# Travelling salesman problem variant without returning to the starting point

The actual requirement is to traverse all paths without returning to the start point with minimum distance to travel.

Then I found this link on stackoverflow https://stackoverflow.com/a/7158721/3016453

I added a dummy point and run the first algorithm but not get the expected output. But this is upvoted more than 35 times. I don't know where I am wrong.

I ran the below code with both above-mentioned method:

import json

import numpy as np
from ortools.constraint_solver import routing_enums_pb2
from ortools.constraint_solver import pywrapcp

app.config["DEBUG"] = True

def create_data_model(distance_input_matrix):
"""Stores the data for the problem."""
data = {'distance_matrix': distance_input_matrix, 'num_vehicles': 1, 'depot': 0}
# data['distance_matrix'] = [
#     [0, 2451, 713, 1018, 1631, 1374, 2408, 213, 2571, 875, 1420, 2145, 1972],
#     [2451, 0, 1745, 1524, 831, 1240, 959, 2596, 403, 1589, 1374, 357, 579],
#     [713, 1745, 0, 355, 920, 803, 1737, 851, 1858, 262, 940, 1453, 1260],
#     [1018, 1524, 355, 0, 700, 862, 1395, 1123, 1584, 466, 1056, 1280, 987],
#     [1631, 831, 920, 700, 0, 663, 1021, 1769, 949, 796, 879, 586, 371],
#     [1374, 1240, 803, 862, 663, 0, 1681, 1551, 1765, 547, 225, 887, 999],
#     [2408, 959, 1737, 1395, 1021, 1681, 0, 2493, 678, 1724, 1891, 1114, 701],
#     [213, 2596, 851, 1123, 1769, 1551, 2493, 0, 2699, 1038, 1605, 2300, 2099],
#     [2571, 403, 1858, 1584, 949, 1765, 678, 2699, 0, 1744, 1645, 653, 600],
#     [875, 1589, 262, 466, 796, 547, 1724, 1038, 1744, 0, 679, 1272, 1162],
#     [1420, 1374, 940, 1056, 879, 225, 1891, 1605, 1645, 679, 0, 1017, 1200],
#     [2145, 357, 1453, 1280, 586, 887, 1114, 2300, 653, 1272, 1017, 0, 504],
#     [1972, 579, 1260, 987, 371, 999, 701, 2099, 600, 1162, 1200, 504, 0],
# ]  # yapf: disable
return data

def print_solution(manager, routing, solution):
"""Prints solution on console."""
# print('Objective: {} miles'.format(solution.ObjectiveValue()))
index = routing.Start(0)
# plan_output = 'Route for vehicle 0:\n'
plan_output = ''
route_distance = 0
while not routing.IsEnd(index):
plan_output += '{}->'.format(manager.IndexToNode(index))
previous_index = index
index = solution.Value(routing.NextVar(index))
route_distance += routing.GetArcCostForVehicle(previous_index, index, 0)
plan_output += '{}'.format(manager.IndexToNode(index))
return plan_output
# print(plan_output)
# plan_output += 'Route distance: {}miles\n'.format(route_distance)

def main(distance_input_matrix=None):
"""Entry point of the program."""
# Instantiate the data problem.
data = create_data_model(distance_input_matrix)

# Create the routing index manager.
manager = pywrapcp.RoutingIndexManager(len(data['distance_matrix']),
data['num_vehicles'], data['depot'])

# Create Routing Model.
routing = pywrapcp.RoutingModel(manager)

def distance_callback(from_index, to_index):
"""Returns the distance between the two nodes."""
# Convert from routing variable Index to distance matrix NodeIndex.
from_node = manager.IndexToNode(from_index)
to_node = manager.IndexToNode(to_index)
return data['distance_matrix'][from_node][to_node]

transit_callback_index = routing.RegisterTransitCallback(distance_callback)

# Define cost of each arc.
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)

# Setting first solution heuristic.
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)

# Solve the problem.
solution = routing.SolveWithParameters(search_parameters)

# Print solution on console.
if solution:
return print_solution(manager, routing, solution)

@app.route('/', methods=['GET'])
def home():
return main()

@app.route('/optimize', methods=['POST'])
def optimize():
if request.json:
data_matrix = request.json['data']
narrows = len(data_matrix)  # 3 rows in your example
narcs = len(data_matrix[0])
a = np.zeros((narrows + 1, narcs + 1), dtype='int32').tolist()
for i in range(len(data_matrix)):
for j in range(len(data_matrix[i])):
a[i][j] = data_matrix[i][j]
#result = main(a)
result = main(data_matrix)
r_l = result.split('->')
#r_l.remove(str(narrows))
return jsonify({'data': r_l})

app.run()

• I am not completely sure about what your problem is. But if it is a "TSP with a fixed starting point and no return to start" you can solve an ordinary TSP with all in-going arcs to the starting point having zero cost. – Sune Apr 26 at 13:04
• I have updated the Input Martix as you said . but still not getting the corrected result. here the updated matrix. { "data" : [ [0, 2451, 713, 200, 16310, 1374, 2408], [0, 0, 1745, 1524, 831, 1240, 959], [0, 1745, 0, 355, 920, 803, 1737], [0, 1524, 355, 0, 700, 862, 1395], [0, 831, 920, 700, 0, 663, 1021], [0, 1240, 803, 862, 663, 0, 1681], [0, 959, 1737, 1395, 1021, 1681, 0] ] } – dev21 Apr 26 at 14:22
• I think a methematical model, or a more detailed description of the problem, would help. As I said in the comment before, I am not completely sure what problem you want to solve. – Sune Apr 26 at 18:53
• Hi @Sune I think its working now. I provided the wrong input to the algorithm. Thanks for your help. – dev21 Apr 27 at 5:18
• that's good you figured it out. Did my comment answer your question. If so, I will turn it into an answer for future visiters – Sune Apr 27 at 6:09