TY - JOUR
T1 - Using the averaged hausdorff distance as a performance measure in evolutionary multiobjective optimization
AU - Schütze, Oliver
AU - Esquivel, Xavier
AU - Lara, Adriana
AU - Coello, Carlos A.Coello
N1 - Funding Information:
Manuscript received October 8, 2010; revised February 25, 2011; accepted June 18, 2011. Date of publication February 10, 2012; date of current version July 26, 2012. The work of O. Schütze was supported by DAAD, under Project 146776. The work of X. Esquivel and A. Lara was supported by CONACyT through a scholarship to pursue graduate studies at the Department of Computer Science, CINVESTAV-IPN. The work of C. A. Coello Coello was supported by CONACyT, under Project 103570.
PY - 2012
Y1 - 2012
N2 - The Hausdorff distance d H is a widely used tool to measure the distance between different objects in several research fields. Possible reasons for this might be that it is a natural extension of the well-known and intuitive distance between points and/or the fact that d H defines in certain cases a metric in the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is typically to compute the entire solution setthe so-called Pareto setrespectively its image, the Pareto front. Hence, d H should, at least at first sight, be a natural choice to measure the performance of the outcome set in particular since it is related to the terms spread and convergence as used in EMO literature. However, so far, d H does not find the general approval in the EMO community. The main reason for this is that d H penalizes single outliers of the candidate set which does not comply with the use of stochastic search algorithms such as evolutionary strategies. In this paper, we define a new performance indicator, Δ p, which can be viewed as an averaged Hausdorff distance between the outcome set and the Pareto front and which is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We will discuss theoretical properties of Δ p (as well as for GD and IGD) such as the metric properties and the compliance with state-of-the-art multiobjective evolutionary algorithms (MOEAs), and will further on demonstrate by empirical results the potential of Δ p as a new performance indicator for the evaluation of MOEAs.
AB - The Hausdorff distance d H is a widely used tool to measure the distance between different objects in several research fields. Possible reasons for this might be that it is a natural extension of the well-known and intuitive distance between points and/or the fact that d H defines in certain cases a metric in the mathematical sense. In evolutionary multiobjective optimization (EMO) the task is typically to compute the entire solution setthe so-called Pareto setrespectively its image, the Pareto front. Hence, d H should, at least at first sight, be a natural choice to measure the performance of the outcome set in particular since it is related to the terms spread and convergence as used in EMO literature. However, so far, d H does not find the general approval in the EMO community. The main reason for this is that d H penalizes single outliers of the candidate set which does not comply with the use of stochastic search algorithms such as evolutionary strategies. In this paper, we define a new performance indicator, Δ p, which can be viewed as an averaged Hausdorff distance between the outcome set and the Pareto front and which is composed of (slight modifications of) the well-known indicators generational distance (GD) and inverted generational distance (IGD). We will discuss theoretical properties of Δ p (as well as for GD and IGD) such as the metric properties and the compliance with state-of-the-art multiobjective evolutionary algorithms (MOEAs), and will further on demonstrate by empirical results the potential of Δ p as a new performance indicator for the evaluation of MOEAs.
KW - Averaged Hausdorff distance
KW - generational distance
KW - inverted generational distance
KW - multiobjective optimization
KW - performance indicator
UR - http://www.scopus.com/inward/record.url?scp=84864615370&partnerID=8YFLogxK
U2 - 10.1109/TEVC.2011.2161872
DO - 10.1109/TEVC.2011.2161872
M3 - Artículo
SN - 1089-778X
VL - 16
SP - 504
EP - 522
JO - IEEE Transactions on Evolutionary Computation
JF - IEEE Transactions on Evolutionary Computation
IS - 4
M1 - 6151115
ER -