Minimal Sets of Quality Metrics

Numerous quality assessment metrics have been developed by researchers to compare the performance of different multi-objective evolutionary algorithms. These metrics show different properties and address various aspects of solution set quality. In this paper, we propose a conceptual framework for selection of a handful of these metrics such that all desired aspects of quality are addressed with minimum or no redundancy. Indeed, we prove that such sets of metrics, referred to as 'minimal sets', must be constructed based on a one-to-one correspondence with those aspects of quality that are desirable to a decision-maker.

[1]  Marco Laumanns,et al.  Why Quality Assessment Of Multiobjective Optimizers Is Difficult , 2002, GECCO.

[2]  H. Enderton.  Elements of Set Theory , 1977 .

[3]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[4]  Joshua D. Knowles.  Local-search and hybrid evolutionary algorithms for Pareto optimization , 2002 .

[5]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[6]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .

[7]  Shapour Azarm,et al.  Metrics for Quality Assessment of a Multiobjective Design Optimization Solution Set , 2001 .

[8]  Serpil Sayin,et al.  Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming , 2000, Math. Program..

[9]  Marc Despontin,et al.  Multiple Criteria Optimization: Theory, Computation, and Application, Ralph E. Steuer (Ed.). Wiley, Palo Alto, CA (1986) , 1987 .

[10]  A. Farhang-Mehr,et al.  Diversity assessment of Pareto optimal solution sets: an entropy approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[11]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

[12]  D. Corne,et al.  On Metrics for Comparing Non Dominated Sets , 2001 .

[13]  Jason R. Schott.  Fault Tolerant Design Using Single and Multicriteria Genetic Algorithm Optimization. , 1995 .

[14]  Ralph E. Steuer.  Multiple criteria optimization , 1986 .

[15]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[16]  Joshua D. Knowles,et al.  On metrics for comparing nondominated sets , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).