On scalability of Adaptive Weighted Aggregation for multiobjective function optimization

In our previous study, we have proposed Adaptive Weighted Aggregation (AWA), a framework of multi-starting optimization methods based on scalarization for solving multi-objective function optimization problems. The experiments in the proposal show that AWA outperforms conventional multi-starting descent methods at coverage of solutions. However, the suitable termination condition for AWA has not been understood. Coverage of AWA's solutions and computational cost of AWA strongly depends on the termination condition. In this paper, we derive the necessary and sufficient iteration count to achieve high coverage and the number of approximate solutions generated until AWA stops. Numerical experiments show that AWA still achieves better coverage than the conventional methods under the derived termination condition.

[1]  Claus Hillermeier,et al.  Nonlinear Multiobjective Optimization , 2001 .

[2]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[3]  Shigenobu Kobayashi,et al.  Hybridization of genetic algorithm and local search in multiobjective function optimization: recommendation of GA then LS , 2006, GECCO '06.

[4]  Peter A. N. Bosman,et al.  Exploiting gradient information in numerical multi--objective evolutionary optimization , 2005, GECCO '05.

[5]  Isao Ono,et al.  Local Search for Multiobjective Function Optimization: Pareto Descent Method , 2006 .

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

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

[8]  Gabriele Eichfelder,et al.  Adaptive Scalarization Methods in Multiobjective Optimization , 2008, Vector Optimization.

[9]  C. Hillermeier.  Nonlinear Multiobjective Optimization: A Generalized Homotopy Approach , 2001 .

[10]  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).

[11]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[12]  Naoki Hamada,et al.  Functional-Specialization Multi-Objective Real-Coded Genetic Algorithm: FS-MOGA , 2008, PPSN.

[13]  Naoki Hamada,et al.  Adaptive weighted aggregation: A multiobjective function optimization framework taking account of spread and evenness of approximate solutions , 2010, IEEE Congress on Evolutionary Computation.