mco (version 1.0-15.1)

generationalDistance: Quality measures for MCO solutions

Description

Functions to evaulate the quality of the estimated pareto front.

Usage

generationalDistance(x, o)
generalizedSpread(x, o)
epsilonIndicator(x, o)
dominatedHypervolume(x, ref)

Arguments

x

Estimated pareto front or an object which has a paretoFront method

o

True pareto front or an object which has a paretoFront method

ref

Reference point (may be omitted).

Value

The respective quality measure.

Details

Instead of the pareto front, one can also pass an object for which a paretoFront method exists to both methods.

For dominatedHypervolume, if no reference point is given, the maximum in each dimension is used as the reference point.

References

Carlos M. Fonseca, Luis Paquete, and Manuel Lopez-Ibanez. An improved dimension-sweep algorithm for the hypervolume indicator. In IEEE Congress on Evolutionary Computation, pages 1157-1163, Vancouver, Canada, July 2006.

Nicola Beume, Carlos M. Fonseca, Manuel Lopez-Ibanez, Luis Paquete, and J. Vahrenhold. On the complexity of computing the hypervolume indicator. IEEE Transactions on Evolutionary Computation, 13(5):1075-1082, 2009.

Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., and Grunert da Fonseca, V (2003): Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation, 7(2), 117-132.

Examples

# NOT RUN {
## Estimate true front:
# }
# NOT RUN {
tf <- nsga2(fonseca2, 2, 2,
            lower.bounds=c(-4, -4), upper.bounds=c(4, 4),
            popsize=1000, generations=100)
res <- nsga2(fonseca2, 2, 2,
             lower.bounds=c(-4, -4), upper.bounds=c(4, 4),
             popsize=16, generations=c(2, 4, 6, 8, 10, 20, 50))
n <- length(res)
sapply(1:n, function(i) dominatedHypervolume(res[[i]], c(1, 1)))
sapply(1:n, function(i) generationalDistance(res[[i]], tf))
sapply(1:n, function(i) generalizedSpread(res[[i]], tf))
sapply(1:n, function(i) epsilonIndicator(res[[i]], tf))
# }