旅行商问题（TSP）及其解决算法

TSP解决算法

1. 蛮力法（Brute Force）

function bruteForceTSP(graph):
shortestPath = null
shortestDistance = INFINITY

for each permutation in allPermutations(graph.cities):
currentDistance = calculatePathDistance(permutation, graph)
if currentDistance < shortestDistance:
shortestDistance = currentDistance
shortestPath = permutation

return shortestPath

2. 动态规划法（Dynamic Programming）

function dynamicProgrammingTSP(graph):
n = graph.numCities
dp = create2DArray(n, 2^N, INFINITY)

for each city in range(n):
dp[city][0] = graph.distance(city, 0)

for each subsetSize in range(3, n):
for each subset in allSubsetsOfSize(subsetSize, n):
for each destination in subset:
if destination != 0:
dp[destination][subset] = min(
dp[destination][subset],
graph.distance(destination, k) + dp[k][subset - {destination}]
)

return min(dp[1..n-1][allCities])

3. 遗传算法（Genetic Algorithm）

function geneticAlgorithmTSP(graph, populationSize, generations):
population = generateRandomPopulation(graph.numCities, populationSize)

for each generation in range(generations):
population = selectParents(population, graph)
population = crossover(population)
population = mutate(population)

return getBestIndividual(population)

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