R: Implementation of the NSGA-II EMOA algorithm by Deb.

asemoa {ecr}

R Documentation

Implementation of the NSGA-II EMOA algorithm by Deb.

Description

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.

Usage

asemoa(fitness.fun, n.objectives = NULL, minimize = NULL, n.dim = NULL,
  lower = NULL, upper = NULL, mu = 10L, aspiration.set = NULL,
  normalize.fun = NULL, dist.fun = ecr:::computeEuclideanDistance, p = 1,
  parent.selector = setup(selSimple), mutator = setup(mutPolynomial, eta =
  25, p = 0.2, lower = lower, upper = upper), recombinator = setup(recSBX, eta
  = 15, p = 0.7, lower = lower, upper = upper),
  terminators = list(stopOnIters(100L)))

Arguments

`fitness.fun`	[`function`] The fitness function.
`n.objectives`	[`integer(1)`] Number of objectives of `obj.fun`. Optional if `obj.fun` is a benchmark function from package smoof.
`minimize`	[`logical(n.objectives)`] Logical vector with ith entry `TRUE` if the ith objective of `fitness.fun` shall be minimized. If a single logical is passed, it is assumed to be valid for each objective.
`n.dim`	[`integer(1)`] Dimension of the decision space.
`lower`	[`numeric`] Vector of minimal values for each parameter of the decision space in case of float or permutation encoding. Optional if `obj.fun` is a benchmark function from package smoof.
`upper`	[`numeric`] Vector of maximal values for each parameter of the decision space in case of float or permutation encoding. Optional if `obj.fun` is a benchmark function from package smoof.
`mu`	[`integer(1)`] Population size. Default is 10.
`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`.
`terminators`	[`list`] List of stopping conditions of type “ecr_terminator”. Default is to stop after 100 iterations.

Value

[ecr_multi_objective_result]

Note

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.

References

[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.

[Package ecr version 2.1.0 Index]