asemoa function

Implementation of the NSGA-II EMOA algorithm by Deb.

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(
  fitness.fun,
  n.objectives = NULL,
  minimize = NULL,
  n.dim = NULL,
  lower = NULL,
  upper = NULL,
  mu = 10L,
  aspiration.set = NULL,
  normalize.fun = NULL,
  dist.fun = 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.

Returns

[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.