# Sequential Multi-Objective Bayesian Optimization via SMS-EGO

Source:`R/bayesopt_smsego.R`

`mlr_loop_functions_smsego.Rd`

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::Archive 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.

## 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::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: 0.7656336 <list[1]> 0.5861948 1.5236605
#> 2: 1.2089058 <list[1]> 1.4614532 0.6258301
# }
```