Multi-Objective Bayesian Optimization via ParEGO

Loop function for multi-objective Bayesian Optimization via ParEGO. Normally used inside an OptimizerMbo.

In each iteration after the initial design, the observed objective function values are normalized and q candidates are obtained by scalarizing these values via the augmented Tchebycheff function, updating the surrogate with respect to these scalarized values and optimizing the acquisition function.

Usage

bayesopt_parego(
  instance,
  surrogate,
  acq_function,
  acq_optimizer,
  init_design_size = NULL,
  q = 1L,
  s = 100L,
  rho = 0.05,
  random_interleave_iter = 0L
)

Arguments

instance: (bbotk::OptimInstanceBatchMultiCrit)
The bbotk::OptimInstanceBatchMultiCrit to be optimized.
surrogate: (SurrogateLearner)
SurrogateLearner to be used as a surrogate.
acq_function: (AcqFunction)
AcqFunction 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.
q: (integer(1))
Batch size, i.e., the number of candidates to be obtained for a single batch. Default is 1.
s: (integer(1))
$s$ in Equation 1 in Knowles (2006). Determines the total number of possible random weight vectors. Default is 100.
rho: (numeric(1))
$\rho$ in Equation 2 in Knowles (2006) scaling the linear part of the augmented Tchebycheff function. Default is 0.05
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.
The scalarizations of the objective function values are stored as the y_scal column in the bbotk::ArchiveBatch of the bbotk::OptimInstanceBatchMultiCrit.
To make use of parallel evaluations in the case of `q > 1, the objective function of the bbotk::OptimInstanceBatchMultiCrit must be implemented accordingly.

References

Knowles, Joshua (2006). “ParEGO: A Hybrid Algorithm With On-Line Landscape Approximation for Expensive Multiobjective Optimization Problems.” IEEE Transactions on Evolutionary Computation, 10(1), 50–66.

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, n_learner = 1)

  acq_function = acqf("ei")

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

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

  optimizer$optimize(instance)
}
#> WARN  [17:04:31.670] [bbotk] Task 'surrogate_task' has missing values in column(s) 'y_scal', but learner 'regr.km' does not support this
#> WARN  [17:04:31.696] [bbotk] Could not update the surrogate a final time after the optimization process has terminated.
#>            x  x_domain        y1       y2
#>        <num>    <list>     <num>    <num>
#> 1: 0.7590663 <list[1]> 0.5761817 1.539916
# }