A Python Implementation of a Genetic Algorithm-based Solution to Vehicle Routing Problem with Time Windows (VRPTW)
Important
This project is originated from a university course project.
In 2016, a friend of mine, majoring in logistic engineering, came to me to discuss his course work project. He wanted to solve VRPTW using genetic algorithm, which I happened to know. The discussion went well and my friend got what he needed.
After that, I implemented the approach in Python. The first version of the this project came out that night.
I wrote this project on the spur of that moment. However, after running a few tests with several combinations of parameters and set-ups, I realized that implementing the idea is one thing, and tuning the algorithm to yield a converged result is another thing. The latter would definitely require much more effort.
Therefore, I should say, to be precise, the performances of the given examples are very poor.
Of course, tuning improvements of this algorithm and forks are always welcome.
- Installation
- Quick Start
- Problem Sets
- GA Implementation
- API Reference
- File Structure
- Further Reading
- References
- License
On Unix, Linux, BSD, macOS, and Cygwin:
git clone https://github.com/iRB-Lab/py-ga-VRPTW.git
cd py-ga-VRPTW
python3 -m venv venv
source venv/bin/activate
pip install -r requirements.txtSee sample codes.
Solomon's VRPTW Benchmark Problems1
| Problem Set | Random | Clustered | Random & Clustered |
|---|---|---|---|
| Short Scheduling Horizon | R1-type | C1-type | RC1-type |
| Long Scheduling Horizon | R2-type | C2-type | RC2-type |
Note
-
Solomon generated six sets of problems. Their design highlights several factors that affect the behavior of routing and scheduling algorithms. They are:
- geographical data;
- the number of customers serviced by a vehicle;
- percent of time-constrained customers; and
- tightness and positioning of the time windows.
-
The geographical data are randomly generated in problem sets R1 and R2, clustered in problem sets C1 and C2, and a mix of random and clustered structures in problem sets by RC1 and RC2.
-
Problem sets R1, C1 and RC1 have a short scheduling horizon and allow only a few customers per route (approximately 5 to 10). In contrast, the sets R2, C2 and RC2 have a long scheduling horizon permitting many customers (more than 30) to be serviced by the same vehicle.
-
The customer coordinates are identical for all problems within one type (i.e., R, C and RC).
-
The problems differ with respect to the width of the time windows. Some have very tight time windows, while others have time windows which are hardly constraining. In terms of time window density, that is, the percentage of customers with time windows, I created problems with 25, 50, 75 and 100% time windows.
-
The larger problems are 100 customer euclidean problems where travel times equal the corresponding distances. For each such problem, smaller problems have been created by considering only the first 25 or 50 customers.
See Solomon's website.
The text files corresponding to the problem instances can be found under the data/text/ directory. Each text file is named with respect to its corresponding instance name, e.g.: the text file corresponding to problem instance C101 is C101.txt, and locates at data/text/C101.txt.
Below is a description of the format of the text file that defines each problem instance (assuming 100 customers).
<Instance name>
<empty line>
VEHICLE
NUMBER CAPACITY
K Q
<empty line>
CUSTOMER
CUST NO. XCOORD. YCOORD. DEMAND READY TIME DUE DATE SERVICE TIME
<empty line>
0 x0 y1 q0 e0 l0 s0
1 x1 y2 q1 e1 l1 s1
... ... ... ... ... ... ...
100 x100 y100 q100 e100 l100 s100
Note
- All constants are integers.
CUST NO.0 denotes the depot, where all vehicles must start and finish.Kis the maximum number of vehicles.Qthe capacity of each vehicle.READY TIMEis the earliest time at which service may start at the given customer/depot.DUE DATEis the latest time at which service may start at the given customer/depot.- The value of time is equal to the value of distance.
- As a backup, you can download a zip-file with the 100 customers instance definitions2 here.
For the further convenience, a Python script named text2json.py is written to convert problem instances from the text file format to JSON format and stored under the data/json/ directory. Like the text files, each JSON file is named with respect to its corresponding instance name, e.g.: the JSON file corresponding to problem instance C101 is C101.json, and locates at data/json/C101.json.
Below is a description of the format of the JSON file that defines each problem instance (assuming 100 customers).
{
"instance_name" : "<Instance name>",
"max_vehicle_number" : K,
"vehicle_capacity" : Q,
"depart" : {
"coordinates" : {
"x" : x0,
"y" : y0
},
"demand" : q0,
"ready_time" : e0,
"due_time" : l0,
"service_time" : s0
},
"customer_1" : {
"coordinates" : {
"x" : x1,
"y" : y2
},
"demand" : q1,
"ready_time" : e1,
"due_time" : l1,
"service_time" : s1
},
...
"customer_100" : {
"coordinates" : {
"x" : x100,
"y" : y100
},
"demand" : q100,
"ready_time" : e100,
"due_time" : l100,
"service_time" : s100
},
"distance_matrix" : [
[dist0_0, dist0_1, ..., dist0_100],
[dist1_0, dist1_1, ..., dist1_100],
...
[dist100_0, dist100_1, ..., dist0_0]
]
}Note
dist1_1denotes the distance between Customer 1 and Customer 1, which should be 0, obviously.- To obtain the distance value between Customer 1 and Customer 2 in Python can be done by using
<json_data>['distance_matrix'][1][2], where<json_data>denotes the name of a Pythondictobject.
You can customize your own problem instances.
The customized problem instance data file should be either text file format or JSON format, exactly the same as the above given examples.
Customized *.txt files should be put under the data\text_customize\ directory, and customized *.json files should be put under the data\json_customize\ directory.
Run the text2json_customize.py script to convert *.txt file containing customized problem instance data to *.json file.
python text2json_customize.pyThe customize_data flag of the run_gavrptw() method should be set to True. For further understanding, please refer to the sample codes section at the end of this document.
All visited customers of a route (including several sub-routes) are coded into an individual in turn. For example, the following route
Sub-route 1: 0 - 5 - 3 - 2 - 0
Sub-route 2: 0 - 7 - 1 - 6 - 9 - 0
Sub-route 3: 0 - 8 - 4 - 0
are coded as 5 3 2 7 1 6 9 8 4, which can be stored in a Python list object, i.e., [5, 3, 2, 7, 1, 6, 9, 8, 4].
ind2route(individual, instance)decodes individual to route representation. To show the difference between an individual and a route, an example is given below.
# individual
[5, 3, 2, 7, 1, 6, 9, 8, 4]
# route
[[5, 3, 2], [7, 1, 6, 9], [8, 4]]individual– An individual to be decoded.instance– A problem instancedictobject, which can be loaded from a JSON format file.
- A list of decoded sub-routes corresponding to the input individual.
def ind2route(individual, instance):
route = []
vehicle_capacity = instance['vehicle_capacity']
depart_due_time = instance['depart']['due_time']
# Initialize a sub-route
sub_route = []
vehicle_load = 0
elapsed_time = 0
last_customer_id = 0
for customer_id in individual:
# Update vehicle load
demand = instance[f'customer_{customer_id}']['demand']
updated_vehicle_load = vehicle_load + demand
# Update elapsed time
service_time = instance[f'customer_{customer_id}']['service_time']
return_time = instance['distance_matrix'][customer_id][0]
updated_elapsed_time = elapsed_time + \
instance['distance_matrix'][last_customer_id][customer_id] + service_time + return_time
# Validate vehicle load and elapsed time
if (updated_vehicle_load <= vehicle_capacity) and (updated_elapsed_time <= depart_due_time):
# Add to current sub-route
sub_route.append(customer_id)
vehicle_load = updated_vehicle_load
elapsed_time = updated_elapsed_time - return_time
else:
# Save current sub-route
route.append(sub_route)
# Initialize a new sub-route and add to it
sub_route = [customer_id]
vehicle_load = demand
elapsed_time = instance['distance_matrix'][0][customer_id] + service_time
# Update last customer ID
last_customer_id = customer_id
if sub_route != []:
# Save current sub-route before return if not empty
route.append(sub_route)
return routeprint_route(route, merge=False)prints sub-routes information to screen.
route– Aroutedecoded byind2route(individual, instance).merge– IfTure, detailed sub-routes are displayed in a single line.
- None
def print_route(route, merge=False):
route_str = '0'
sub_route_count = 0
for sub_route in route:
sub_route_count += 1
sub_route_str = '0'
for customer_id in sub_route:
sub_route_str = f'{sub_route_str} - {customer_id}'
route_str = f'{route_str} - {customer_id}'
sub_route_str = f'{sub_route_str} - 0'
if not merge:
print(f' Vehicle {sub_route_count}\'s route: {sub_route_str}')
route_str = f'{route_str} - 0'
if merge:
print(route_str)eval_vrptw(individual, instance, unit_cost=1.0, init_cost=0, wait_cost=0, delay_cost=0)takes one individual as argument and returns its fitness as a Python tuple object.
individual- An individual to be evaluated.instance- A problem instancedictobject, which can be loaded from a JSON format file.unit_cost- The transportation cost of one vehicle for a unit distance.init_cost- The start-up cost of a vehicle.wait_cost- Cost per unit time if the vehicle arrives early than the customer's ready time.delay_cost- Cost per unit time if the vehicle arrives later than the due time.
- A tuple of one fitness value of the evaluated individual.
def eval_vrptw(individual, instance, unit_cost=1.0, init_cost=0, wait_cost=0, delay_cost=0):
total_cost = 0
route = ind2route(individual, instance)
total_cost = 0
for sub_route in route:
sub_route_time_cost = 0
sub_route_distance = 0
elapsed_time = 0
last_customer_id = 0
for customer_id in sub_route:
# Calculate section distance
distance = instance['distance_matrix'][last_customer_id][customer_id]
# Update sub-route distance
sub_route_distance = sub_route_distance + distance
# Calculate time cost
arrival_time = elapsed_time + distance
time_cost = wait_cost * max(instance[f'customer_{customer_id}']['ready_time'] - \
arrival_time, 0) + delay_cost * max(arrival_time - \
instance[f'customer_{customer_id}']['due_time'], 0)
# Update sub-route time cost
sub_route_time_cost = sub_route_time_cost + time_cost
# Update elapsed time
elapsed_time = arrival_time + instance[f'customer_{customer_id}']['service_time']
# Update last customer ID
last_customer_id = customer_id
# Calculate transport cost
sub_route_distance = sub_route_distance + instance['distance_matrix'][last_customer_id][0]
sub_route_transport_cost = init_cost + unit_cost * sub_route_distance
# Obtain sub-route cost
sub_route_cost = sub_route_time_cost + sub_route_transport_cost
# Update total cost
total_cost = total_cost + sub_route_cost
fitness = 1.0 / total_cost
return (fitness, )deap.tools.selRoulette(individuals, k)selects k individuals from the input individuals using k spins of a roulette. The selection is made by looking only at the first objective of each individual. The list returned contains references to the input individuals.
individuals– A list of individuals to select from.k– The number of individuals to select.
- A list of selected individuals.
def selRoulette(individuals, k):
s_inds = sorted(individuals, key=attrgetter(fit_attr), reverse=True)
sum_fits = sum(getattr(ind, fit_attr).values[0] for ind in individuals)
chosen = []
for i in range(k):
u = random.random() * sum_fits
sum_ = 0
for ind in s_inds:
sum_ += getattr(ind, fit_attr).values[0]
if sum_ > u:
chosen.append(ind)
break
return chosencx_partially_matched(ind1, ind2)executes a partially matched crossover (PMX) on the input individuals. The two individuals are modified in place. This crossover expects sequence individuals of indexes, the result for any other type of individuals is unpredictable.
ind1– The first individual participating in the crossover.ind2– The second individual participating in the crossover.
- A tuple of two individuals.
def cx_partially_matched(ind1, ind2):
cxpoint1, cxpoint2 = sorted(random.sample(range(min(len(ind1), len(ind2))), 2))
part1 = ind2[cxpoint1:cxpoint2+1]
part2 = ind1[cxpoint1:cxpoint2+1]
rule1to2 = list(zip(part1, part2))
is_fully_merged = False
while not is_fully_merged:
rule1to2, is_fully_merged = merge_rules(rules=rule1to2)
rule2to1 = {rule[1]: rule[0] for rule in rule1to2}
rule1to2 = dict(rule1to2)
ind1 = [gene if gene not in part2 else rule2to1[gene] for gene in ind1[:cxpoint1]] + part2 + \
[gene if gene not in part2 else rule2to1[gene] for gene in ind1[cxpoint2+1:]]
ind2 = [gene if gene not in part1 else rule1to2[gene] for gene in ind2[:cxpoint1]] + part1 + \
[gene if gene not in part1 else rule1to2[gene] for gene in ind2[cxpoint2+1:]]
return ind1, ind2mut_inverse_indexes(individual)inverses the attributes between two random points of the input individual and return the mutant. This mutation expects sequence individuals of indexes, the result for any other type of individuals is unpredictable.
individual– Individual to be mutated.
- A tuple of one individual.
def mut_inverse_indexes(individual):
start, stop = sorted(random.sample(range(len(individual)), 2))
temp = individual[start:stop+1]
temp.reverse()
individual[start:stop+1] = temp
return (individual, )run_gavrptw(instance_name, unit_cost, init_cost, wait_cost, delay_cost, ind_size, pop_size, \
cx_pb, mut_pb, n_gen, export_csv=False, customize_data=False)implements a genetic algorithm-based solution to vehicle routing problem with time windows (VRPTW).
instance_name- A problem instance name provided in Solomon's VRPTW benchmark problems.unit_cost- The transportation cost of one vehicle for a unit distance.init_cost- The start-up cost of a vehicle.wait_cost- Cost per unit time if the vehicle arrives early than the customer's ready time.delay_cost- Cost per unit time if the vehicle arrives later than the due time.ind_size- Size of an individual.pop_size- Size of a population.cx_pb- Probability of crossover.mut_pb- Probability of mutation.n_gen- Maximum number of generations to terminate evolution.export_csv- IfTrue, a CSV format log file will be exported to theresults\directory.customize_data- IfTure, customized JSON format problem instance file will be loaded fromdata\json_customized\directory.
- None
def run_gavrptw(instance_name, unit_cost, init_cost, wait_cost, delay_cost, ind_size, pop_size, \
cx_pb, mut_pb, n_gen, export_csv=False, customize_data=False):
if customize_data:
json_data_dir = os.path.join(BASE_DIR, 'data', 'json_customize')
else:
json_data_dir = os.path.join(BASE_DIR, 'data', 'json')
json_file = os.path.join(json_data_dir, f'{instance_name}.json')
instance = load_instance(json_file=json_file)
if instance is None:
return
creator.create('FitnessMax', base.Fitness, weights=(1.0, ))
creator.create('Individual', list, fitness=creator.FitnessMax)
toolbox = base.Toolbox()
# Attribute generator
toolbox.register('indexes', random.sample, range(1, ind_size + 1), ind_size)
# Structure initializers
toolbox.register('individual', tools.initIterate, creator.Individual, toolbox.indexes)
toolbox.register('population', tools.initRepeat, list, toolbox.individual)
# Operator registering
toolbox.register('evaluate', eval_vrptw, instance=instance, unit_cost=unit_cost, \
init_cost=init_cost, wait_cost=wait_cost, delay_cost=delay_cost)
toolbox.register('select', tools.selRoulette)
toolbox.register('mate', cx_partially_matched)
toolbox.register('mutate', mut_inverse_indexes)
pop = toolbox.population(n=pop_size)
# Results holders for exporting results to CSV file
csv_data = []
print('Start of evolution')
# Evaluate the entire population
fitnesses = list(map(toolbox.evaluate, pop))
for ind, fit in zip(pop, fitnesses):
ind.fitness.values = fit
print(f' Evaluated {len(pop)} individuals')
# Begin the evolution
for gen in range(n_gen):
print(f'-- Generation {gen} --')
# Select the next generation individuals
offspring = toolbox.select(pop, len(pop))
# Clone the selected individuals
offspring = list(map(toolbox.clone, offspring))
# Apply crossover and mutation on the offspring
for child1, child2 in zip(offspring[::2], offspring[1::2]):
if random.random() < cx_pb:
toolbox.mate(child1, child2)
del child1.fitness.values
del child2.fitness.values
for mutant in offspring:
if random.random() < mut_pb:
toolbox.mutate(mutant)
del mutant.fitness.values
# Evaluate the individuals with an invalid fitness
invalid_ind = [ind for ind in offspring if not ind.fitness.valid]
fitnesses = map(toolbox.evaluate, invalid_ind)
for ind, fit in zip(invalid_ind, fitnesses):
ind.fitness.values = fit
print(f' Evaluated {len(invalid_ind)} individuals')
# The population is entirely replaced by the offspring
pop[:] = offspring
# Gather all the fitnesses in one list and print the stats
fits = [ind.fitness.values[0] for ind in pop]
length = len(pop)
mean = sum(fits) / length
sum2 = sum([x**2 for x in fits])
std = abs(sum2 / length - mean**2)**0.5
print(f' Min {min(fits)}')
print(f' Max {max(fits)}')
print(f' Avg {mean}')
print(f' Std {std}')
# Write data to holders for exporting results to CSV file
if export_csv:
csv_row = {
'generation': gen,
'evaluated_individuals': len(invalid_ind),
'min_fitness': min(fits),
'max_fitness': max(fits),
'avg_fitness': mean,
'std_fitness': std,
}
csv_data.append(csv_row)
print('-- End of (successful) evolution --')
best_ind = tools.selBest(pop, 1)[0]
print(f'Best individual: {best_ind}')
print(f'Fitness: {best_ind.fitness.values[0]}')
print_route(ind2route(best_ind, instance))
print(f'Total cost: {1 / best_ind.fitness.values[0]}')
if export_csv:
csv_file_name = f'{instance_name}_uC{unit_cost}_iC{init_cost}_wC{wait_cost}' \
f'_dC{delay_cost}_iS{ind_size}_pS{pop_size}_cP{cx_pb}_mP{mut_pb}_nG{n_gen}.csv'
csv_file = os.path.join(BASE_DIR, 'results', csv_file_name)
print(f'Write to file: {csv_file}')
make_dirs_for_file(path=csv_file)
if not exist(path=csv_file, overwrite=True):
with io.open(csv_file, 'wt', newline='') as file_object:
fieldnames = [
'generation',
'evaluated_individuals',
'min_fitness',
'max_fitness',
'avg_fitness',
'std_fitness',
]
writer = DictWriter(file_object, fieldnames=fieldnames, dialect='excel')
writer.writeheader()
for csv_row in csv_data:
writer.writerow(csv_row)# -*- coding: utf-8 -*-
'''sample_R101.py'''
import random
from gavrptw.core import run_gavrptw
def main():
'''main()'''
random.seed(64)
instance_name = 'R101'
unit_cost = 8.0
init_cost = 60.0
wait_cost = 0.5
delay_cost = 1.5
ind_size = 25
pop_size = 80
cx_pb = 0.85
mut_pb = 0.01
n_gen = 100
export_csv = True
run_gavrptw(instance_name=instance_name, unit_cost=unit_cost, init_cost=init_cost, \
wait_cost=wait_cost, delay_cost=delay_cost, ind_size=ind_size, pop_size=pop_size, \
cx_pb=cx_pb, mut_pb=mut_pb, n_gen=n_gen, export_csv=export_csv)
if __name__ == '__main__':
main()# -*- coding: utf-8 -*-
'''sample_C204.py'''
import random
from gavrptw.core import run_gavrptw
def main():
'''main()'''
random.seed(64)
instance_name = 'C204'
unit_cost = 8.0
init_cost = 100.0
wait_cost = 1.0
delay_cost = 1.5
ind_size = 100
pop_size = 400
cx_pb = 0.85
mut_pb = 0.02
n_gen = 300
export_csv = True
run_gavrptw(instance_name=instance_name, unit_cost=unit_cost, init_cost=init_cost, \
wait_cost=wait_cost, delay_cost=delay_cost, ind_size=ind_size, pop_size=pop_size, \
cx_pb=cx_pb, mut_pb=mut_pb, n_gen=n_gen, export_csv=export_csv)
if __name__ == '__main__':
main()# -*- coding: utf-8 -*-
'''sample_customized_data.py'''
import random
from gavrptw.core import run_gavrptw
def main():
'''main()'''
random.seed(64)
instance_name = 'Customized_Data'
unit_cost = 8.0
init_cost = 100.0
wait_cost = 1.0
delay_cost = 1.5
ind_size = 100
pop_size = 400
cx_pb = 0.85
mut_pb = 0.02
n_gen = 300
export_csv = True
customize_data = True
run_gavrptw(instance_name=instance_name, unit_cost=unit_cost, init_cost=init_cost, \
wait_cost=wait_cost, delay_cost=delay_cost, ind_size=ind_size, pop_size=pop_size, \
cx_pb=cx_pb, mut_pb=mut_pb, n_gen=n_gen, export_csv=export_csv, \
customize_data=customize_data)
if __name__ == '__main__':
main()The sample codes will print logs on the screen. Meanwhile, a CSV format log file will be saved in the results\ directory after running each sample code, which can be canceled by setting the export_csv flag to False, i.e.,
# -*- coding: utf-8 -*-
# sample_R101.py
...
export_csv = False
run_gavrptw(instance_name=instance_name, unit_cost=unit_cost, init_cost=init_cost, \
wait_cost=wait_cost, delay_cost=delay_cost, ind_size=ind_size, pop_size=pop_size, \
cx_pb=cx_pb, mut_pb=mut_pb, n_gen=n_gen, export_csv=export_csv)
...Excerpt from gavrptw/__init__.py:
BASE_DIR = os.path.abspath(os.path.dirname(os.path.dirname(__file__)))route = ind2route(individual, instance)print_route(route, merge=False)eval_vrptw(individual, instance, unit_cost=1.0, init_cost=0, wait_cost=0, delay_cost=0)ind1, ind2 = cx_partially_matched(ind1, ind2)individual, = mut_inverse_indexes(individual)run_gavrptw(instance_name, unit_cost, init_cost, wait_cost, delay_cost, ind_size, pop_size, \
cx_pb, mut_pb, n_gen, export_csv=False, customize_data=False)make_dirs_for_file(path)guess_path_type(path)exist(path, overwrite=False, display_info=True)load_instance(json_file)merge_rules(rules)calculate_distance(customer1, customer2)text2json(customize=False)├── data/
│ ├── json/
│ │ ├── <Instance name>.json
│ │ └── ...
│ ├── json_customize/
│ │ ├── <Customized instance name>.json
│ │ └── ...
│ ├── text/
│ │ ├── <Instance name>.txt
│ │ └── ...
│ └── text_customize/
│ ├── <Customized instance name>.txt
│ └── ...
├── results/
│ └── ...
├── gavrptw/
│ ├── __init__.py
│ ├── core.py
│ └── utils.py
├── text2json.py
├── text2json_customize.py
├── sample_R101.py
├── sample_C204.py
├── sample_customized_data.py
├── requirements.txt
├── README.md
├── LICENSE
├── .travis.yml
└── .gitignore
Distributed Evolutionary Algorithms in Python (DEAP)