Morbit

RbfConfig(; kwarg1 = val1, … )

Configuration type for local RBF surrogate models.

To choose a kernel, use the kwarg kernel and a value of either :cubic (default), :multiquadric, :exp or :thin_plate_spline. The kwarg shape_parameter takes a constant number or a string that defines a calculation on Δ, e.g, "Δ/10".

To see other configuration parameters use fieldnames(Morbit.RbfConfig). They have individual docstrings attached.

Unscale the point x̂ from internal to original domain.

Add an objective function to MOP with specified output indices.

Perform a backtracking loop starting at x with an initial step of step_size .* dir and return trial point x₊, the surrogate value-vector m_x₊ and the final step s = x₊ .- x.

Remove an objective function from MOP.

Get real-valued shape parameter for RBF model from current iter data. cfg allows for a string expression which would be evaluated here.

Return an ExactModel build from a VectorObjectiveFunction objf. Model is the same inside and outside of criticality round.

Return a TaylorModel build from a VectorObjectiveFunction objf.

Return smallest positive and biggest negative and σ₊ and σ₋ so that x .+ σ± .* d stays within bounds.

Return lower and upper bound vectors combining global and trust region constraints.

Factorial of a multinomial.

Position of objf in list_of_objectives(mop).

A general constructor.

add_objective!( mop :: MixedMOP, func :: T where{T <: Function}, type :: Symbol = :expensive, n_out :: Int64 = 1, can_batch :: Bool = false )

Add scalar-valued objective function func to mop structure. func must take an RVec as its (first) argument, i.e. represent a function $f: ℝ^n → ℝ$. type must either be :expensive or :cheap to determine whether the function is replaced by a surrogate model or not.

If type is :cheap and func takes 1 argument only then its gradient is calculated by ForwardDiff. A cheap function func with custom gradient function grad (representing $∇f : ℝ^n → ℝ^n$) is added by

add_objective!(mop, func, grad)

The optional argument n_out allows for the specification of vector-valued objective functions. This is mainly meant to be used for expensive functions that are in some sense inter-dependent.

The flag can_batch defaults to false so that the objective function is simply looped over a bunch of arguments if required. If can_batch == true then the objective function must be able to return an array of results when provided an array of input vectors (whilst still returning a single result, not a singleton array containing the result, for a single input vector).

Examples

# Define 2 scalar objective functions and a MOP ℝ^2 → ℝ^2

f1(x) =  x[1]^2 + x[2]

f2(x) = exp(sum(x))
∇f2(x) = exp(sum(x)) .* ones(2);

mop = MixedMOP()
add_objective!(mop, f1, :cheap)     # gradient will be calculated using ForwardDiff
add_objective!(mop, f2, ∇f2 )       # gradient is provided

add_objective!( mop :: MixedMOP, func :: T where{T <: Function}, grad :: T where{T <: Function})

Add scalar-valued objective function func and its vector-valued gradient grad to mop struture.

Add a scalar objective to mop::MixedMOP modelled according to model_config.

Add a vector objective to mop::MixedMOP modelled according to model_config.

Combine two objectives. Only needed if combinable can return true.

Get a new function function handle stacking the output of func1 and func2.

Delete surrogate wrapper at position si from list sc.surrogates.

(Internally) Evaluate all objectives at site x̂::RVec. Objective order might differ from order in which they were added.

Evaluate all objectives at site x̂::RVec and sort the result according to the order in which objectives were added.

Return a function that evaluates an objective at a scaled site.

Evaluate output ℓ of the ExactModel em at scaled site x̂.

Evaluate the ExactModel em at scaled site x̂.

Return model value for output l of sc at x̂. Index l is assumed to be an internal index in the range of 1,…,nobjfs, where nobjfs is the total number of (scalarized) objectives stored in sc.

Evaluate the objective at scaled site(s). and increase counter.

Find affinely independent results in database box of radius Δ around x Results are saved in rbf.tdata[tdata_index]. Both rbf.Y and rbf.Z are changed.

Indices of sites in database that lie in box with bounds lb and ub.

Return lower variable bounds for scaled variables.

Return upper variable bounds for scaled variables.

Gradient vector of output ℓ of em at scaled site x̂.

Return a gradient for output l of sc at x̂. Index 4 is assumed to be an internal index in the range of 1,…,nobjfs, where nobjfs is the total number of (scalarized) objectives stored in sc.

Jacobian Matrix of ExactModel em at scaled site x̂.

Return a function handle to be used with NLopt for output l of sc. Index l is assumed to be an internal index in the range of 1,…,nobjfs, where nobjfs is the total number of (scalarized) objectives stored in sc.

Return a function handle to be used with NLopt for output ℓ of model. That is, if model is a surrogate for two scalar objectives, then ℓ must be either 1 or 2.

Increase evaluation count by N

Return a SurrogateContainer initialized from the information provided in mop.

Perform initialization of the data passed to optimize function.

load_config(fn :: AbstractString)

Load and return the AbstractConfig that was saved previously with save_config. Return nothing on error.

load_database(fn :: AbstractString)

Load and return the <:AbstractDB that was saved previously with save_database. Return nothing on error.

load_iter_data(fn :: AbstractString)

Load and return the <:AbstractIterData that was saved previously with save_iter_data. Return nothing on error.

Local bounds vectors lb_eff and ub_eff using scaled variable constraints from mop.

Set upper bound of № evaluations to N

(Soft) upper bound on the number of function calls.

Return surrogate configuration used to model the objective internally.

Return array of solution vectors [x1, …, xlen] to the equation $x_1 + … + x_len = rhs$ where the variables must be non-negative integers.

Set evaluation counter to N.

Number of calls to the original objective function.

Number of scalar-valued objectives of the problem.

Remove objf from list_of_objectives(mop) and return its output indices.

Specify local algorithm to polish Pascoletti-Serafini solution. Uses 1/4 of maximum allowed evals.

Set evaluation counter to 0 for each VectorObjectiveFunction in m.vector_of_objectives.

Sort an interal objective vector so that the objectives are in the order in which they were added.

Return index vector so that an internal objective vector is sorted according to the order the objectives where added.

save_config(filename, ac :: AbstractConfig )

Save the configuration object ac at path filename. Ensures, that the file extension is .jld2. The fieldname to retrieve the database object is database.

Returns the save path if successful and nothing else.

save_database(filename, DB :: AbstractDB )

Save the database DB at path filename. Ensures, that the file extension is .jld2. The fieldname to retrieve the database object is database.

Returns the save path if successful and nothing else.

save_database(filename, id :: AbstractIterData )

Save the database that is referenced by db(id) at path filename. Ensures, that the file extension is .jld2. The fieldname to retrieve the database object is database.

Returns the save path if successful and nothing else.

save_iter_data(filename, id :: AbstractIterData )

Save the whole object id at path filename. Ensures, that the file extension is .jld2. The fieldname to retrieve the database object is database.

Returns the save path if successful and nothing else.

Scale variables fully constrained to a closed interval to [0,1] internally.

Modify/initialize thec exact model mod so that we can differentiate it later.

Modify/initialize thec exact model mod so that we can differentiate it later.

Require a descent in all model objective components. Applies only to backtracking descent steps, i.e., :steepest_descent.

Reverse scaling for fully constrained variables from [0,1] to their former domain.