smoof (version 1.7.0)

makeMNKFunction: Generators for (r)MNK-landscapes

Description

Generators for multi-objective NK-landscapes, i.e., with at least two objectives. Function makeMNKLandscape(M, N, K) create NK-landscapes with M (\(\geq 2\)) objectives, input dimension N, and epistatic links specified via parameter K. K can be a single integer value, a vector of M integers or a list of length-N integer vectors (see parameter description for details) which allow for maximum flexibility. It is also possible to compose a MNK-landscape by passing a list of single-objective NK-landscapes via argument funs.

Usage

makeMNKFunction(M, N, K, funs = NULL)
makeRMNKFunction(M, N, K, rho = 0)

Value

[smoof_multi_objective_function]

Arguments

M

[integer(1)]
Number of objectives (at least two).

N

[integer(1)]
Length of the bit-string (decision space dimension).

K

[integer]
Epistatic links. Possible values are a a) single integer which is used for all bits and positions, b) an integer vector of N integers that are used across the objectives, c) a list of M length-N integers to define specific epistatic links for every bit position of every objective.

funs

[list | NULL]
Allows for an alternative way to build a MNK-landscape by passing a list of at least two single-objective NK-landscapes. In this case all other parameters M, N, K and rho are ignored. Note that the passed functions must be compatible, i.e., a) the input dimension N needs to match and b) all pased functions need to be multi-objective. Default is NULL.

rho

[numeric(1)]
Correlation between objectives (value between -1 and 1).

Details

Function makeRMNKLandscape(M, N, K, rho) generates a MNK-landscape with correlated objective function values. The correlation can be adjusted by setting the rho parameter to a value between minus one and one.

References

H. E. Aguirre and K. Tanaka, Insights on properties of multiobjective MNK-landscapes, Proceedings of the 2004 Congress on Evolutionary Computation, Portland, OR, USA, 2004, pp. 196-203 Vol.1, doi: 10.1109/CEC.2004.1330857.

See Also

makeNKFunction

Other nk_landscapes: exportNKFunction(), makeNKFunction()

Examples

# generate homogeneous uncorrelated bi-objective MNK-landscape with each
# three epistatic links
M = 2L
N = 20L
K = 3L
fn = makeMNKFunction(M, N, K)

# generate MNK-landscape where the first function has 3 epistatic links
# per bit while the second function has 2
fn = makeMNKFunction(M, N, K = c(3L, 2L))

# sample the number of epistatic links individually from {1, ..., 5} for
# every bit position and every objective
K = lapply(seq_len(M), function(m) sample(1:(N-1), size = N, replace = TRUE))
fn = makeMNKFunction(M, N, K = K)

#' # generate strongly positively correlated objectives
fn = makeRMNKFunction(M, N, K, rho = 0.9)

# alternative constructor: generate two single-objective NK-landscapes
# and combine into bi-objective problem
soofn1 = makeNKFunction(N, K = 2L) # homegeneous in K
K = sample(2:3, size = N, replace = TRUE)
soofn2 = makeNKFunction(N, K = K) # heterogeneous in K
moofn = makeMNKFunction(funs = list(soofn1, soofn2))
getNumberOfObjectives(moofn)