R-HV: A Metric for Computing Hyper-volume for Reference Point Based EMOs

For evaluating performance of a multi-objective optimization for finding the entire efficient front, a number of metrics, such as hyper-volume, inverse generational distance, etc. exists. However, for evaluating an EMO algorithm for finding a subset of the efficient frontier, the existing metrics are inadequate. There does not exist many performance metrics for evaluating a partial preferred efficient set. In this paper, we suggest a metric which can be used for such purposes for both attainable and unattainable reference points. Results on a number of two-objective problems reveal its working principle and its importance in assessing different algorithms. The results are promising and encouraging for its further use.

[1]  Nicola Beume,et al.  On the Complexity of Computing the Hypervolume Indicator , 2009, IEEE Transactions on Evolutionary Computation.

[2]  Kalyanmoy Deb,et al.  Light beam search based multi-objective optimization using evolutionary algorithms , 2007, 2007 IEEE Congress on Evolutionary Computation.

[3]  Carlos M. Fonseca,et al.  An Improved Dimension-Sweep Algorithm for the Hypervolume Indicator , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[4]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[5]  Kalyanmoy Deb,et al.  Faster Hypervolume-Based Search Using Monte Carlo Sampling , 2008, MCDM.

[6]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

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

[8]  Anne Auger,et al.  Theoretically Investigating Optimal µ-Distributions for the Hypervolume Indicator: First Results for Three Objectives , 2010, PPSN.

[9]  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).

[10]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[11]  Lucas Bradstreet,et al.  A Fast Incremental Hypervolume Algorithm , 2008, IEEE Transactions on Evolutionary Computation.

[12]  Martin J. Oates,et al.  The Pareto Envelope-Based Selection Algorithm for Multi-objective Optimisation , 2000, PPSN.

[13]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

[14]  Kalyanmoy Deb,et al.  Reference point based multi-objective optimization using evolutionary algorithms , 2006, GECCO '06.

[15]  Andrzej P. Wierzbicki,et al.  The Use of Reference Objectives in Multiobjective Optimization , 1979 .

[16]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[17]  Kalyanmoy Deb,et al.  Evaluating the -Domination Based Multi-Objective Evolutionary Algorithm for a Quick Computation of Pareto-Optimal Solutions , 2005, Evolutionary Computation.

[18]  R. Lyndon While,et al.  A faster algorithm for calculating hypervolume , 2006, IEEE Transactions on Evolutionary Computation.

[19]  Kalyanmoy Deb,et al.  Interactive evolutionary multi-objective optimization and decision-making using reference direction method , 2007, GECCO '07.