TY - JOUR
T1 - U-Measure
T2 - A Quality Measure for Multiobjective Programming
AU - LEUNG, Yiu Wing
AU - Wang, Yuping
N1 - Funding Information:
Manuscript received March 12, 2001; revised April 8, 2003. This work was supported by the Hong Kong Baptist University under Research Grant FRG II-62. This paper was recommended by Associate Editor J. Lambert. Y.-W. Leung is with the Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong (e-mail: ywleung@comp.hkbu.edu.hk). Y. Wang is with the Department of Mathematics Science, Faculty of Science, Xidian University, Xian, China. Digital Object Identifier 10.1109/TSMCA.2003.817059
PY - 2003/5
Y1 - 2003/5
N2 - A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and so their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier. This frontier is a nonlinear hyper-surface. We measure the uniformity over this hyper-surface in three main steps: 1) determine the domains of the Pareto frontier over which uniformity is measured, 2) determine the nearest neighbors of each solution in the objective space, and 3) compute the discrepancy among the distances between nearest neighbors. The U-measure is equal to this discrepancy where a smaller discrepancy indicates a better uniformity. We can apply the U-measure to complement the other quality measures so that we can evaluate and compare multiobjective programming algorithms from different perspectives.
AB - A multiobjective programming algorithm may find multiple nondominated solutions. If these solutions are scattered more uniformly over the Pareto frontier in the objective space, they are more different choices and so their quality is better. In this paper, we propose a quality measure called U-measure to measure the uniformity of a given set of nondominated solutions over the Pareto frontier. This frontier is a nonlinear hyper-surface. We measure the uniformity over this hyper-surface in three main steps: 1) determine the domains of the Pareto frontier over which uniformity is measured, 2) determine the nearest neighbors of each solution in the objective space, and 3) compute the discrepancy among the distances between nearest neighbors. The U-measure is equal to this discrepancy where a smaller discrepancy indicates a better uniformity. We can apply the U-measure to complement the other quality measures so that we can evaluate and compare multiobjective programming algorithms from different perspectives.
KW - Multiobjective programming
KW - Nondominated solutions
KW - Pareto-optimality
KW - Quality measures
UR - http://www.scopus.com/inward/record.url?scp=0141638719&partnerID=8YFLogxK
U2 - 10.1109/TSMCA.2003.817059
DO - 10.1109/TSMCA.2003.817059
M3 - Article
AN - SCOPUS:0141638719
VL - 33
SP - 337
EP - 343
JO - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
JF - IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans
SN - 1083-4427
IS - 3
ER -