R: Pruefer-EMOA for the multi-objective MST problem.

mcMSTEmoaZhou {mcMST}

R Documentation

Pruefer-EMOA for the multi-objective MST problem.

Description

Evolutionary multi-objective algorithm to solve the multi-objective minimum spanning tree problem. The algorithm adopts the so-called Pruefer-number as the encoding for spanning trees. A Pruefer-number for a graph with nodes V = \{1, \ldots, n\} is a sequence of n - 2 numbers from V. Cayleys theorem states, that a complete graph width n nodes has exactly n^{n-2} spanning trees. The algorithm uses mutation only: each component of an individual is replaced uniformly at random with another node number from the node set.

Usage

mcMSTEmoaZhou(
  instance,
  mu,
  lambda = mu,
  mut = mutUniformPruefer,
  selMating = ecr::selSimple,
  selSurvival = ecr::selNondom,
  ref.point = NULL,
  max.iter = 100L
)

Arguments

`instance`	[`grapherator`] Multi-objective graph.
`mu`	[`integer(1)`] Population size.
`lambda`	[`integer(1)`] Number of offspring generated in each generation. Default is `mu`.
`mut`	[`ecr_mutator`] Mutation operator. Defaults to `mutUniformPruefer`, i.e., each digit of the Pruefer encoding is replaced with some probability with a random number from `V = \{1, \ldots, n\}`.
`selMating`	[`ecr_selector`] Mating selector. Default is `selSimple`.
`selSurvival`	[`ecr_selector`] Survival selector. Default is `link[ecr]{selNondom}`.
`ref.point`	[`numeric(n.objectives) \| NULL`] Reference point for hypervolume computation used for logging. If `NULL` the sum of the `n` largest edges in each objective is used where `n` is the number of nodes of `instance`. This is an upper bound for the size of each spanning tree with `(n-1)` edges.
`max.iter`	[`integer(1)`] Maximal number of iterations. Default is `100`.

Value

[ecr_result] List of type ecr_result with the following components:

task: The ecr_optimization_task.
log: Logger object.
pareto.idx: Indizes of the non-dominated solutions in the last population.
pareto.front: (n x d) matrix of the approximated non-dominated front where n is the number of non-dominated points and d is the number of objectives.
pareto.set: Matrix of decision space values resulting with objective values given in pareto.front.
last.population: Last population.
message: Character string describing the reason of termination.

References