How well do multi-objective evolutionary algorithms scale to large problems

In spite of large amount of research work in multi- objective evolutionary algorithms, most have evaluated their algorithms on problems with only two to four objectives. Little has been done to understand the performance of the multi- objective evolutionary algorithms on problems with a larger number of objectives. It is unclear whether the conclusions drawn from the experiments on problems with a small number of objectives could be generalised to those with a large number of objectives. In fact, some of our preliminary work [1] has indicated that such generalisation may not be possible. This paper first presents a comprehensive set of experimental studies, which show that the performance of multi-objective evolutionary algorithms, such as NSGA-II and SPEA2, deteriorates substantially as the number of objectives increases. NSGA-II, for example, did not even converge for problems with six or more objectives. This paper analyses why this happens and proposes several new methods to improve the convergence of NSGA-II for problems with a large number of objectives. The proposed methods categorise members of an archive into small groups (non-dominated solutions with or without domination), using dominance relationship between the new and existing members in the archive. New removal strategies are introduced. Our experimental results show that the proposed methods clearly outperform NSGA-II in terms of convergence.

[1]  Kalyanmoy Deb,et al.  Real-coded Genetic Algorithms with Simulated Binary Crossover: Studies on Multimodal and Multiobjective Problems , 1995, Complex Syst..

[2]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

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

[4]  J. Periaux,et al.  Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems , 2001 .

[5]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[6]  M. Farina,et al.  On the optimal solution definition for many-criteria optimization problems , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[7]  Kalyanmoy Deb,et al.  Running performance metrics for evolutionary multi-objective optimizations , 2002 .

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

[9]  E. Hughes Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[10]  Peter J. Fleming,et al.  Evolutionary many-objective optimisation: an exploratory analysis , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Marco Farina,et al.  Fuzzy Optimality and Evolutionary Multiobjective Optimization , 2003, EMO.

[12]  Xin Yao,et al.  Performance Scaling of Multi-objective Evolutionary Algorithms , 2003, EMO.

[13]  Peter J. Fleming,et al.  Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation , 2003, EMO.

[14]  M. Koppen,et al.  A fuzzy scheme for the ranking of multivariate data and its application , 2004, IEEE Annual Meeting of the Fuzzy Information, 2004. Processing NAFIPS '04..

[15]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[16]  U. Aickelin,et al.  The Application of Bayesian Optimization and Classifier Systems in Nurse Scheduling , 2004, PPSN.

[17]  Marco Farina,et al.  A fuzzy definition of "optimality" for many-criteria optimization problems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

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

[19]  Nicola Beume,et al.  Multi-objective optimisation using S-metric selection: application to three-dimensional solution spaces , 2005, 2005 IEEE Congress on Evolutionary Computation.

[20]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[21]  Mario Köppen,et al.  Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization , 2005, EMO.

[22]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[23]  Evan J. Hughes,et al.  Evolutionary many-objective optimisation: many once or one many? , 2005, 2005 IEEE Congress on Evolutionary Computation.

[24]  Nicola Beume,et al.  Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization , 2007, EMO.

[25]  Kalyanmoy Deb,et al.  A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems , 2006, PPSN.

[26]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.

[27]  Xin Yao,et al.  A New Multi-objective Evolutionary Optimisation Algorithm: The Two-Archive Algorithm , 2006, 2006 International Conference on Computational Intelligence and Security.

[28]  Soon-Thiam Khu,et al.  An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization , 2007, IEEE Transactions on Evolutionary Computation.

[29]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .