Implementation of the SMS-EMOA by Emmerich et al.

Pure R implementation of the SMS-EMOA. This algorithm belongs to the group of indicator based multi-objective evolutionary algorithms. In each generation, the SMS-EMOA selects two parents uniformly at, applies recombination and mutation and finally selects the best subset of individuals among all subsets by maximizing the Hypervolume indicator.

smsemoa(fitness.fun, n.objectives = NULL, n.dim = NULL, minimize = NULL,
  lower = NULL, upper = NULL, mu = 100L, ref.point = NULL,
  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.
n.dim

[integer(1)] Dimension of the decision space.
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.
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)] Number of individuals in the population. Default is 100.
ref.point

[numeric] Reference point for the hypervolume computation. Default is (11, ..., 11)' with the corresponding dimension.
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.
...

[any] Further arguments passed down to fitness function.

Value

[ecr_multi_objective_result]

Note

This helper function hides the regular ecr interface and offers a more R like interface of this state of the art EMOA.

References

Beume, N., Naujoks, B., Emmerich, M., SMS-EMOA: Multiobjective selection based on dominated hypervolume, European Journal of Operational Research, Volume 181, Issue 3, 16 September 2007, Pages 1653-1669.