asemoa: Implementation of the NSGA-II EMOA algorithm by Deb.
In jakobbossek/ecr: Evolutionary Computing in R

Description Usage Arguments Value Note References Examples

The AS-EMOA, short for aspiration set evolutionary multi-objective algorithm aims to incorporate expert knowledge into multi-objective optimization [1]. The algorithm expects an aspiration set, i.e., a set of reference points. It then creates an approximation of the pareto front close to the aspiration set utilizing the average Hausdorff distance.

asemoa(task, n.population = 10L, n.archive = NULL, aspiration.set = NULL,
  normalize.fun = NULL, dist.fun = ecr:::computeEuclideanDistance, p = 1,
  parent.selector = setupSimpleSelector(),
  mutator = setupPolynomialMutator(eta = 25, p = 0.2),
  recombinator = setupSBXRecombinator(eta = 15, p = 0.7), max.iter = 100L,
  max.evals = NULL, max.time = NULL, ...)

`task`	[`ecr_optimization_task`] Optimization task. If a `smoof_function` is passed it is automatically converted into a task.
`n.population`	[`integer(1)`] Population size. Default is `10`.
`n.archive`	[`integer(1)`] Archive size. Default is the number of points in the `aspiration.set`.
`aspiration.set`	[`matrix`] The aspiration set. Each column contains one point of the set.
`normalize.fun`	[`function`] Function used to normalize fitness values of the individuals before computation of the average Hausdorff distance. The function must have the formal arguments “set” and “aspiration.set”. Default is `NULL`, i.e., no normalization at all.
`dist.fun`	[`function`] Distance function used internally by Hausdorff metric to compute distance between two points. Expects a single vector of coordinate-wise differences between points. Default is `computeEuclideanDistance`.
`p`	[`numeric(1)`] Parameter p for the average Hausdorff metric. Default is 1.
`parent.selector`	[`ecr_selector`] Selection operator which implements a procedure to copy individuals from a given population to the mating pool, i. e., allow them to become parents.
`mutator`	[`ecr_mutator`] Mutation operator of type `ecr_mutator`.
`recombinator`	[`ecr_recombinator`] Recombination operator of type `ecr_recombinator`.
`max.iter`	[`integer(1)`] Maximal number of iterations. Default ist `100L`.
`max.evals`	[`integer(1)`] Maximal number of iterations/generations. Default is `Inf`.
`max.time`	[`integer(1)`] Time budget in seconds. Default ist `Inf`.
`...`	[any] Further arguments passed to `setupECRControl`.

[ecr_asemoa_result, ecr_multi_objective_result]

This is a pure R implementation of the AS-EMOA algorithm. It hides the regular ecr interface and offers a more R like interface while still being quite adaptable.

[1] Rudolph, G., Schuetze, S., Grimme, C., Trautmann, H: An Aspiration Set EMOA Based on Averaged Hausdorff Distances. LION 2014: 153-156. [2] G. Rudolph, O. Schuetze, C. Grimme, and H. Trautmann: A Multiobjective Evolutionary Algorithm Guided by Averaged Hausdorff Distance to Aspiration Sets, pp. 261-273 in A.-A. Tantar et al. (eds.): Proceedings of EVOLVE - A bridge between Probability, Set Oriented Numerics and Evolutionary Computation V, Springer: Berlin Heidelberg 2014.

library(smoof)

obj.fn = makeDTLZ2Function(dimensions = 2L, n.objectives = 2L)

# define the aspiration set, i.e., a set of reference points
aspiration.set = matrix(
  c(0.1531, 0.1594, 0.1656, 0.1719, 0.1781, 0.1844, 0.1906, 0.1969, 0.2031, 0.2094,
    0.2094, 0.2031, 0.1969, 0.1906, 0.1844, 0.1781, 0.1719, 0.1656, 0.1594, 0.1531),
  byrow = TRUE,
  nrow = 2L
)

## Not run: 
res = asemoa(
  task = obj.fn,
  n.population = 10L,
  aspiration.set = aspiration.set,
  max.evals = 1000L
)

## End(Not run)