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::OptimInstanceMultiCrit)
The bbotk::OptimInstanceMultiCrit 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::Archive 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::Archive of the bbotk::OptimInstanceMultiCrit.

• The scalarizations of the objective function values are stored as the y_scal column in the bbotk::Archive of the bbotk::OptimInstanceMultiCrit.

• To make use of parallel evaluations in the case of `q > 1, the objective function of the bbotk::OptimInstanceMultiCrit must be implemented accordingly.

• 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.