Improving the efficiency of ϵ-dominance based grids

In this paper, we deal with the problem of handling solutions in an external archive with the use of a relaxed form of Pareto dominance called @e-dominance and a variation of it called pa@e-dominance. These two relaxed forms of Pareto dominance have been used as archiving strategies in some multi-objective evolutionary algorithms (MOEAs). The main objective of this work is to improve the @e-dominance based schemes to handle nondominated solutions, or to retain nondominated solutions in an external archive. Thus, our main contribution is to add an extra objective function only at the time of accepting a nondominated solution into the external archive, in order to preserve some solutions which are normally lost when using any of the aforementioned relaxed forms of Pareto dominance. Such a proposal is inexpensive (computationally speaking) and quite effective, since it is able to produce Pareto fronts of much better quality than the aforementioned archiving techniques.

[1]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

[2]  Martin J. Oates,et al.  PESA-II: region-based selection in evolutionary multiobjective optimization , 2001 .

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

[4]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

[5]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

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

[7]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

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

[9]  Wenyin Gong,et al.  An improved multiobjective differential evolution based on Pareto-adaptive epsilon-dominance and orthogonal design , 2009, Eur. J. Oper. Res..

[10]  Jan Golinski,et al.  Optimal synthesis problems solved by means of nonlinear programming and random methods , 1970 .

[11]  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).

[12]  Daniel Merkle,et al.  A New Multi-objective Particle Swarm Optimization Algorithm Using Clustering Applied to Automated Docking , 2005, Hybrid Metaheuristics.

[13]  K. M. Ragsdell,et al.  Optimal Design of a Class of Welded Structures Using Geometric Programming , 1976 .

[14]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[15]  Carlos A. Coello Coello,et al.  A Short Tutorial on Evolutionary Multiobjective Optimization , 2001, EMO.

[16]  Carlos A. Coello Coello,et al.  DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems , 2010, Comput. Oper. Res..

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

[18]  H. Kita,et al.  Failure of Pareto-based MOEAs: does non-dominated really mean near to optimal? , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[19]  Carlos A. Coello Coello,et al.  Pareto-adaptive -dominance , 2007, Evolutionary Computation.

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

[21]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[22]  Prospero C. Naval,et al.  An effective use of crowding distance in multiobjective particle swarm optimization , 2005, GECCO '05.

[23]  David W. Corne,et al.  Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy , 2000, Evolutionary Computation.

[24]  Carlos A. Coello Coello,et al.  Handling multiple objectives with particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[25]  Joel N. Morse,et al.  Reducing the size of the nondominated set: Pruning by clustering , 1980, Comput. Oper. Res..

[26]  Jürgen Branke,et al.  Empirical comparison of MOPSO methods - Guide selection and diversity preservation - , 2009, 2009 IEEE Congress on Evolutionary Computation.

[27]  Ponnuthurai N. Suganthan,et al.  Multi-objective evolutionary algorithms based on the summation of normalized objectives and diversified selection , 2010, Inf. Sci..

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

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

[30]  Ponnuthurai N. Suganthan,et al.  Multi-objective evolutionary programming without non-domination sorting is up to twenty times faster , 2009, 2009 IEEE Congress on Evolutionary Computation.