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Simulated Annealing for TSP
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/// 1- Generate a random solution | |
func randomSolution(tspProblem: [[Int]]) -> [Int] { | |
var cities = Array(1...tspProblem.count) | |
var randomSoultion:[Int] = [] | |
randomSoultion.append(1) | |
cities.removeAll(where: { $0 == 1}) | |
for _ in 1 ..< tsp.count { | |
let randomCity = cities.shuffled().last! | |
randomSoultion.append(randomCity) | |
cities.removeAll(where: { $0 == randomCity }) | |
} | |
randomSoultion.append(1) | |
return randomSoultion | |
} | |
/// 2- Route Length for a solution | |
func routeLength(for solution: [Int], in tsp: [[Int]]) -> Int { | |
var totalRouteLength = 0 | |
for cityIndex in 0 ... tsp.count - 1 { | |
let distanceFrom = solution[cityIndex] | |
let distanceTo = solution[cityIndex + 1] | |
let length = tsp[distanceFrom - 1][distanceTo - 1] | |
//print("Should get distance from city \(distanceFrom) to city \(distanceTo) is: \(length)") | |
totalRouteLength += length | |
} | |
return totalRouteLength | |
} | |
/// Get Neighbours of a given solution, without changing first element, and last element | |
/// - Parameter solution: an array of numbers | |
/// - Returns: array of array of numbers, where each array is a neighbor | |
func getNeighbours(of solution: [Int]) -> [[Int]] { | |
var neighbours: [[Int]] = [] | |
for i in 1 ... solution.count - 2 { | |
for j in 1 ... solution.count - 2 { | |
var neighbour = solution | |
neighbour[i] = solution[j] | |
neighbour[j] = solution[i] | |
neighbours.append(neighbour) | |
//print(neighbour) | |
} | |
} | |
// print(neighbours) | |
return neighbours | |
} | |
/// Implemntion for Simulating Annealing problem | |
/// - Parameters: | |
/// - tsp: the distance matrix for cities | |
func SimulatedAnnealing(tsp: [[Int]], coolingFunction: (Int) -> Float) { | |
// 1- Generate first solution x₀ | |
var currentSolution = randomSolution(tspProblem: tsp) | |
// 2- get the current routeLength of solution, f(x₀) | |
var currentRouteLength = routeLength(for: currentSolution, in: tsp) | |
var randomSolution:[Int] | |
var randomSolutionLength: Int | |
// 5- the implention of algroithm | |
for currentIteration in 0 ... 100 { | |
randomSolution = getNeighbours(of: currentSolution).randomElement()! | |
randomSolutionLength = routeLength(for: randomSolution, in: tsp) | |
if randomSolutionLength <= currentRouteLength { | |
currentRouteLength = randomSolutionLength | |
currentSolution = randomSolution | |
} else { | |
let randomNumber = Float.random(in: 0 ... 1) | |
let expValue = Float(currentRouteLength - randomSolutionLength) / coolingFunction(currentIteration) | |
if randomNumber < exp(expValue) { | |
currentRouteLength = randomSolutionLength | |
currentSolution = randomSolution | |
} | |
} | |
print("best distance is for \(currentSolution) which is \(currentRouteLength) for index \(currentIteration)") | |
} | |
} | |
var tsp = [ | |
[0,4,10,19,13,15,12,5], | |
[4,0,11,15,14,16,16,9], | |
[10,11,0,9,3,5,8,6], | |
[19,15,9,0,6,5,11,15], | |
[13,14,3,6,0,2,5,9], | |
[15,16,5,5,2,0,7,11], | |
[12,16,8,11,5,7,0,7], | |
[5,9,15,18,12,14,7,0] | |
] | |
var linearFunction: (Int) -> Float = { k in | |
let To: Float = 10 //100 will increase the exploration over explotiaion | |
let η: Float = 0.1 //0.1 provides best / fastest values after 18 iteration 48, or 49 after 15 | |
let Tminimum: Float = 1 | |
return max(To - η * Float(k), Tminimum) | |
} | |
SimulatedAnnealing(tsp: tsp, coolingFunction: linearFunction) |
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