An Algorithm for Finding Non-dominated Set Based on Two-Dimension Sorting

The complexity of multi-objective evolutionary algorithms based on the non-dominated principles mainly depends on finding non-dominated fronts. In order to reduce complexity and improve construction efficiency, this paper introduces a non-dominated set construction algorithm based on Two Dimensional Sequence (TSNS). When the non-dominated set closes to the Pareto optimal front, it always maintains one dimension by ascending order while the other dimension by descending order. In order to verify the effectiveness of the proposed algorithm, we integrate the algorithm into GA, DE, PSO, then we tested and compared it with classical benchmark functions. The experimental results indicate that the proposed algorithm performs better than NSGA-II in terms of the quality of solutions and the speed of convergence.

[1]  Jin-Hua Zheng,et al.  An Indicator for Assessing the Spread of Solutions in Multi-Objective Evolutionary Algorithm: An Indicator for Assessing the Spread of Solutions in Multi-Objective Evolutionary Algorithm , 2011 .

[2]  Kalyanmoy Deb,et al.  Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[3]  Rolf Drechsler,et al.  Multi-Objective BDD Optimization with Evolutionary Algorithms , 2015, GECCO.

[4]  Peter J. Fleming,et al.  Methods for multi-objective optimization: An analysis , 2015, Inf. Sci..

[5]  Hui Li,et al.  Non-dominated sorting genetic algorithm with decomposition to solve constrained optimisation problems , 2013, Int. J. Bio Inspired Comput..

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

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

[8]  Carlos A. Brizuela,et al.  A survey on multi-objective evolutionary algorithms for many-objective problems , 2014, Computational Optimization and Applications.

[9]  Fang Liu,et al.  Memetic Immune Algorithm for Multiobjective Optimization: Memetic Immune Algorithm for Multiobjective Optimization , 2014 .

[10]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[11]  Zeng Wen.  A Fast Bi-Objective Non-Dominated Sorting Algorithm , 2011 .

[12]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[14]  Dieter Hogrefe,et al.  Multi-objective ant colony optimisation-based routing in WSNs , 2014, Int. J. Bio Inspired Comput..

[15]  Zhou Cao-che.  Survey of Many-objective Optimization Algorithms , 2014 .

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

[17]  Kiyoshi Tanaka,et al.  Attempt to reduce the computational complexity in multi-objective differential evolution algorithms , 2013, GECCO '13.