PyVRP

The top-level pyvrp module exposes several core classes needed to run the VRP solver. These include the core GeneticAlgorithm, and the Population that manages a Solution pool. Most classes take parameter objects that allow for advanced configuration - but sensible defaults are also provided. Finally, after running, the GeneticAlgorithm returns a Result object. This object can be used to obtain the best observed solution, and detailed runtime statistics.

Hint

Have a look at the examples to see how these classes relate!

class Model

A simple interface for modelling vehicle routing problems with PyVRP.

Attributes:

locations: Returns all locations (depots and clients) in the current model.
vehicle_types: Returns the vehicle types in the current model.

Methods

`add_client`(x, y[, demand, service_duration, ...])	Adds a client with the given attributes to the model.
`add_depot`(x, y[, tw_early, tw_late])	Adds a depot with the given attributes to the model.
`add_edge`(frm, to, distance[, duration])	Adds an edge \((i, j)\) between `frm` (\(i\)) and `to` (\(j\)).
`add_vehicle_type`(capacity, num_available)	Adds a vehicle type with the given number of available vehicles of given capacity to the model.
`data`()	Creates and returns a `ProblemData` instance from this model's attributes.
`from_data`(data)	Constructs a model instance from the given data.
`solve`(stop[, seed])	Solve this model.

add_client(x: int, y: int, demand: int = 0, service_duration: int = 0, tw_early: int = 0, tw_late: int = 0, release_time: int = 0, prize: int = 0, required: bool = True) → Client: Adds a client with the given attributes to the model. Returns the created Client instance.

add_depot(x: int, y: int, tw_early: int = 0, tw_late: int = 0) → Client: Adds a depot with the given attributes to the model. Returns the created Client instance.

Warning

PyVRP does not yet support multi-depot VRPs. For now, only one depot can be added to the model.

add_edge(frm: Client, to: Client, distance: int, duration: int = 0) → Edge

Adds an edge \((i, j)\) between frm (\(i\)) and to (\(j\)). The edge can be given distance and duration attributes. Distance is required, but the default duration is zero. Returns the created edge.

Raises:

ValueError: When either distance or duration is a negative value.

add_vehicle_type(capacity: int, num_available: int) → VehicleType

Adds a vehicle type with the given number of available vehicles of given capacity to the model. Returns the created vehicle type.

Raises:

ValueError: When the number of available vehicles or capacity is not a positive value.

data() → ProblemData: Creates and returns a ProblemData instance from this model’s attributes.

classmethod from_data(data: ProblemData) → Model

Constructs a model instance from the given data.

Parameters:

data: Problem data to feed into the model.

Returns:

Model: A model instance representing the given data.

property locations: List[Client]: Returns all locations (depots and clients) in the current model. The clients in the routes of the solution returned by solve() can be used to index these locations.

solve(stop: StoppingCriterion, seed: int = 0) → Result

Solve this model.

Parameters:

stop: Stopping criterion to use.
seed, optional: Seed value to use for the PRNG, by default 0.

Returns:

Result: The solution result object, containing the best found solution.

property vehicle_types: List[VehicleType]: Returns the vehicle types in the current model. The routes of the solution returned by solve() have a property vehicle_type() that can be used to index these vehicle types.

class GeneticAlgorithmParams(repair_probability: 'float' = 0.8, collect_statistics: 'bool' = False, intensify_probability: 'float' = 0.15, intensify_on_best: 'bool' = True, nb_iter_no_improvement: 'int' = 20000)

class GeneticAlgorithm(data: ProblemData, penalty_manager: PenaltyManager, rng: XorShift128, population: Population, local_search: LocalSearch, crossover_op: CrossoverOperator, initial_solutions: Collection[Solution], params: GeneticAlgorithmParams = GeneticAlgorithmParams(repair_probability=0.8, collect_statistics=False, intensify_probability=0.15, intensify_on_best=True, nb_iter_no_improvement=20000))

Creates a GeneticAlgorithm instance.

Parameters:

data: Data object describing the problem to be solved.
penalty_manager: Penalty manager to use.
rng: Random number generator.
population: Population to use.
local_search: Local search instance to use.
crossover_op: Crossover operator to use for generating offspring.
initial_solutions: Initial solutions to use to initialise the population.
params: Genetic algorithm parameters. If not provided, a default will be used.

Raises:

ValueError: When the population is empty.

Methods

run(stop)

Runs the genetic algorithm with the provided stopping criterion.

run(stop: StoppingCriterion)

Runs the genetic algorithm with the provided stopping criterion.

Parameters:

stop: Stopping criterion to use. The algorithm runs until the first time the stopping criterion returns True.

Returns:

Result: A Result object, containing statistics and the best found solution.

class PenaltyParams(init_capacity_penalty: int = 20, init_time_warp_penalty: int = 6, repair_booster: int = 12, num_registrations_between_penalty_updates: int = 50, penalty_increase: float = 1.34, penalty_decrease: float = 0.32, target_feasible: float = 0.43)

The penalty manager parameters.

Parameters:

init_capacity_penalty: Initial penalty on excess capacity. This is the amount by which one unit of excess load capacity is penalised in the objective, at the start of the search.
init_time_warp_penalty: Initial penalty on time warp. This is the amount by which one unit of time warp (time window violations) is penalised in the objective, at the start of the search.
repair_booster: A repair booster value \(r \ge 1\). This value is used to temporarily multiply the current penalty terms, to force feasibility. See also get_booster_cost_evaluator().
num_registrations_between_penalty_updates: Number of feasibility registrations between penalty value updates. The penalty manager updates the penalty terms every once in a while based on recent feasibility registrations. This parameter controls how often such updating occurs.
penalty_increase: Amount \(p_i \ge 1\) by which the current penalties are increased when insufficient feasible solutions (see target_feasible) have been found amongst the most recent registrations. The penalty values \(v\) are updated as \(v \gets p_i v\).
penalty_decrease: Amount \(p_d \in [0, 1]\) by which the current penalties are decreased when sufficient feasible solutions (see target_feasible) have been found amongst the most recent registrations. The penalty values \(v\) are updated as \(v \gets p_d v\).
target_feasible: Target percentage \(p_f \in [0, 1]\) of feasible registrations in the last num_registrations_between_penalty_updates registrations. This percentage is used to update the penalty terms: when insufficient feasible solutions have been registered, the penalties are increased; similarly, when too many feasible solutions have been registered, the penalty terms are decreased. This ensures a balanced population, with a fraction \(p_f\) feasible and a fraction \(1 - p_f\) infeasible solutions.

Attributes:

init_capacity_penalty: Initial penalty on excess capacity.
init_time_warp_penalty: Initial penalty on time warp.
repair_booster: A repair booster value.
num_registrations_between_penalty_updates: Number of feasibility registrations between penalty value updates.
penalty_increase: Amount \(p_i \ge 1\) by which the current penalties are increased when insufficient feasible solutions (see target_feasible) have been found amongst the most recent registrations.
penalty_decrease: Amount \(p_d \in [0, 1]\) by which the current penalties are decreased when sufficient feasible solutions (see target_feasible) have been found amongst the most recent registrations.
target_feasible: Target percentage \(p_f \in [0, 1]\) of feasible registrations in the last num_registrations_between_penalty_updates registrations.

class PenaltyManager(params: PenaltyParams = PenaltyParams(init_capacity_penalty=20, init_time_warp_penalty=6, repair_booster=12, num_registrations_between_penalty_updates=50, penalty_increase=1.34, penalty_decrease=0.32, target_feasible=0.43))

Creates a PenaltyManager instance.

This class manages time warp and load penalties, and provides penalty terms for given time warp and load values. It updates these penalties based on recent history, and can be used to provide a temporary penalty booster object that increases the penalties for a short duration.

Parameters:

params, optional: PenaltyManager parameters. If not provided, a default will be used.

Methods

`get_booster_cost_evaluator`()	Get a cost evaluator for the boosted current penalty values.
`get_cost_evaluator`()	Get a cost evaluator for the current penalty values.
`register_load_feasible`(is_load_feasible)	Registers another capacity feasibility result.
`register_time_feasible`(is_time_feasible)	Registers another time feasibility result.

get_booster_cost_evaluator()

Get a cost evaluator for the boosted current penalty values.

Returns:

CostEvaluator: A CostEvaluator instance that uses the booster penalty values.

get_cost_evaluator() → CostEvaluator

Get a cost evaluator for the current penalty values.

Returns:

CostEvaluator: A CostEvaluator instance that uses the current penalty values.

register_load_feasible(is_load_feasible: bool)

Registers another capacity feasibility result. The current load penalty is updated once sufficiently many results have been gathered.

Parameters:

is_load_feasible: Boolean indicating whether the last solution was feasible w.r.t. the capacity constraint.

register_time_feasible(is_time_feasible: bool)

Registers another time feasibility result. The current time warp penalty is updated once sufficiently many results have been gathered.

Parameters:

is_time_feasible: Boolean indicating whether the last solution was feasible w.r.t. the time constraint.

class PopulationParams(min_pop_size: int = 25, generation_size: int = 40, nb_elite: int = 4, nb_close: int = 5, lb_diversity: float = 0.1, ub_diversity: float = 0.5)

generation_size

lb_diversity

property max_pop_size

min_pop_size

nb_close

nb_elite

ub_diversity

class Population(diversity_op: ~typing.Callable[[~pyvrp._pyvrp.Solution, ~pyvrp._pyvrp.Solution], float], params: ~pyvrp._pyvrp.PopulationParams = <pyvrp._pyvrp.PopulationParams object>)

Creates a Population instance.

Parameters:

diversity_op: Operator to use to determine pairwise diversity between solutions. Have a look at pyvrp.diversity for available operators.
params, optional: Population parameters. If not provided, a default will be used.

Methods

`add`(solution, cost_evaluator)	Adds the given solution to the population.
`clear`()	Clears the population by removing all solutions currently in the population.
`get_tournament`(rng, cost_evaluator[, k])	Selects a solution from this population by k-ary tournament, based on the (internal) fitness values of the selected solutions.
`num_feasible`()	Returns the number of feasible solutions in the population.
`num_infeasible`()	Returns the number of infeasible solutions in the population.
`select`(rng, cost_evaluator[, k])	Selects two (if possible non-identical) parents by tournament, subject to a diversity restriction.

__iter__() → Generator[Solution, None, None]

Iterates over the solutions contained in this population.

Yields:

iterable: An iterable object of solutions.

__len__() → int

Returns the current population size.

Returns:

int: Population size.

add(solution: Solution, cost_evaluator: CostEvaluator)

Adds the given solution to the population. Survivor selection is automatically triggered when the population reaches its maximum size.

Parameters:

solution: Solution to add to the population.
cost_evaluator: CostEvaluator to use to compute the cost.

clear(): Clears the population by removing all solutions currently in the population.

get_tournament(rng: XorShift128, cost_evaluator: CostEvaluator, k: int = 2) → Solution

Selects a solution from this population by k-ary tournament, based on the (internal) fitness values of the selected solutions.

Parameters:

rng: Random number generator.
cost_evaluator: Cost evaluator to use when computing the fitness.
k: The number of solutions to draw for the tournament. Defaults to two, which results in a binary tournament.

Returns:

Solution: The selected solution.

num_feasible() → int

Returns the number of feasible solutions in the population.

Returns:

int: Number of feasible solutions.

num_infeasible() → int

Returns the number of infeasible solutions in the population.

Returns:

int: Number of infeasible solutions.

select(rng: XorShift128, cost_evaluator: CostEvaluator, k: int = 2) → Tuple[Solution, Solution]

Selects two (if possible non-identical) parents by tournament, subject to a diversity restriction.

Parameters:

rng: Random number generator.
cost_evaluator: Cost evaluator to use when computing the fitness.
k: The number of solutions to draw for the tournament. Defaults to two, which results in a binary tournament.

Returns:

tuple: A solution pair (parents).

read(where: str | ~pathlib.Path, instance_format: str = 'vrplib', round_func: str | ~typing.Callable[[~numpy.ndarray], ~numpy.ndarray] = <function no_rounding>) → ProblemData

Reads the VRPLIB file at the given location, and returns a ProblemData instance.

Parameters:

where

File location to read. Assumes the data on the given location is in VRPLIB format.

instance_format, optional

File format of the instance to read, one of 'vrplib' (default) or 'solomon'.

round_func, optional

Optional rounding function. Will be applied to round data if the data is not already integer. This can either be a function or a string:

'round' rounds the values to the nearest integer;

'trunc' truncates the values to be integral;

'trunc1' or 'dimacs' scale and truncate to the nearest decimal;

'none' does no rounding. This is the default.

Returns:

ProblemData: Data instance constructed from the read data.

read_solution(where: str | Path) → List[List[int]]

Reads a solution in VRPLIB format from file at the given location, and returns the routes contained in it.

Parameters:

where: File location to read. Assumes the solution in the file on the given location is in VRPLIB solution format.

Returns:

list: List of routes, where each route is a list of client numbers.

class Result(best: Solution, stats: Statistics, num_iterations: int, runtime: float)

Stores the outcomes of a single run. An instance of this class is returned once the GeneticAlgorithm completes.

Parameters:

best: The best observed solution.
stats: A Statistics object containing runtime statistics. These are only collected and available if statistics were collected for the given run.
num_iterations: Number of iterations performed by the genetic algorithm.
runtime: Total runtime of the main genetic algorithm loop.

Raises:

ValueError: When the number of iterations or runtime are negative.

Methods

`cost`()	Returns the cost (objective) value of the best solution.
`has_statistics`()	Returns whether detailed statistics were collected.
`is_feasible`()	Returns whether the best solution is feasible.

cost() → float

Returns the cost (objective) value of the best solution. Returns inf if the best solution is infeasible.

Returns:

float: Objective value.

has_statistics() → bool

Returns whether detailed statistics were collected. If statistics are not availabe, the plotting methods cannot be used.

Returns:

bool: True when detailed statistics are available, False otherwise.

is_feasible() → bool

Returns whether the best solution is feasible.

Returns:

bool: True when the solution is feasible, False otherwise.

show_versions()

This function prints version information that is useful when filing bug reports.

Examples

Calling this function should print information like the following (dependency versions in your local installation will likely differ):

>>> import pyvrp
>>> pyvrp.show_versions()
INSTALLED VERSIONS
------------------
     pyvrp: 1.0.0
     numpy: 1.24.2
matplotlib: 3.7.0
    vrplib: 1.0.1
      tqdm: 4.64.1
     tomli: 2.0.1
    Python: 3.9.13

class Statistics(runtimes: ~typing.List[float] = <factory>, num_iterations: int = 0, feas_stats: ~typing.List[~pyvrp.Statistics._Datum] = <factory>, infeas_stats: ~typing.List[~pyvrp.Statistics._Datum] = <factory>)

The Statistics object tracks various (population-level) statistics of genetic algorithm runs. This can be helpful in analysing the algorithm’s performance.

Methods

`collect_from`(population, cost_evaluator)	Collects statistics from the given population object.
`from_csv`(where[, delimiter])	Reads a Statistics object from the CSV file at the given filesystem location.
`to_csv`(where[, delimiter, quoting])	Writes this Statistics object to the given location, as a CSV file.

collect_from(population: Population, cost_evaluator: CostEvaluator)

Collects statistics from the given population object.

Parameters:

population: Population instance to collect statistics from.
cost_evaluator: CostEvaluator used to compute costs for solutions.

classmethod from_csv(where: Path | str, delimiter: str = ',', **kwargs)

Reads a Statistics object from the CSV file at the given filesystem location.

Parameters:

where: Filesystem location to read from.
delimiter: Value separator. Default comma.
kwargs: Additional keyword arguments. These are passed to csv.DictReader.

Returns:

Statistics: Statistics object populated with the data read from the given filesystem location.

to_csv(where: Path | str, delimiter: str = ',', quoting: int = 0, **kwargs)

Writes this Statistics object to the given location, as a CSV file.

Parameters:

where: Filesystem location to write to.
delimiter: Value separator. Default comma.
quoting: Quoting strategy. Default only quotes values when necessary.
kwargs: Additional keyword arguments. These are passed to csv.DictWriter.

class CostEvaluator(capacity_penalty: int = 0, tw_penalty: int = 0)

Creates a CostEvaluator instance.

This class contains time warp and load penalties, and can compute penalties for a given time warp and load.

Parameters:

capacity_penalty: The penalty for each unit of excess load over the vehicle capacity.
tw_penalty: The penalty for each unit of time warp.

cost(solution: Solution)

Evaluates and returns the cost/objective of the given solution. Hand-waving some details, let \(x_{ij} \in \{ 0, 1 \}\) indicate if edge \((i, j)\) is used in the solution encoded by the given solution, and \(y_i \in \{ 0, 1 \}\) indicate if client \(i\) is visited. The objective is then given by

\[\sum_{(i, j)} d_{ij} x_{ij} + \sum_{i} p_i (1 - y_i),\]

where the first part lists the distance costs, and the second part the prizes of the unvisited clients.

load_penalty(load: int, vehicle_capacity: int)

penalised_cost(solution: Solution)

tw_penalty(time_warp: int)

class Route(data: ProblemData, visits: List[int], vehicle_type: int)

A simple class that stores the route plan and some statistics.

centroid(): Center point of the client locations on this route.

demand(): Total client demand on this route.

distance(): Total distance travelled on this route.

duration(): Total route duration, including waiting time.

excess_load(): Demand in excess of the vehicle’s capacity.

has_excess_load()

has_time_warp()

is_feasible()

prizes(): Total prize value collected on this route.

release_time(): Release time of visits on this route.

service_duration(): Total duration of service on the route.

time_warp(): Any time warp incurred along the route.

vehicle_type(): Index of the type of vehicle used on this route.

visits(): Route visits, as a list of clients.

wait_duration(): Total waiting duration on this route.

class Solution(data: ProblemData, routes: List[Route] | List[List[int]])

Encodes VRP solutions.

Parameters:

data: Data instance.
routes: Route list to use. Can be a list of Route objects, or a lists of client visits. In case of the latter, all routes are assigned vehicles of the first type. That need not be a feasible assignment!

Raises:

RuntimeError: When the number of routes in the routes argument exceeds num_vehicles, when an empty route has been passed as part of routes, or when too many vehicles of a particular type have been used.

distance()

Returns the total distance over all routes.

Returns:

int: Total distance over all routes.

excess_load()

Returns the total excess load over all routes.

Returns:

int: Total excess load over all routes.

get_neighbours()

Returns a list of neighbours for each client, by index. Also includes the depot at index 0, which only neighbours itself.

Returns:

list: A list of (pred, succ) tuples that encode for each client their predecessor and successors in this solutions’s routes.

get_routes()

The solution’s routing decisions.

Note

The length of this list is equal to the number of non-empty routes, which is at most equal to num_vehicles.

Returns:

list: A list of routes. Each Route starts and ends at the depot (0), but that is implicit: the depot is not part of the returned routes.

has_excess_load()

Returns whether this solution violates capacity constraints.

Returns:

bool: True if the solution is not capacity feasible, False otherwise.

has_time_warp()

Returns whether this solution violates time window constraints.

Returns:

bool: True if the solution is not time window feasible, False otherwise.

is_feasible()

Whether this solution is feasible. This is a shorthand for checking that has_excess_load() and has_time_warp() both return false.

Returns:

bool: Whether the solution of this solution is feasible with respect to capacity and time window constraints.

classmethod make_random(data: ProblemData, rng: XorShift128)

Creates a randomly generated solution.

Parameters:

data: Data instance.
rng: Random number generator to use.

Returns:

Solution: The randomly generated solution.

num_clients()

Number of clients in this solution.

Returns:

int: Number of clients in this solution.

num_routes()

Number of routes in this solution.

Returns:

int: Number of routes.

prizes()

Returns the total collected prize value over all routes.

Returns:

int: Value of collected prizes.

time_warp()

Returns the total time warp load over all routes.

Returns:

int: Total time warp over all routes.

uncollected_prizes()

Total prize value of all clients not visited in this solution.

Returns:

int: Value of uncollected prizes.

class Client(x: int, y: int, demand: int = 0, service_duration: int = 0, tw_early: int = 0, tw_late: int = 0, release_time: int = 0, prize: int = 0, required: bool = True)

Simple data object storing all client data as (read-only) properties.

Parameters:

x: Horizontal coordinate of this client, that is, the ‘x’ part of the client’s (x, y) location tuple.
y: Vertical coordinate of this client, that is, the ‘y’ part of the client’s (x, y) location tuple.
demand: The amount this client’s demanding. Default 0.
service_duration: This client’s service duration, that is, the amount of time we need to visit the client for. Service should start (but not necessarily end) within the [tw_early, tw_late] interval. Default 0.
tw_early: Earliest time at which we can visit this client. Default 0.
tw_late: Latest time at which we can visit this client. Default 0.
release_time: Earliest time at which this client is released, that is, the earliest time at which a vehicle may leave the depot to visit this client. Default 0.
prize: Prize collected by visiting this client. Default 0.
required: Whether this client must be part of a feasible solution. Default True.

demand

prize

release_time

required

service_duration

tw_early

tw_late

x

y

class VehicleType(capacity: int, num_available: int)

Simple data object storing all vehicle type data as properties.

Attributes:

capacity: Capacity (maximum total demand) of this vehicle type.
num_available: Number of vehicles of this type that are available.

capacity

num_available

class ProblemData(clients: List[Client], vehicle_types: List[VehicleType], distance_matrix: List[List[int]], duration_matrix: List[List[int]])

Creates a problem data instance. This instance contains all information needed to solve the vehicle routing problem.

Parameters:

clients: List of clients. The first client (at index 0) is assumed to be the depot. The time window for the depot is assumed to describe the overall time horizon. The depot should have 0 demand and 0 service duration.
vehicle_types: List of vehicle types in the problem instance.
duration_matrix: A matrix that gives the travel times between clients (and the depot at index 0).

centroid()

Center point of all client locations (excluding the depot).

Returns:

tuple: Centroid of all client locations.

client(client: int)

Returns client data for the given client.

Parameters:

client: Client number whose information to retrieve.

Returns:

Client: A simple data object containing the requested client’s information.

depot()

Returns ‘client’ information for the depot, which is stored internally as the client with number 0.

Returns:

Client: A simple data object containing the depot’s information.

dist(first: int, second: int)

Returns the travel distance between the first and second argument, according to this instance’s travel distance matrix.

Parameters:

first: Client or depot number.
second: Client or depot number.

Returns:

int: Travel distance between the given clients.

duration(first: int, second: int)

Returns the travel duration between the first and second argument, according to this instance’s travel duration matrix.

Parameters:

first: Client or depot number.
second: Client or depot number.

Returns:

int: Travel duration between the given clients.

property num_clients

Number of clients in this problem instance.

Returns:

int: Number of clients in the instance.

property num_vehicle_types

Number of vehicle types in this problem instance.

Returns:

int: Number of vehicle types in this problem instance.

property num_vehicles

Number of vehicles in this problem instance.

Returns:

int: Number of vehicles in this problem instance.

vehicle_type(vehicle_type: int)

Returns vehicle type data for the given vehicle type.

Parameters:

vehicle_type: Vehicle type number whose information to retrieve.

Returns:

VehicleType: A simple data object containing the vehicle type information.

class XorShift128(seed: int)

__call__()

__init__(seed: int)

static max()

static min()

rand()

randint(high: int)