def test_3_opt_2(self):
route = [0, 3, 2, 1, 4, 5, 6, 7, 8]
result = tsp_3_opt(self.graph2, route)
new_route_cost = route_cost(self.graph2, result)
old_route_cost = route_cost(self.graph2, route)
print(new_route_cost)
print(old_route_cost)
assert new_route_cost < old_route_cost
def test_permutation_algorithm():
graph = np.array([[0, 5, 2, 1, 1, 4], [5, 0, 6, 2, 2,
5], [2, 6, 0, 7, 4, 2],
[1, 2, 7, 0, 8, 4], [1, 2, 4, 8, 0, 5],
[4, 5, 2, 4, 5, 0]])
route = [0, 1, 2, 3, 4, 5]
result = permutations_tsp(graph)
print(result)
assert route_cost(graph, route) > route_cost(graph, result)
def test_permutation_algorithm_2():
graph = np.array([[0, 4, 3, 4, 5, 1, 2, 3, 4], [4, 0, 1, 4, 3, 4, 6, 2, 1],
[3, 1, 0, 1, 4, 3, 2, 1, 9], [4, 4, 1, 0, 4, 6, 1, 2, 3],
[5, 3, 4, 4, 0, 1, 2, 5, 3], [1, 4, 3, 6, 1, 0, 2, 5, 3],
[2, 6, 2, 1, 2, 2, 0, 3, 5], [3, 2, 1, 2, 5, 5, 3, 0, 9],
[4, 1, 9, 3, 3, 3, 5, 0, 0]])
route = [0, 1, 2, 3, 4, 5, 6, 7, 8]
result = permutations_tsp(graph)
print(route_cost(graph, result))
assert route_cost(graph, route) > route_cost(graph, result)
def test_2_opt_algorithm(self):
graph = np.array([[0, 5, 2, 1, 1, 4],
[5, 0, 6, 2, 2, 5],
[2, 6, 0, 7, 4, 2],
[1, 2, 7, 0, 8, 4],
[1, 2, 4, 8, 0, 5],
[4, 5, 2, 4, 5, 0]])
route = [0, 1, 2, 3, 4, 5]
result = tsp_2_opt(graph, route)
new_route_cost = route_cost(graph, result)
old_route_cost = route_cost(graph, route)
print(new_route_cost)
print(old_route_cost)
print(result)
assert old_route_cost > new_route_cost
def branch_and_bound_tsp_bfs(graph: ndarray):
""" Branch and bound by BFS, lower bound is spanning tree"""
number_of_nodes = len(graph)
bnb_tree = Tree(number_of_nodes)
# top level node
top_lower_bound = 0
for node in graph:
top_lower_bound += np.sum(np.sort(node[node.nonzero()])[:2])
# top node
top_node = Node(top_lower_bound / 2, [0], graph)
bnb_tree.add_leaf(top_node)
while not bnb_tree.optimized():
most_promising_leaf = bnb_tree.get_leaf_with_lowest_bound()
bnb_tree.remove_leaf_from_list(most_promising_leaf)
unvisited_nodes = list(bnb_tree.node_indexes -
set(most_promising_leaf.visited_nodes))
for vertex in unvisited_nodes:
lower_bound = calculate_two_neighbor_bound(graph,
most_promising_leaf,
vertex)
new_leaf = Node(lower_bound,
most_promising_leaf.visited_nodes + [vertex],
most_promising_leaf)
bnb_tree.add_leaf(new_leaf)
if len(new_leaf.visited_nodes) is number_of_nodes:
new_leaf.visited_nodes.append(0)
bnb_tree.set_solution(route_cost(graph,
new_leaf.visited_nodes))
print(*new_leaf.visited_nodes, sep=", ")
print('Solution found %s' %
(str(route_cost(graph, new_leaf.visited_nodes))))
bnb_tree.remove_leaf_from_list(new_leaf)
print('Best solution found: %s' % str(bnb_tree.best_solution_value))
def simulated_annealing(graph,
path=None,
temperature=1,
n_of_iter=1000,
alpha=0.95):
if path is None:
path = christofides_tsp(graph)
changed = True
while changed:
temp_solution = [node for node in path]
for iter in range(n_of_iter):
new_solution = _get_next_solution(path)
new_route_cost = route_cost(graph, new_solution)
current_route_cost = route_cost(graph, path)
if new_route_cost < current_route_cost:
path = new_solution
else:
if np.exp(
(current_route_cost - new_route_cost) /
(temperature * Constants.BOLTZMANN)) > random.random():
path = new_solution
temperature = _decrease_temperature(temperature, alpha)
if temp_solution == path:
changed = False
# just to start with the same node -> we will need to cycle the results.
cycled = cycle(path)
skipped = dropwhile(lambda x: x != 0, cycled)
sliced = islice(skipped, None, len(path))
path = list(sliced)
return path
def tsp_2_opt(graph, route):
"""
Approximate the optimal path of travelling salesman according to 2-opt algorithm
Args:
graph: 2d numpy array as graph
route: list of nodes
Returns:
optimal path according to 2-opt algorithm
Examples:
>>> import numpy as np
>>> graph = np.array([[ 0, 300, 250, 190, 230],
>>> [300, 0, 230, 330, 150],
>>> [250, 230, 0, 240, 120],
>>> [190, 330, 240, 0, 220],
>>> [230, 150, 120, 220, 0]])
>>> tsp_2_opt(graph)
"""
improved = True
best_found_route = route
best_found_route_cost = route_cost(graph, best_found_route)
while improved:
improved = False
for i in range(1, len(best_found_route) - 1):
for k in range(i + 1, len(best_found_route) - 1):
new_route = _swap_2opt(best_found_route, i, k)
new_route_cost = route_cost(graph, new_route)
if new_route_cost < best_found_route_cost:
best_found_route_cost = new_route_cost
best_found_route = new_route
improved = True
break
if improved:
break
return best_found_route
def permutations_tsp(graph):
"""
Creates all permutations from the added graph check all the combinations and the route costs and then
returns the best solution. BEWARE: this method is computationally expensive, therefore it shouldn't be run on over 12 nodes
Args:
graph: graph
Returns:
list of nodes []
"""
route = range(0, len(graph))
# generate all permutations
all_routes = [list(i) for i in permutations(route)]
# calculate all costs
cost_all_routes = [route_cost(graph, i) for i in all_routes]
# find the lowest cost
best_route = all_routes[cost_all_routes.index(min(cost_all_routes))]
return best_route
