Sequential Multi-Objective Bayesian Optimization via SMS-EGO

Loop function for sequential multi-objective Bayesian Optimization via SMS-EGO. Normally used inside an OptimizerMbo.

In each iteration after the initial design, the surrogate and acquisition function (mlr_acqfunctions_smsego) are updated and the next candidate is chosen based on optimizing the acquisition function.

Usage

bayesopt_smsego(
  instance,
  surrogate,
  acq_function,
  acq_optimizer,
  init_design_size = NULL,
  random_interleave_iter = 0L
)

Arguments

instance

(bbotk::OptimInstanceBatchMultiCrit)
The bbotk::OptimInstanceBatchMultiCrit to be optimized.

surrogate

(SurrogateLearnerCollection)
SurrogateLearnerCollection to be used as a surrogate.

acq_function

(mlr_acqfunctions_smsego)
mlr_acqfunctions_smsego to be used as acquisition function.

acq_optimizer

(AcqOptimizer)
AcqOptimizer to be used as acquisition function optimizer.

init_design_size

(NULL | integer(1))
Size of the initial design. If NULL and the bbotk::ArchiveBatch contains no evaluations, 4 * d is used with d being the dimensionality of the search space. Points are generated via a Sobol sequence.

random_interleave_iter

(integer(1))
Every random_interleave_iter iteration (starting after the initial design), a point is sampled uniformly at random and evaluated (instead of a model based proposal). For example, if random_interleave_iter = 2, random interleaving is performed in the second, fourth, sixth, ... iteration. Default is 0, i.e., no random interleaving is performed at all.

Value

invisible(instance)
The original instance is modified in-place and returned invisible.

Note

• The acq_function$surrogate, even if already populated, will always be overwritten by the surrogate.

• The acq_optimizer$acq_function, even if already populated, will always be overwritten by acq_function.

• The surrogate$archive, even if already populated, will always be overwritten by the bbotk::ArchiveBatch of the bbotk::OptimInstanceBatchMultiCrit.

• Due to the iterative computation of the epsilon within the mlr_acqfunctions_smsego, requires the bbotk::Terminator of the bbotk::OptimInstanceBatchMultiCrit to be a bbotk::TerminatorEvals.

References

• Beume N, Naujoks B, Emmerich M (2007). “SMS-EMOA: Multiobjective selection based on dominated hypervolume.” European Journal of Operational Research, 181(3), 1653–1669.

• Ponweiser, Wolfgang, Wagner, Tobias, Biermann, Dirk, Vincze, Markus (2008). “Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted S-Metric Selection.” In Proceedings of the 10th International Conference on Parallel Problem Solving from Nature, 784–794.

See also

Other Loop Function: loop_function, mlr_loop_functions, mlr_loop_functions_ego, mlr_loop_functions_emo, mlr_loop_functions_mpcl, mlr_loop_functions_parego

Examples

# \donttest{
if (requireNamespace("mlr3learners") &
    requireNamespace("DiceKriging") &
    requireNamespace("rgenoud")) {

  library(bbotk)
  library(paradox)
  library(mlr3learners)

  fun = function(xs) {
    list(y1 = xs$x^2, y2 = (xs$x - 2) ^ 2)
  }
  domain = ps(x = p_dbl(lower = -10, upper = 10))
  codomain = ps(y1 = p_dbl(tags = "minimize"), y2 = p_dbl(tags = "minimize"))
  objective = ObjectiveRFun$new(fun = fun, domain = domain, codomain = codomain)

  instance = OptimInstanceBatchMultiCrit$new(
    objective = objective,
    terminator = trm("evals", n_evals = 5))

  surrogate = default_surrogate(instance)

  acq_function = acqf("smsego")

  acq_optimizer = acqo(
    optimizer = opt("random_search", batch_size = 100),
    terminator = trm("evals", n_evals = 100))

  optimizer = opt("mbo",
    loop_function = bayesopt_smsego,
    surrogate = surrogate,
    acq_function = acq_function,
    acq_optimizer = acq_optimizer)

  optimizer$optimize(instance)
}
#>              x  x_domain          y1          y2
#>          <num>    <list>       <num>       <num>
#> 1: -0.08059442 <list[1]> 0.006495461 4.328873142
#> 2:  1.95018192 <list[1]> 3.803209514 0.002481841
# }