
|
||||
"kernelspec": {
|
||||
"display_name": "Julia 1.9.0",
|
||||
"display_name": "Julia 1.9.1",
|
||||
"language": "julia",
|
||||
"name": "julia-1.9"
|
||||
},
|
||||
@ -322,7 +510,7 @@
|
||||
"file_extension": ".jl",
|
||||
"mimetype": "application/julia",
|
||||
"name": "julia",
|
||||
"version": "1.9.0"
|
||||
"version": "1.9.1"
|
||||
}
|
||||
},
|
||||
"nbformat": 4,
|
||||
|
||||
122
notebooks/tsp-parallel.jl
Normal file
122
notebooks/tsp-parallel.jl
Normal file
@ -0,0 +1,122 @@
|
||||
using Distributed
|
||||
|
||||
if procs() == workers()
|
||||
addprocs(4)
|
||||
end
|
||||
|
||||
@everywhere function visited(city,hops,path)
|
||||
for i = 1:hops
|
||||
if path[i] == city
|
||||
return true
|
||||
end
|
||||
end
|
||||
return false
|
||||
end
|
||||
|
||||
# solution [1, 4, 5, 2, 3, 6], distance = 222
|
||||
connections = [
|
||||
[(1,0),(4,39),(5,76), (6,78),(3,94),(2,97)],
|
||||
[(2,0),(5,25),(4,58),(3,62),(1,97),(6,109)],
|
||||
[(3,0),(6,58),(2,62),(4,68),(5,70),(1,94)],
|
||||
[(4,0),(5,38),(1,39),(2,58),(3,68),(6,78)],
|
||||
[(5,0),(2,25),(4,38),(3,70),(1,76),(6,104)],
|
||||
[(6,0),(3,58),(1,78),(4,78),(5,104),(2,109)]
|
||||
]
|
||||
|
||||
# Shortest route with start 1: 1-3-2-4 (distance: 7)
|
||||
con2 = [
|
||||
[(1,0), (2,2), (3,3), (4,4)],
|
||||
[(2,0), (4,1), (1,2), (3,3)],
|
||||
[(3,0), (1,3), (2,3), (4,10)],
|
||||
[(4,0), (2,1), (1,4), (3,10)]
|
||||
]
|
||||
|
||||
|
||||
## TSP distributed
|
||||
@everywhere function tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl, max_hops,jobs_chnl,ftr_result)
|
||||
num_cities = length(connections)
|
||||
if hops == num_cities
|
||||
min_distance = fetch(min_dist_chnl)
|
||||
if current_distance < min_distance
|
||||
take!(min_dist_chnl)
|
||||
# Wait until results are written to future
|
||||
if ftr_result !== nothing
|
||||
@spawnat 1 begin
|
||||
result = fetch(ftr_result)
|
||||
result.path .= path
|
||||
result.min_distance_ref[] = current_distance
|
||||
end |> wait
|
||||
end
|
||||
# Unblock waiting processes
|
||||
put!(min_dist_chnl, current_distance)
|
||||
end
|
||||
elseif hops <= max_hops
|
||||
current_city = path[hops]
|
||||
next_hops = hops + 1
|
||||
for (next_city,distance_increment) in connections[current_city]
|
||||
if !visited(next_city,hops,path)
|
||||
path[next_hops] = next_city
|
||||
next_distance = current_distance + distance_increment
|
||||
min_distance = fetch(min_dist_chnl)
|
||||
if next_distance < min_distance
|
||||
tsp_dist_impl(connections,next_hops,path,next_distance,min_dist_chnl,max_hops,jobs_chnl,ftr_result)
|
||||
end
|
||||
end
|
||||
end
|
||||
else
|
||||
if jobs_chnl !== nothing
|
||||
# Allocate new memory so paths are not overwritten in queue
|
||||
path_copy = copy(path)
|
||||
put!(jobs_chnl,(;hops,path=path_copy,current_distance))
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
function tsp_dist(connections,city)
|
||||
max_hops = 2
|
||||
num_cities = length(connections)
|
||||
path=zeros(Int,num_cities)
|
||||
result_path=zeros(Int, num_cities)
|
||||
hops = 1
|
||||
path[hops] = city
|
||||
current_distance = 0
|
||||
min_distance = typemax(Int)
|
||||
jobs_chnl = RemoteChannel(()->Channel{Any}(10))
|
||||
# Initialize min distance channel with Intmax
|
||||
min_dist_chnl = RemoteChannel(()->Channel{Int}(1))
|
||||
put!(min_dist_chnl, min_distance)
|
||||
# Future to store overall result
|
||||
ftr_result = @spawnat 1 (;path=result_path,min_distance_ref=Ref(min_distance))
|
||||
@async begin
|
||||
tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl,max_hops,jobs_chnl,nothing)
|
||||
for w in workers()
|
||||
put!(jobs_chnl,nothing)
|
||||
end
|
||||
end
|
||||
@sync for w in workers()
|
||||
@spawnat w begin
|
||||
path = zeros(Int, num_cities)
|
||||
max_hops = typemax(Int)
|
||||
jobs_channel = nothing
|
||||
while true
|
||||
job = take!(jobs_chnl)
|
||||
if job == nothing
|
||||
break
|
||||
end
|
||||
hops = job.hops
|
||||
path = job.path
|
||||
current_distance = job.current_distance
|
||||
# Prune this job if current distance exeeds search threshold
|
||||
min_distance = fetch(min_dist_chnl)
|
||||
if current_distance < min_distance
|
||||
tsp_dist_impl(connections,hops,path,current_distance,min_dist_chnl,max_hops,jobs_channel,ftr_result)
|
||||
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
result = fetch(ftr_result)
|
||||
(;path = result.path, distance = result.min_distance_ref[])
|
||||
end
|
||||
city = 1
|
||||
tsp_dist(connections,city)
|
||||
66
notebooks/tsp-serial.jl
Normal file
66
notebooks/tsp-serial.jl
Normal file
@ -0,0 +1,66 @@
|
||||
using Distributed
|
||||
|
||||
connections = [
|
||||
[(1,0),(4,39),(5,76), (6,78),(3,94),(2,97)],
|
||||
[(2,0),(5,25),(4,58),(3,62),(1,97),(6,109)],
|
||||
[(3,0),(6,58),(2,62),(4,68),(5,70),(1,94)],
|
||||
[(4,0),(5,38),(1,39),(2,58),(3,68),(6,78)],
|
||||
[(5,0),(2,25),(4,38),(3,70),(1,76),(6,104)],
|
||||
[(6,0),(3,58),(1,78),(4,78),(5,104),(2,109)]
|
||||
]
|
||||
|
||||
# Shortest route with start 1: 1-3-2-4 (distance: 7)
|
||||
con2 = [
|
||||
[(1,0), (2,2), (3,3), (4,4)],
|
||||
[(2,0), (4,1), (1,2), (3,3)],
|
||||
[(3,0), (1,3), (2,3), (4,10)],
|
||||
[(4,0), (2,1), (1,4), (3,10)]
|
||||
]
|
||||
|
||||
@everywhere function visited(city,hops,path)
|
||||
for i = 1:hops
|
||||
if path[i] == city
|
||||
return true
|
||||
end
|
||||
end
|
||||
return false
|
||||
end
|
||||
|
||||
## TSP serial
|
||||
function tsp_serial_impl(connections,hops,path,current_distance, min_path, min_distance)
|
||||
num_cities = length(connections)
|
||||
if hops == num_cities
|
||||
if current_distance < min_distance
|
||||
min_path .= path
|
||||
return min_path, current_distance
|
||||
end
|
||||
else
|
||||
current_city = path[hops]
|
||||
next_hops = hops + 1
|
||||
for (next_city,distance_increment) in connections[current_city]
|
||||
if !visited(next_city,hops,path)
|
||||
path[next_hops] = next_city
|
||||
next_distance = current_distance + distance_increment
|
||||
if next_distance < min_distance
|
||||
min_path, min_distance = tsp_serial_impl(connections,next_hops,path,next_distance,min_path,min_distance)
|
||||
end
|
||||
end
|
||||
end
|
||||
end
|
||||
return min_path, min_distance
|
||||
end
|
||||
|
||||
function tsp_serial(connections,city)
|
||||
num_cities = length(connections)
|
||||
path=zeros(Int,num_cities)
|
||||
hops = 1
|
||||
path[hops] = city
|
||||
min_path = zeros(Int, num_cities)
|
||||
current_distance = 0
|
||||
min_distance = typemax(Int)
|
||||
min_path, min_distance = tsp_serial_impl(connections,hops,path,current_distance, min_path, min_distance)
|
||||
(;path=min_path,distance=min_distance)
|
||||
end
|
||||
|
||||
city = 1
|
||||
tsp_serial(connections,city)
|
||||
Loading…
x
Reference in New Issue
Block a user