Package 'heumilkr'

Clarke-Wright algorithm, a Capacitated Vehicle Routing Problem solver

Description

Finds a quasi-optimal solution to the Capacitated Vehicle Routing Problem (CVRP). It is assumed that all demands will be satisfied by a single source.

Usage

clarke_wright(demand, distances, vehicles, restrictions = NULL)

Arguments

demand	A numeric vector consisting of "demands" indexed by sites. The ith entry refers to the demand of site i (and the length of the vector equals the number of sites N with demands). The units of demand values need to match the units of vehicle capacity values. NA values are not allowed.
distances	An object of class dist, created by stats::dist(), with (N + 1) locations describing the distances between individual sites. The first index refers to the source site. The (i+1)th index refers to site i (as defined by demand).
vehicles	A data.frame() describing available vehicle types and their respective capacities. One row per vehicle type. The data frame is expected to have two columns: n - Number of available vehicles. This can be set to NA if the number is "infinite" (i.e. effectively the maximal integer value on your machine.). It is recommended to keep at least one vehicle type as "infinite", otherwise the solver might raise a run time error due to initially not having enough vehicles available (even though the final solution might satisfy the availability restrictions). caps - The vehicle capacity in same units as demand. The order of the data.frame() is relevant and determines the prioritization of vehicle assignments to runs (in case two or more vehicle types are eligible for assignment the "first" vehicle is chosen). In a typical scenario "more expensive" vehicles should be further down in the list (so the cheaper one is chosen in case there is doubt). Since higher capacity vehicles usually involve higher costs sorting the data frame by capacity is usually a good rule of thumb.
restrictions	An optional data.frame() that allows to define vehicle type restrictions for particular sites in the form of a blacklist. The data frame is expected to have two columns: vehicle - The vehicle type index. site - The site index (i.e. the index of the demand vector) Each row defines a restriction: vehicle type vehicle can not approach site site. Defaults to NULL, i.e. no restrictions are enforced.

Details

See the original paper, Clarke, G. and Wright, J.R. (1964) doi:10.1287/opre.12.4.568, for a detailed explanation of the Clarke-Wright algorithm.

Value

Returns a "heumilkr_solution" object, a data.frame() with one row per site-run combination bestowed with additional attributes. Its columns consist of:

• site - The site index (i.e. the index of the demand vector) associated to the run.

• run - Identifies the run the site is assigned to.

• order - Integer values providing the visiting order within each run.

• vehicle - The vehicle type index (as provided in vehicles) associated to the run.

• load - The actual load in units of demand on the particular run.

• distance - The travel distance of the particular run.

Unless a site demand exceeds the vehicle capacities it is always assigned to only a single run.

Examples

demand <- c(3, 2, 4, 2)

positions <-
  data.frame(
    pos_x = c(0, 1, -1, 2, 3),
    pos_y = c(0, 1, 1, 2, 3)
  )

clarke_wright(
  demand,
  dist(positions),
  data.frame(n = NA_integer_, caps = 6)
)

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Applying clarke_wright() to CVRPLIB data

Description

Applying clarke_wright() to CVRPLIB data

Usage

clarke_wright_cvrplib(instance)

Arguments

instance

A "heumilkr_solution". See cvrplib_download() or bundled CVRPLIB data like cvrplib_A.

Value

A "heumilkr_solution" object. See clarke_wright().

See Also

Other cvrplib: cvrplib_download(), cvrplib_ls()

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CVRP instance data by Augerat, 1995

Description

A collection of CVRP instances by Augerat, 1995, provided courtesy of CVRPLIB. See CVRPLIB for visualizations of the instances and their solutions as well as a multitude of alternative instance data.

Usage

cvrplib_A

Format

cvrplib_A

A list of CVRP instances as "cvrplib_instance" objects. The instances can be directly fed into solver algorithm, e.g. via clarke_wright_cvrplib().

Source

http://vrp.atd-lab.inf.puc-rio.br

---

CVRP instance data by Augerat, 1995

Description

A collection of CVRP instances by Augerat, 1995, provided courtesy of CVRPLIB. See CVRPLIB for visualizations of the instances and their solutions as well as a multitude of alternative instance data.

Usage

cvrplib_B

Format

cvrplib_B

A list of CVRP instances as "cvrplib_instance" objects. The instances can be directly fed into solver algorithm, e.g. via clarke_wright_cvrplib().

Source

http://vrp.atd-lab.inf.puc-rio.br

---

CVRPLIB problem instance downloader

Description

CVRLIB offers a selection of CVRP problem instances. This function downloads the instance data and conveniently makes it available to be fed into solver functions, e.g. with clarke_wright_cvrplib(). The primary purpose for those instances is benchmarking / comparing speed as well as performance of solvers.

Usage

cvrplib_download(qualifier)

Arguments

qualifier

The qualifier of the problem instance. E.g. "tai/tai150d". This can either be inferred directly from the website or by the output of cvrplib_ls().

Value

Returns a "cvrplib_instance" object which contains CVRPLIB problem instance data.

See Also

Other cvrplib: clarke_wright_cvrplib(), cvrplib_ls()

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CVRP instance data by Christofides and Eilon, 1969

Description

A collection of CVRP instances by Christofides and Eilon, 1969, provided courtesy of CVRPLIB. See CVRPLIB for visualizations of the instances and their solutions as well as a multitude of alternative instance data.

Usage

cvrplib_E

Format

cvrplib_E

A list of CVRP instances as "cvrplib_instance" objects. The instances can be directly fed into solver algorithm, e.g. via clarke_wright_cvrplib().

Source

http://vrp.atd-lab.inf.puc-rio.br

---

CVRP instance data by Fisher, 1994

Description

A collection of CVRP instances by Fisher, 1994, provided courtesy of CVRPLIB. See CVRPLIB for visualizations of the instances and their solutions as well as a multitude of alternative instance data.

Usage

cvrplib_F

Format

cvrplib_F

A list of CVRP instances as "cvrplib_instance" objects. The instances can be directly fed into solver algorithm, e.g. via clarke_wright_cvrplib().

Source

http://vrp.atd-lab.inf.puc-rio.br

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List available CVRPLIB online data

Description

Scrapes the CVRPLIB website to look for available data sets. This function call can take some time.

Usage

cvrplib_ls()

Value

A vector of data set qualifiers which can be used with cvrplib_download().

See Also

Other cvrplib: clarke_wright_cvrplib(), cvrplib_download()

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CVRP instance data by Rochat and Taillard, 1995

Description

A collection of CVRP instances by Rochat and Taillard, 1995, provided courtesy of CVRPLIB. See CVRPLIB for visualizations of the instances and their solutions as well as a multitude of alternative instance data.

Usage

cvrplib_Tai

Format

cvrplib_Tai

A list of CVRP instances as "cvrplib_instance" objects. The instances can be directly fed into solver algorithm, e.g. via clarke_wright_cvrplib().

Source

http://vrp.atd-lab.inf.puc-rio.br

---

Vehicle runs cost / distance

Description

Calculates the total distance associated to a clarke_wright() result. This is the measure that the corresponding Capacitated Vehicle Routing Problem minimizes.

Usage

milkr_cost(solution)

Arguments

solution

A "heumilkr_solution" object, typically obtained by clarke_wright().

Value

The total traveled distance.

Examples

demand <- c(3, 2, 4, 2)

positions <-
  data.frame(
    pos_x = c(0, 1, -1, 2, 3),
    pos_y = c(0, 1, 1, 2, 3)
  )

solution <- clarke_wright(
  demand,
  dist(positions),
  data.frame(n = NA_integer_, caps = 6)
)

milkr_cost(solution)

---

Vehicle run saving

Description

Measures the saving that was achieved by the heuristic optimization algorithm clarke_wright() compared to the naive vehicle run assignment, i.e. one run per site.

Usage

milkr_saving(solution, relative = FALSE)

Arguments

solution	A "heumilkr_solution" object, typically obtained by clarke_wright().
relative	Should the saving be given as dimensionful value (in units of distance as provided to clarke_wright()), or as percentage relative to the naive costs. Defaults to FALSE, i.e. a dimensionful value.

Value

The savings either as dimensionful value or as percentage relative to the naive costs, depending on relative.

Examples

demand <- c(3, 2, 4, 2)

positions <-
  data.frame(
    pos_x = c(0, 1, -1, 2, 3),
    pos_y = c(0, 1, 1, 2, 3)
  )

solution <- clarke_wright(
  demand,
  dist(positions),
  data.frame(n = NA_integer_, caps = 6)
)

print(milkr_saving(solution))
print(milkr_saving(solution, relative = TRUE))

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