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.

class Model[source]¶

A simple interface for modelling vehicle routing problems with PyVRP.

Attributes

groups	Returns all client groups currently in the model.
locations	Returns all locations (depots and clients) in the current model.
profiles	Returns all routing profiles currently in the model.
vehicle_types	Returns the vehicle types in the current model.

Methods

add_client(x, y[, delivery, pickup, ...])	Adds a client with the given attributes to the model.
add_client_group([required])	Adds a new, possibly optional, client group to the model.
add_depot(x, y, *[, name])	Adds a depot with the given attributes to the model.
add_edge(frm, to, distance[, duration, profile])	Adds an edge \((i, j)\) between frm (\(i\)) and to (\(j\)).
add_profile()	Adds a new routing profile to the model.
add_vehicle_type([num_available, capacity, ...])	Adds a vehicle type with the given attributes 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, collect_stats, display, ...])	Solve this model.

property locations : list[Client | Depot]¶

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.

property groups : list[ClientGroup]¶

Returns all client groups currently in the model.

property profiles : list[Profile]¶

Returns all routing profiles currently in the model.

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.

classmethod from_data(data: ProblemData) → Model[source]¶

Constructs a model instance from the given data.

Parameters:

data: ProblemData¶

Problem data to feed into the model.

Returns:

A model instance representing the given data.

Return type:

Model

add_client(x: int, y: int, delivery: int | list[int] = [], pickup: int | list[int] = [], service_duration: int = 0, tw_early: int = 0, tw_late: int = np.iinfo(np.int64).max, release_time: int = 0, prize: int = 0, required: bool = True, group: ClientGroup | None = None, *, name: str = '') → Client[source]¶

Adds a client with the given attributes to the model. Returns the created Client instance.

Raises:

ValueError – When group is not None, and the given group is not part of this model instance, or when a required client is being added to a mutually exclusive client group.

add_client_group(required: bool = True) → ClientGroup[source]¶

Adds a new, possibly optional, client group to the model. Returns the created group.

add_depot(x: int, y: int, *, name: str = '') → Depot[source]¶

Adds a depot with the given attributes to the model. Returns the created Depot instance.

add_edge(frm: Client | Depot, to: Client | Depot, distance: int, duration: int = 0, profile: Profile | None = None) → Edge[source]¶

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.

Note

If profile is not provided, the edge is a base edge that will be set for all profiles in the model. Any profile-specific edge takes precendence over a base edge with the same frm and to locations.

add_profile() → Profile[source]¶

Adds a new routing profile to the model.

add_vehicle_type(num_available: int = 1, capacity: int | list[int] = [], start_depot: Depot | None = None, end_depot: Depot | None = None, fixed_cost: int = 0, tw_early: int = 0, tw_late: int = np.iinfo(np.int64).max, max_duration: int = np.iinfo(np.int64).max, max_distance: int = np.iinfo(np.int64).max, unit_distance_cost: int = 1, unit_duration_cost: int = 0, profile: Profile | None = None, start_late: int | None = None, *, name: str = '') → VehicleType[source]¶

Adds a vehicle type with the given attributes to the model. Returns the created VehicleType instance.

Note

The vehicle type is assigned to the first depot if no depot information is provided.

Raises:

ValueError – When the given depot or profile arguments are not in this model instance.

data() → ProblemData[source]¶

Creates and returns a ProblemData instance from this model’s attributes.

solve(stop: StoppingCriterion, seed: int = 0, collect_stats: bool = True, display: bool = True, params: SolveParams = SolveParams()) → Result[source]¶

Solve this model.

Parameters:

stop: StoppingCriterion¶

Stopping criterion to use.

seed: int = 0¶

Seed value to use for the random number stream. Default 0.

collect_stats: bool = True¶

Whether to collect statistics about the solver’s progress. Default True.

display: bool = True¶

Whether to display information about the solver progress. Default True. Progress information is only available when collect_stats is also set, which it is by default.

params: SolveParams = SolveParams()¶

Solver parameters to use. If not provided, a default will be used.

Returns:

A Result object, containing statistics (if collected) and the best found solution.

Return type:

Result

class Edge(frm: Client | Depot, to: Client | Depot, distance: int, duration: int)[source]¶

Stores an edge connecting two locations.

Raises:

ValueError – When either distance or duration is a negative value, or when self loops have nonzero distance or duration values.

Attributes

distance
duration
frm
to

class Profile[source]¶

Stores a routing profile.

A routing profile is a collection of edges with distance and duration attributes that together define a complete distance and duration matrix. These can be used to model, for example, the road uses of different types of vehicles, like trucks, cars, or bicyclists. Each VehicleType is associated with a routing profile.

Methods

add_edge(frm, to, distance[, duration])

Adds a new edge to this routing profile.

add_edge(frm: Client | Depot, to: Client | Depot, distance: int, duration: int = 0) → Edge[source]¶

Adds a new edge to this routing profile.

class GeneticAlgorithmParams(repair_probability: float = 0.8, nb_iter_no_improvement: int = 20000)[source]¶

Parameters for the genetic algorithm.

Parameters:

repair_probability : ¶

Probability (in \([0, 1]\)) of repairing an infeasible solution. If the reparation makes the solution feasible, it is also added to the population in the same iteration.

nb_iter_no_improvement : ¶

Number of iterations without any improvement needed before a restart occurs.

repair_probability¶

Probability of repairing an infeasible solution.

Type:

float

nb_iter_no_improvement¶

Number of iterations without improvement before a restart occurs.

Type:

int

Raises:

ValueError – When repair_probability is not in \([0, 1]\), or nb_iter_no_improvement is negative.

class GeneticAlgorithm(data: ProblemData, penalty_manager: PenaltyManager, rng: RandomNumberGenerator, population: Population, search_method: SearchMethod, crossover_op: Callable[[tuple[Solution, Solution], ProblemData, CostEvaluator, RandomNumberGenerator], Solution], initial_solutions: Collection[Solution], params: GeneticAlgorithmParams = GeneticAlgorithmParams())[source]¶

Creates a GeneticAlgorithm instance.

Parameters:

data: ProblemData¶

Data object describing the problem to be solved.

penalty_manager: PenaltyManager¶

Penalty manager to use.

rng: RandomNumberGenerator¶

Random number generator.

population: Population¶

Population to use.

search_method: SearchMethod¶

Search method to use.

crossover_op: Callable[[tuple[Solution, Solution], ProblemData, CostEvaluator, RandomNumberGenerator], Solution]¶

Crossover operator to use for generating offspring.

initial_solutions: Collection[Solution]¶

Initial solutions to use to initialise the population.

params: GeneticAlgorithmParams = GeneticAlgorithmParams()¶

Genetic algorithm parameters. If not provided, a default will be used.

Raises:

ValueError – When the population is empty.

Methods

run(stop[, collect_stats, display])

Runs the genetic algorithm with the provided stopping criterion.

run(stop: StoppingCriterion, collect_stats: bool = True, display: bool = False)[source]¶

Runs the genetic algorithm with the provided stopping criterion.

Parameters:

stop: StoppingCriterion¶

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

collect_stats: bool = True¶

Whether to collect statistics about the solver’s progress. Default True.

display: bool = False¶

Whether to display information about the solver progress. Default False. Progress information is only available when collect_stats is also set.

Returns:

A Result object, containing statistics (if collected) and the best found solution.

Return type:

Result

minimise_fleet(data: ProblemData, stop: StoppingCriterion, seed: int = 0, params: SolveParams = SolveParams()) → VehicleType[source]¶

Attempts to reduce the number of vehicles needed to achieve a feasible solution to the given problem instance, subject to a stopping criterion.

Warning

This function is currently unable to solve instances with multiple vehicle types. Support for such a setting may be added in future versions of PyVRP.

Parameters:

data: ProblemData¶

Problem instance with a given vehicle composition.

stop: StoppingCriterion¶

Stopping criterion that determines how much effort to spend on finding smaller fleet compositions.

seed: int = 0¶

Seed value to use for the random number stream. Default 0.

params: SolveParams = SolveParams()¶

Solver parameters to use. If not provided, a default will be used.

Returns:

The smallest fleet composition admitting a feasible solution to the problem instance that could be found before the stopping criterion was hit. The original fleet is returned if no feasible solution was found.

Return type:

VehicleType

Raises:

ValueError – When the instance contains more than one vehicle type. That setting is not yet supported. Alternatively, when the instance contains optional clients. This method attempts to find a good upper bound on the number of vehicles needed to solve the complete problem.

class PenaltyParams(repair_booster: int = 12, solutions_between_updates: int = 50, penalty_increase: float = 1.34, penalty_decrease: float = 0.32, target_feasible: float = 0.43)[source]¶

The penalty manager parameters.

Parameters:

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 booster_cost_evaluator().

solutions_between_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 solutions_between_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.

repair_booster¶

A repair booster value.

Type:

int

solutions_between_updates¶

Number of feasibility registrations between penalty value updates.

Type:

int

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.

Type:

float

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.

Type:

float

target_feasible¶

Target percentage \(p_f \in [0, 1]\) of feasible registrations in the last solutions_between_updates registrations.

Type:

float

class PenaltyManager(initial_penalties: tuple[list[float], float, float], params: PenaltyParams = PenaltyParams())[source]¶

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.

Note

Consider initialising using init_from() to compute initial penalty values that are scaled according to the data instance.

Parameters:

initial_penalties: tuple[list[float], float, float]¶

Initial penalty values for units of load (idx 0), duration (1), and distance (2) violations. These values are clipped to the range [MIN_PENALTY, MAX_PENALTY].

params: PenaltyParams = PenaltyParams()¶

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

Methods

booster_cost_evaluator()	Get a cost evaluator using the boosted current penalty values.
cost_evaluator()	Get a cost evaluator using the current penalty values.
init_from(data[, params])	Initialises from the given data instance and parameter object.
penalties()	Returns the current penalty values.
register(sol)	Registers the feasibility dimensions of the given solution.

penalties() → tuple[list[float], float, float][source]¶

Returns the current penalty values.

classmethod init_from(data: ProblemData, params: PenaltyParams = PenaltyParams()) → PenaltyManager[source]¶

Initialises from the given data instance and parameter object. The initial penalty values are computed from the problem data.

Parameters:

data: ProblemData¶

Data instance to use when computing penalty values.

params: PenaltyParams = PenaltyParams()¶

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

register(sol: Solution)[source]¶

Registers the feasibility dimensions of the given solution.

cost_evaluator() → CostEvaluator[source]¶

Get a cost evaluator using the current penalty values.

booster_cost_evaluator() → CostEvaluator[source]¶

Get a cost evaluator using the boosted current penalty values.

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)¶

Parameter configuration for the Population.

min_pop_size¶

Minimum subpopulation size. This is the size of the subpopulation after survivor selection.

generation_size¶

The size of a single generation, that is, the number of new solutions inserted into a subpopulation between survivor selections.

nb_elite¶

Number of elite solutions. This number of fittest solutions are always survivors.

nb_close¶

Number of close solutions. These are used to determine similarity between solutions, which is an important component of fitness.

lb_diversity¶

A lower bound on the diversity of the solutions selected for tournament. See select() for details.

ub_diversity¶

An upper bound on the diversity of the solutions selected for tournament. See select() for details.

Attributes

max_pop_size

Returns the maximum subpopulation size.

generation_size
lb_diversity
min_pop_size
nb_close
nb_elite
ub_diversity

property max_pop_size : int¶

Returns the maximum subpopulation size.

class Population(diversity_op: Callable[[Solution, Solution], float], params: PopulationParams | None = None)[source]¶

Creates a Population instance.

Parameters:

diversity_op: Callable[[Solution, Solution], float]¶

Operator to use to determine pairwise diversity between solutions. Have a look at pyvrp.diversity for available operators.

params: PopulationParams | None = None¶

Population parameters. If not provided, a default will be used.

Methods

add(solution, cost_evaluator)	Inserts the given solution in the appropriate feasible or infeasible (sub)population.
clear()	Clears the population by removing all solutions currently in the population.
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.
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.

__iter__() → Generator[Solution, None, None][source]¶

Iterates over the solutions contained in this population.

__len__() → int[source]¶

Returns the current population size.

num_feasible() → int[source]¶

Returns the number of feasible solutions in the population.

num_infeasible() → int[source]¶

Returns the number of infeasible solutions in the population.

add(solution: Solution, cost_evaluator: CostEvaluator)[source]¶

Inserts the given solution in the appropriate feasible or infeasible (sub)population.

Note

Survivor selection is automatically triggered when the subpopulation reaches its maximum size, given by max_pop_size.

Parameters:

solution: Solution¶

Solution to add to the population.

cost_evaluator: CostEvaluator¶

CostEvaluator to use to compute the cost.

clear()[source]¶

Clears the population by removing all solutions currently in the population.

select(rng: RandomNumberGenerator, cost_evaluator: CostEvaluator, k: int = 2) → tuple[Solution, Solution][source]¶

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

Parameters:

rng: RandomNumberGenerator¶

Random number generator.

cost_evaluator: CostEvaluator¶

Cost evaluator to use when computing the fitness.

k: int = 2¶

The number of solutions to draw for the tournament. Defaults to two, which results in a binary tournament.

Returns:

A solution pair (parents).

Return type:

tuple

tournament(rng: RandomNumberGenerator, cost_evaluator: CostEvaluator, k: int = 2) → Solution[source]¶

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

Parameters:

rng: RandomNumberGenerator¶

Random number generator.

cost_evaluator: CostEvaluator¶

Cost evaluator to use when computing the fitness.

k: int = 2¶

The number of solutions to draw for the tournament. Defaults to two, which results in a binary tournament.

Returns:

The selected solution.

Return type:

Solution

read(where: str | Path, round_func: str | Callable[[ndarray], ndarray] = 'none') → ProblemData[source]¶

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

Note

See the VRPLIB format explanation page for more details.

Parameters:

where: str | Path¶

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

round_func: str | Callable[[ndarray], ndarray] = 'none'¶

Optional rounding function that is applied to all data values in the instance. This can either be a function or a string:

• 'round' rounds the values to the nearest integer;

• 'trunc' truncates the values to an integer;

• 'dimacs' scales by 10 and truncates the values to an integer;

• 'exact' scales by 1000 and rounds to the nearest integer.

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

Raises:

• TypeError – When round_func does not name a rounding function, or is not callable.

• ValueError – When the data file does not provide information on the problem size.

Returns:

Data instance constructed from the read data.

Return type:

ProblemData

read_solution(where: str | Path) → list[list[int]][source]¶

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

Parameters:

where: str | Path¶

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

Returns:

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

Return type:

list

class Result(best: Solution, stats: Statistics, num_iterations: int, runtime: float)[source]¶

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.

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.
is_feasible()	Returns whether the best solution is feasible.
summary()	Returns a nicely formatted result summary.

cost() → float[source]¶

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

is_feasible() → bool[source]¶

Returns whether the best solution is feasible.

summary() → str[source]¶

Returns a nicely formatted result summary.

show_versions()[source]¶

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 SolveParams(genetic: GeneticAlgorithmParams = GeneticAlgorithmParams(), penalty: PenaltyParams = PenaltyParams(), population: PopulationParams = PopulationParams(), neighbourhood: NeighbourhoodParams = NeighbourhoodParams(), node_ops: list[type[NodeOperator]] = NODE_OPERATORS, route_ops: list[type[RouteOperator]] = ROUTE_OPERATORS)[source]¶

Solver parameters for PyVRP’s hybrid genetic search algorithm.

Parameters:

genetic: GeneticAlgorithmParams = GeneticAlgorithmParams()¶

Genetic algorithm parameters.

penalty: PenaltyParams = PenaltyParams()¶

Penalty parameters.

population: PopulationParams = PopulationParams()¶

Population parameters.

neighbourhood: NeighbourhoodParams = NeighbourhoodParams()¶

Neighbourhood parameters.

node_ops: list[type[NodeOperator]] = NODE_OPERATORS¶

Node operators to use in the search.

route_ops: list[type[RouteOperator]] = ROUTE_OPERATORS¶

Route operators to use in the search.

Attributes

genetic
neighbourhood
node_ops
penalty
population
route_ops

Methods

from_file(loc)

Loads the solver parameters from a TOML file.

classmethod from_file(loc: str | Path)[source]¶

Loads the solver parameters from a TOML file.

solve(data: ProblemData, stop: StoppingCriterion, seed: int = 0, collect_stats: bool = True, display: bool = False, params: SolveParams = SolveParams()) → Result[source]¶

Solves the given problem data instance.

Parameters:

data: ProblemData¶

Problem data instance to solve.

stop: StoppingCriterion¶

Stopping criterion to use.

seed: int = 0¶

Seed value to use for the random number stream. Default 0.

collect_stats: bool = True¶

Whether to collect statistics about the solver’s progress. Default True.

display: bool = False¶

Whether to display information about the solver progress. Default False. Progress information is only available when collect_stats is also set, which it is by default.

params: SolveParams = SolveParams()¶

Solver parameters to use. If not provided, a default will be used.

Returns:

A Result object, containing statistics (if collected) and the best found solution.

Return type:

Result

class Statistics(collect_stats: bool = True)[source]¶

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

Parameters:

collect_stats: bool = True¶

Whether to collect statistics at all. This can be turned off to avoid excessive memory use on long runs.

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.

is_collecting

collect_from(population: Population, cost_evaluator: CostEvaluator)[source]¶

Collects statistics from the given population object.

Parameters:

population: Population¶

Population instance to collect statistics from.

cost_evaluator: CostEvaluator¶

CostEvaluator used to compute costs for solutions.

classmethod from_csv(where: Path | str, delimiter: str = ',', **kwargs)[source]¶

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

Parameters:

where: Path | str¶

Filesystem location to read from.

delimiter: str = ','¶

Value separator. Default comma.

**kwargs¶

Additional keyword arguments. These are passed to csv.DictReader.

Returns:

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

Return type:

Statistics

to_csv(where: Path | str, delimiter: str = ',', quoting: int = csv.QUOTE_MINIMAL, **kwargs)[source]¶

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

Parameters:

where: Path | str¶

Filesystem location to write to.

delimiter: str = ','¶

Value separator. Default comma.

quoting: int = csv.QUOTE_MINIMAL¶

Quoting strategy. Default only quotes values when necessary.

**kwargs¶

Additional keyword arguments. These are passed to csv.DictWriter.

class CostEvaluator(load_penalties: list[float], tw_penalty: float, dist_penalty: float)¶

Creates a CostEvaluator instance.

This class stores various penalty terms, and can be used to determine the costs of certain constraint violations.

Parameters:

load_penalties: list[float]¶

The penalty terms (one for each load dimension) for each unit of load in excess of the vehicle capacity.

tw_penalty: float¶

The penalty for each unit of time warp.

dist_penalty: float¶

The penalty for each unit of distance in excess of the vehicle’s maximum distance constraint.

Methods

cost(self, solution)	Hand-waving some details, each solution consists of a set of non-empty routes \(\mathcal{R}\).
dist_penalty(self, distance, max_distance)	Computes the time warp penalty for the given time warp.
load_penalty(self, load, capacity, dimension)	Computes the total excess load penalty for the given load and vehicle capacity, and dimension.
penalised_cost(self, solution)	Computes a smoothed objective (penalised cost) for a given solution.
tw_penalty(self, time_warp)	Computes the time warp penalty for the given time warp.

cost(self, solution: Solution) → int¶

Hand-waving some details, each solution consists of a set of non-empty routes \(\mathcal{R}\). Each route \(R \in \mathcal{R}\) is a sequence of edges, starting and ending at a depot. Each route \(R\) has an assigned vehicle type, through which the route is equipped with a fixed vehicle cost \(f_R\), and unit distance and duration costs \(c^\text{distance}_R\) and \(c^\text{duration}_R\), respectively. Let \(V_R = \{i : (i, j) \in R \}\) be the set of locations visited by route \(R\), and \(d_R\) and \(t_R\) the total route distance and duration, respectively. The objective value is then given by

\[\sum_{R \in \mathcal{R}} \left[ f_R + c^\text{distance}_R d_R + c^\text{duration}_R t_R \right] + \sum_{i \in V} p_i - \sum_{R \in \mathcal{R}} \sum_{i \in V_R} p_i,\]

where the first part lists each route’s fixed, distance and duration costs, respectively, and the second part the uncollected prizes of unvisited clients.

Note

The above cost computation only holds for feasible solutions. If the solution argument is infeasible, we return a very large number. If that is not what you want, consider calling penalised_cost() instead.

dist_penalty(self, distance: int, max_distance: int) → int¶

Computes the time warp penalty for the given time warp.

load_penalty(self, load: int, capacity: int, dimension: int) → int¶

Computes the total excess load penalty for the given load and vehicle capacity, and dimension.

penalised_cost(self, solution: Solution) → int¶

Computes a smoothed objective (penalised cost) for a given solution.

tw_penalty(self, time_warp: int) → int¶

Computes the time warp penalty for the given time warp.

class Route(data: ProblemData, visits: list[int], vehicle_type: int)¶

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

Methods

centroid(self)	Center point of the client locations on this route.
delivery(self)	Total client delivery load on this route.
distance(self)	Total distance travelled on this route.
distance_cost(self)	Total cost of the distance travelled on this route.
duration(self)	Total route duration, including travel, service and waiting time.
duration_cost(self)	Total cost of the duration of this route.
end_depot(self)	Location index of the route's ending depot.
end_time(self)	End time of the route. This is equivalent to
excess_distance(self)	Distance in excess of the vehicle's maximum distance constraint.
excess_load(self)	Pickup or delivery loads in excess of the vehicle's capacity.
has_excess_distance(self)	Returns whether this route violates maximum distance constraints.
has_excess_load(self)	Returns whether this route violates capacity constraints.
has_time_warp(self)	Returns whether this route violates time window or maximum duration constraints.
is_feasible(self)	Returns whether this route is feasible.
pickup(self)	Total client pickup load on this route.
prizes(self)	Total prize value collected on this route.
release_time(self)	Earliest time at which this route can leave the depot.
schedule(self)	Statistics about each client visit and the overall route schedule.
service_duration(self)	Total duration of service on this route.
slack(self)	Time by which departure from the depot can be delayed without resulting in (additional) time warp or increased route duration.
start_depot(self)	Location index of the route's starting depot.
start_time(self)	Start time of this route.
time_warp(self)	Amount of time warp incurred on this route.
travel_duration(self)	Total duration of travel on this route.
vehicle_type(self)	Index of the type of vehicle used on this route.
visits(self)	Route visits, as a list of clients.
wait_duration(self)	Total waiting duration on this route.

centroid(self) → tuple[float, float]¶

Center point of the client locations on this route.

delivery(self) → list[int]¶

Total client delivery load on this route.

distance(self) → int¶

Total distance travelled on this route.

distance_cost(self) → int¶

Total cost of the distance travelled on this route.

duration(self) → int¶

Total route duration, including travel, service and waiting time.

duration_cost(self) → int¶

Total cost of the duration of this route.

end_depot(self) → int¶

Location index of the route’s ending depot.

end_time(self) → int¶

End time of the route. This is equivalent to

start_time + duration - time_warp.

excess_distance(self) → int¶

Distance in excess of the vehicle’s maximum distance constraint.

excess_load(self) → list[int]¶

Pickup or delivery loads in excess of the vehicle’s capacity.

has_excess_distance(self) → bool¶

Returns whether this route violates maximum distance constraints.

has_excess_load(self) → bool¶

Returns whether this route violates capacity constraints.

has_time_warp(self) → bool¶

Returns whether this route violates time window or maximum duration constraints.

is_feasible(self) → bool¶

Returns whether this route is feasible.

pickup(self) → list[int]¶

Total client pickup load on this route.

prizes(self) → int¶

Total prize value collected on this route.

release_time(self) → int¶

Earliest time at which this route can leave the depot. Follows from the release times of clients visited on this route.

Note

The route’s release time should not be later than its start time, unless the route has time warp.

schedule(self) → list[ScheduledVisit]¶

Statistics about each client visit and the overall route schedule.

Note

The schedule assumes the route starts at start_time(). Starting later may be feasible, but shifts the schedule.

service_duration(self) → int¶

Total duration of service on this route.

slack(self) → int¶

Time by which departure from the depot can be delayed without resulting in (additional) time warp or increased route duration.

start_depot(self) → int¶

Location index of the route’s starting depot.

start_time(self) → int¶

Start time of this route. This is the earliest possible time at which the route can leave the depot and have a minimal duration and time warp. If there is positive slack(), the start time can be delayed by at most slack() time units without increasing the total (minimal) route duration, or time warp.

Note

It may be possible to leave before the start time (if the vehicle’s time window allows for it). That will introduce additional waiting time, such that the route duration will then no longer be minimal. Delaying departure by more than slack() time units always increases time warp, which could turn the route infeasible.

time_warp(self) → int¶

Amount of time warp incurred on this route.

travel_duration(self) → int¶

Total duration of travel on this route.

vehicle_type(self) → int¶

Index of the type of vehicle used on this route.

visits(self) → list[int]¶

Route visits, as a list of clients.

wait_duration(self) → int¶

Total waiting duration on this route.

class Solution(data: ProblemData, routes: list[Route] | list[list[int]])¶

Encodes VRP solutions.

Parameters:

data: ProblemData¶

Data instance.

routes: list[Route] | list[list[int]]¶

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 given solution is invalid in one of several ways. In particular when the number of routes in the routes argument exceeds num_vehicles, when an empty route has been passed as part of routes, when too many vehicles of a particular type have been used, or when a client is visited more than once.

Methods

distance(self)	Returns the total distance over all routes.
distance_cost(self)	Total cost of the distance travelled on routes in this solution.
duration(self)	Total duration of all routes in this solution.
duration_cost(self)	Total cost of the duration of all routes in this solution.
excess_distance(self)	Returns the total distance in excess of maximum duration constraints, over all routes.
excess_load(self)	Aggregate pickup or delivery loads in excess of the vehicle's capacity of all routes.
fixed_vehicle_cost(self)	Returns the fixed vehicle cost of all vehicles used in this solution.
has_excess_distance(self)	Returns whether this solution violates maximum distance constraints.
has_excess_load(self)	Returns whether this solution violates capacity constraints.
has_time_warp(self)	Returns whether this solution violates time window or maximum duration constraints.
is_complete(self)	Returns whether this solution is complete, which it is when it has all required clients.
is_feasible(self)	Whether this solution is feasible.
is_group_feasible(self)	Returns whether this solution is feasible w.r.t.
make_random(data, rng)	Creates a randomly generated solution.
neighbours(self)	Returns a list of neighbours for each client, by index.
num_clients(self)	Number of clients in this solution.
num_missing_clients(self)	Number of required clients that are not in this solution.
num_routes(self)	Number of routes in this solution.
prizes(self)	Returns the total collected prize value over all routes.
routes(self)	The solution's routing decisions.
time_warp(self)	Returns the total time warp load over all routes.
uncollected_prizes(self)	Total prize value of all clients not visited in this solution.

distance(self) → int¶

Returns the total distance over all routes.

distance_cost(self) → int¶

Total cost of the distance travelled on routes in this solution.

duration(self) → int¶

Total duration of all routes in this solution.

duration_cost(self) → int¶

Total cost of the duration of all routes in this solution.

excess_distance(self) → int¶

Returns the total distance in excess of maximum duration constraints, over all routes.

excess_load(self) → list[int]¶

Aggregate pickup or delivery loads in excess of the vehicle’s capacity of all routes.

fixed_vehicle_cost(self) → int¶

Returns the fixed vehicle cost of all vehicles used in this solution.

has_excess_distance(self) → bool¶

Returns whether this solution violates maximum distance constraints.

Returns:

True if the solution is not feasible with respect to the maximum distance constraints of the vehicles servicing routes in this solution. False otherwise.

Return type:

bool

has_excess_load(self) → bool¶

Returns whether this solution violates capacity constraints.

has_time_warp(self) → bool¶

Returns whether this solution violates time window or maximum duration constraints.

is_complete(self) → bool¶

Returns whether this solution is complete, which it is when it has all required clients.

is_feasible(self) → bool¶

Whether this solution is feasible.

is_group_feasible(self) → bool¶

Returns whether this solution is feasible w.r.t. the client group restrictions.

make_random(data: ProblemData, rng: RandomNumberGenerator) → Solution¶

Creates a randomly generated solution.

Parameters:

data: ProblemData¶

Data instance.

rng: RandomNumberGenerator¶

Random number generator to use.

Returns:

The randomly generated solution.

Return type:

Solution

neighbours(self) → list[tuple[int, int] | None]¶

Returns a list of neighbours for each client, by index.

Returns:

A list of (pred, succ) tuples that encode for each client their predecessor and successors in this solutions’s routes. None in case the client is not in the solution (or is a depot).

Return type:

list

num_clients(self) → int¶

Number of clients in this solution.

Warning

An empty solution typically indicates that there is a significant difference between the values of the prizes of the optional clients and the other objective terms. This hints at a scaling issue in the data.

num_missing_clients(self) → int¶

Number of required clients that are not in this solution.

num_routes(self) → int¶

Number of routes in this solution.

prizes(self) → int¶

Returns the total collected prize value over all routes.

routes(self) → list[Route]¶

The solution’s routing decisions.

Returns:

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

Return type:

list

time_warp(self) → int¶

Returns the total time warp load over all routes.

uncollected_prizes(self) → int¶

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

class Client(x: int, y: int, delivery: list[int] = [], pickup: list[int] = [], service_duration: int = 0, tw_early: int = 0, tw_late: int = np.iinfo(np.int64).max, release_time: int = 0, prize: int = 0, required: bool = True, group: int | None = None, *, name: str = '')¶

Simple data object storing all client data as properties. See also Concepts for further information about these properties.

Parameters:

x: int¶

Horizontal coordinate of this client, that is, the ‘x’ part of the client’s (x, y) location tuple.

y: int¶

Vertical coordinate of this client, that is, the ‘y’ part of the client’s (x, y) location tuple.

delivery: list[int] = []¶

The amounts this client demands from the depot.

pickup: list[int] = []¶

The amounts this client ships back to the depot.

service_duration: int = 0¶

Amount of time a vehicle needs to spend at this client before resuming its route. Service should start (but not necessarily end) within the [tw_early, tw_late] interval. Default 0.

tw_early: int = 0¶

Earliest time at which this client may be visited to start service. Default 0.

tw_late: int = np.iinfo(np.int64).max¶

Latest time at which this client may be visited to start service. Unconstrained if not provided.

release_time: int = 0¶

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: int = 0¶

Prize collected by visiting this client. Default 0. If this client is not required, the prize needs to be sufficiently large to offset any travel cost before this client will be visited in a solution.

required: bool = True¶

Whether this client must be part of a feasible solution. Default True. Make sure to also update the prize value when setting this argument to False.

group: int | None = None¶

Indicates membership of the given client group, if any. By default clients are not part of any groups.

name: str = ''¶

Free-form name field for this client. Default empty.

x¶

Horizontal coordinate of this client.

y¶

Vertical coordinate of this client.

delivery¶

Client delivery amounts shipped from the depot.

pickup¶

Client pickup amounts returned to the depot.

service_duration¶

Amount of time a vehicle needs to spend at this client before resuming its route.

tw_early¶

Earliest time at which this client may be visited to start service.

tw_late¶

Latest time at which this client may be visited to start service.

release_time¶

Earliest time at which a vehicle may leave the depot to visit this client.

prize¶

Prize collected by visiting this client.

required¶

Whether visiting this client is required.

group¶

Indicates membership of the given client group, if any.

name¶

Free-form name field for this client.

Attributes

delivery
group
name
pickup
prize
release_time
required
service_duration
tw_early
tw_late
x
y

class ClientGroup(clients: list[int] = [], required: bool = True)¶

A client group that imposes additional restrictions on visits to clients in the group.

Note

Only mutually exclusive client groups are supported for now.

Parameters:

clients: list[int] = []¶

The clients in the group.

required: bool = True¶

Whether visiting this client group is required.

clients¶

The clients in the group.

required¶

Whether visiting this client group is required.

mutually_exclusive¶

When True, exactly one of the clients in this group must be visited if the group is required, and at most one if the group is not required.

Raises:

ValueError – When the given clients contain duplicates, or when a client is added to the group twice.

Attributes

clients
mutually_exclusive
required

Methods

add_client(self, client)
clear(self)

__iter__(self) → Iterator[int]¶

__len__(self) → int¶

add_client(self, client: int) → None¶

clear(self) → None¶