Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems

In this paper an algorithm for pruning a set of non-dominated solutions is proposed. The algorithm is based on the crowding distance calculation used in the elitist non-dominated sorting genetic algorithm (NSGA-II). The time complexity class of the new algorithm is estimated and in most cases it is the same as for the original pruning algorithm. Numerical results also support this estimate. For used bi-objective test problems, the proposed pruning algorithm is demonstrated to provide better distribution compared to the original pruning algorithm of NSGA-II. However, with tri-objective test problems there is no improvement and this study reveals that crowding distance does not estimate crowdedness well in this case and presumably also in cases of more objectives.

[1]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

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

[3]  N. Madavan Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[5]  Mikkel T. Jensen,et al.  Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms , 2003, IEEE Trans. Evol. Comput..

[6]  David E. Goldberg,et al.  Dynamic Uniform Scaling for Multiobjective Genetic Algorithms , 2004, GECCO.

[7]  Lishan Kang,et al.  A High Performance Multi-objective Evolutionary Algorithm Based on the Principles of Thermodynamics , 2004, PPSN.

[8]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[9]  Kittipong Boonlong,et al.  Multi-objective Optimisation by Co-operative Co-evolution , 2004, PPSN.

[10]  Jouni Lampinen,et al.  An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints , 2004, PPSN.

[11]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[13]  Graham Kendall,et al.  Handling diversity in evolutionary multiobjective optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[14]  David E. Goldberg,et al.  Limits of scalability of multiobjective estimation of distribution algorithms , 2005, 2005 IEEE Congress on Evolutionary Computation.

[15]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[16]  Kiyoshi Tanaka,et al.  Selection, Drift, Recombination, and Mutation in Multiobjective Evolutionary Algorithms on Scalable MNK-Landscapes , 2005, EMO.

[17]  Kiyoshi Tanaka,et al.  On the locality of dominance and recombination in multiobjective evolutionary algorithms , 2005, 2005 IEEE Congress on Evolutionary Computation.

[18]  Carlos A. Coello Coello,et al.  Improving PSO-Based Multi-objective Optimization Using Crowding, Mutation and epsilon-Dominance , 2005, EMO.

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

[20]  C. Coello,et al.  Improving PSO-based Multi-Objective Optimization using Crowding , Mutation and �-Dominance , 2005 .

[21]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

[22]  Victor J. Rayward-Smith,et al.  Developments on a Multi-objective Metaheuristic (MOMH) Algorithm for Finding Interesting Sets of Classification Rules , 2005, EMO.

[23]  J. Sampson selection , 2006, Algorithm Design with Haskell.

[24]  Kalyanmoy Deb,et al.  Evolutionary multiobjective optimization , 2007, GECCO '07.