In this paper, several new set quality metrics are introduced that can be used to evaluate the “goodness” of an observed Pareto solution set. These metrics, which are formulated in closed-form and geometrically illustrated, include hyperarea difference, Pareto spread, accuracy of an observed Pareto frontier, number of distinct choices and cluster. The metrics should enable a designer to either monitor the quality of an observed Pareto solution set as obtained by a multiobjective optimization method, or compare the quality of observed Pareto solution sets as reported by different multiobjective optimization methods. A vibrating platform example is used to demonstrate the calculation of these metrics for an observed Pareto solution set.

1.
Eschenauer, C. M., Koski, J., and Osyczka, A., eds., 1990, Multicriteria Design Optimization, Springer-Verlag, New York.
2.
Miettinen, K. M., 1999, Nonlinear Multiobjective Optimization, Kluwer Academic, Boston.
3.
Ba¨ck, T., 1996, Evolutionary Algorithms in Theory and Practice, Oxford University Press, New York.
4.
Zitzler, E., and Thiele, L., 1998, “
Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Case Study,” In Eiben, A. E.
, et al., Proc. 5th International Conference: Parallel Problem Solving from Nature—PPSNV, Amsterdam, The Netherlands, Springer, pp. 292–301.
5.
Van Veldhuizen, D. A., 1999, “
Multiobjective Evolutionary Algorithm: Classifications, Analyses, and New Innovations,” Ph.D. Dissertation, Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright-Patterson AFB, Ohio.
6.
Schott, J. R., 1995, “
Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization,” MS Thesis, Department of Aeronautics and Astronautics, MIT, Cambridge, Massachusetts.
7.
Srinivas
,
N.
, and
Deb
,
K.
,
1994
, “
Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithm
,”
Evolu. Comput.
,
2
, No.
3
, pp.
221
248
.
8.
Sayin, S., 1997, “
Measuring the Quality of Discrete Representations of Efficient Sets in Multiple Objective Mathematical Programming,” Working Paper No. 1997/25, Koc¸ University, Turkey.
9.
Messac
,
A.
,
1996
, “
Physical Programming: Effective Optimization for Computational Design
,”
AIAA J.
,
34
, No.
1
, pp.
149
158
.
10.
Azarm, S., Reynolds, B., and Narayanan, S., 1999, “
Comparison of Two Multiobjective Optimization Techniques with and within Genetic Algorithm,” CD-ROM Proceedings of the ASME DETC, Design Automation Conference, Paper No. DETC99/DAC-8584, DETC’99 September 12–16, 1999, Las Vegas, Nevada.
You do not currently have access to this content.