Package 'cmaesr'

Helper to call certain step function of a monitor.

Description

This funtions serves to call a specific monitor step.

Usage

callMonitor(monitor, step, envir = parent.frame())

Arguments

monitor	[CMAES_monitor] Monitor.
step	[character(1)] One of before, step, after.
envir	[environment] The environment to pass.

---

Covariance-Matrix-Adaptation

Description

Performs non-linear, non-convex optimization by means of the Covariance Matrix Adaptation - Evolution Strategy (CMA-ES).

Usage

cmaes(objective.fun, start.point = NULL, monitor = makeSimpleMonitor(),
  control = list(stop.ons = c(getDefaultStoppingConditions())))

Arguments

objective.fun	[smoof_function] Continuous objective function of type smoof_function. The function must expect a vector of numerical values and return a scaler numerical value.
start.point	[numeric] Initial solution vector. If NULL, one is generated randomly within the box constraints offered by the paramter set of the objective function. Default is NULL.
monitor	[cma_monitor] Monitoring object. Default is makeSimpleMonitor, which produces a console output.
control	[list] Futher paramters for the CMA-ES. See the details section for more in-depth information. Stopping conditions are also defined here. By default only some stopping conditions are passed. See getDefaultStoppingConditions.

Details

This is a pure R implementation of the popular CMA-ES optimizer for continuous black box optimization [2, 3]. It features a flexible system of stopping conditions and enables restarts [1], which can be triggered by arbitrary stopping conditions and can lead to superior performance on multimodal problems.

You may pass additional parameters to the CMA-ES via the control argument. This argument must be a named list. The following control elements will be considered by the CMA-ES implementation:

lambda [integer(1)]

Number of offspring generated in each generation.

mu [integer(1)]

Number of individuals in each population. Defaults to $\lfloor \lambda / 2\rfloor$.

weights [numeric]

Numeric vector of positive weights.

sigma [numeric(1)]

Initial step-size. Default is 0.5.

restart.triggers [character]

List of stopping condition codes / short names (see makeStoppingCondition). All stopping conditions which are placed in this vector do trigger a restart instead of leaving the main loop. Default is the empty character vector, i.e., restart is not triggered.

max.restarts [integer(1)]

Maximal number of restarts. Default is 0. If set to >= 1, the CMA-ES is restarted with a higher population size if at least one of the stoppping conditions is defined as a restart trigger restart.triggers.

restart.multiplier [numeric(1)]

Factor which is used to increase the population size after restart. Default is 2.

stop.ons [list]

List of stopping conditions. The default is to stop after 10 iterations or after a kind of a stagnation (see getDefaultStoppingConditions).

log.population [logical(1L)]

Should each population be stored? Default is FALSE.

Value

[cma_result] Result object. Internally a list with the following components:

par.set [ParamSet]

Parameter set of the objective function.

best.param [numeric]

Final best parameter setting.

best.fitness [numeric(1L)]

Fitness value of the best.param

.

n.evals [integer(1L)]

Number of function evaluations performed.

past.time [integer(1L)]

Running time of the optimization in seconds.

n.restarts [integer(1L)]

Number of restarts.

population.trace [list]

Trace of population.

message [character(1L)]

Message generated by stopping condition.

Note

Internally a check for an indefinite covariance matrix is always performed, i.e., this stopping condition is always prepended internally to the list of stopping conditions.

References

[1] Auger and Hansen (2005). A Restart CMA Evolution Strategy With Increasing Population Size. In IEEE Congress on Evolutionary Computation, CEC 2005, Proceedings, pp. 1769-1776. [2] N. Hansen (2006). The CMA Evolution Strategy: A Comparing Review. In J.A. Lozano, P. Larranaga, I. Inza and E. Bengoetxea (Eds.). Towards a new evolutionary computation. Advances in estimation of distribution algorithms. Springer, pp. 75-102. [3] Hansen and Ostermeier (1996). Adapting arbitrary normal mutation distributions in evolution strategies: The covariance matrix adaptation. In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation, pp. 312-317.

Examples

# generate objective function from smoof package
fn = makeRosenbrockFunction(dimensions = 2L)
res = cmaes(
  fn,
  monitor = NULL,
  control = list(
    sigma = 1.5,
    lambda = 40,
    stop.ons = c(list(stopOnMaxIters(100L)), getDefaultStoppingConditions())
  )
)
print(res)

---

Return list of default stopping conditions.

Description

Default stopping conditions which are active in the reference implementation by Nico Hansen in Python.

Usage

getDefaultStoppingConditions()

Value

[list]

---

Factory method for monitor objects.

Description

Monitors can be pluged in the main cmaes function. They have full access to the environment of the optimization routine and can be used to write/log/visualize relevant data in each iteration.

Usage

makeMonitor(before = NULL, step = NULL, after = NULL, ...)

Arguments

before	[function] Function called one time after initialization of the EA.
step	[function] Function applied after each iteration of the algorithm.
after	[function] Function applied after the EA terminated.
...	[any] Not used.

Value

[cma_monitor] Monitor object.

See Also

makeSimpleMonitor, makeVisualizingMonitor

---

Generator for simple monitor.

Description

The simple monitor prints the iteration, current best parameter values and best fitness to the standard output.

Usage

makeSimpleMonitor(max.params = 4L)

Arguments

max.params

[integer(1)] Maximal number of parameters to show in output.

Value

[cma_monitor]

---

Generate a stopping condition object.

Description

A list of stopping conditions can be passed to the cmaes function. Instead of hardconding the stopping criteria into the main function they exist as stand-alone functions for maximal flexibility and extendability.

Usage

makeStoppingCondition(name, message, stop.fun, code = name,
  control = list())

Arguments

name	[character(1)] Name of the stopping condition.
message	[character(1)] Message returned if the stopping conditions is active.
stop.fun	[function] Function which expects an environment envir as its only argument and returns a single logical value.
code	[character(1)] Internal code, i.e., short name used to potentially trigger restarts. Default is name.
control	[list] Control params.

Value

[cma_stopping_condition] Stopping condition object.

---

Generator for visualizing monitor.

Description

This generator visualizes the optimization process for two-dimensional functions by means of ggplot2.

Usage

makeVisualizingMonitor(show.last = FALSE, show.distribution = TRUE,
  xlim = NULL, ylim = NULL)

Arguments

show.last	[logical(1)] Should the last population be visualized as well? Default is FALSE.
show.distribution	[logical(1)] Should an ellipsis of the normal distribution be plotted? Default is TRUE.
xlim	[numeric(2) || NULL] Limits for the first axis. Default is NULL, i.e., the bounds are determined automatically.
ylim	[numeric(2) || NULL] Limits for the second axis. Default is NULL, i.e., the bounds are determined automatically.

Details

The plot contains points representing the current population, the center of mass or mean value of the population respectively. Optionally an ellipsis represneting the normal distribution of the points can be depicted.

Value

[cma_monitor]

---

Stopping condition: high condition number.

Description

Stop if condition number of covariance matrix exceeds tolerance value.

Usage

stopOnCondCov(tol = 1e+14)

Arguments

tol	[numeric(1)] Tolerance value. Default is 1e14.

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnMaxIters, stopOnNoEffectAxis, stopOnNoEffectCoord, stopOnOptParam, stopOnOptValue, stopOnTimeBudget

---

Stopping condition: maximal funtion evaluations.

Description

Stop if maximal number of function evaluations is reached.

Usage

stopOnMaxEvals(max.evals)

Arguments

max.evals

[integer(1)] Maximal number of allowed function evaluations.

Value

[cma_stopping_condition]

---

Stopping condition: maximal iterations.

Description

Stop on maximal number of iterations.

Usage

stopOnMaxIters(max.iter = 100L)

Arguments

max.iter

[integer(1)] Maximal number of iterations. Default is 100.

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnNoEffectAxis, stopOnNoEffectCoord, stopOnOptParam, stopOnOptValue, stopOnTimeBudget

---

Stopping condition: principal axis.

Description

Stop if addition of 0.1 * sigma in a principal axis direction does not change mean value.

Usage

stopOnNoEffectAxis()

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnMaxIters, stopOnNoEffectCoord, stopOnOptParam, stopOnOptValue, stopOnTimeBudget

---

Stopping condition: standard deviation in coordinates.

Description

Stop if addition of 0.2 * standard deviations in any coordinate does not change mean value.

Usage

stopOnNoEffectCoord()

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnMaxIters, stopOnNoEffectAxis, stopOnOptParam, stopOnOptValue, stopOnTimeBudget

---

Stopping condition: optimal params.

Description

Stop if euclidean distance of parameter is below some tolerance value.

Usage

stopOnOptParam(opt.param, tol = 1e-08)

Arguments

opt.param	[numeric] Known optimal parameter settings.
tol	[numeric(1)] Tolerance value. Default is $1e^{-8}$.

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnMaxIters, stopOnNoEffectAxis, stopOnNoEffectCoord, stopOnOptValue, stopOnTimeBudget

---

Stopping condition: optimal objective value.

Description

Stop if best solution is close to optimal objective value.

Usage

stopOnOptValue(opt.value, tol = 1e-08)

Arguments

opt.value	[numeric(1)] Known optimal objective function value.
tol	[numeric(1)] Tolerance value. Default is $1e^{-8}$.

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnMaxIters, stopOnNoEffectAxis, stopOnNoEffectCoord, stopOnOptParam, stopOnTimeBudget

---

Stopping condition: maximal time.

Description

Stop if maximal running time budget is reached.

Usage

stopOnTimeBudget(budget)

Arguments

budget

[integer(1)] Time budget in seconds.

Value

[cma_stopping_condition]

See Also

Other stopping.conditions: stopOnCondCov, stopOnMaxIters, stopOnNoEffectAxis, stopOnNoEffectCoord, stopOnOptParam, stopOnOptValue

---

Stopping condition: low standard deviation.

Description

Stop if the standard deviation falls below a tolerance value in all coordinates?

Usage

stopOnTolX(tol = 1e-12)

Arguments

tol	[integer(1)] Tolerance value.

Value

[cma_stopping_condition]

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