An Spanning Tree based method for pruning non-dominated solutions in multi-objective optimization problems

Diversity maintenance of solutions is a crucial part in multi-objective optimization. However, most of existing studies show a good distribution with a large computational load or a comparative bad distribution quickly. In this paper, a method for pruning a set of non-dominated solutions using a Spanning Tree is proposed. This approach defines a density estimation metric — Spanning Tree Crowding Distance (STCD). Moreover, information of degree of solution combined with STCD is employed to truncate the population. From an extensive comparative study with three other methods on a number of 2, 3 and 4 objective test problems, the proposed method indicates a good balance among uniformity, spread and execution time.

[1]  Jinhua Zheng,et al.  An efficient mufti-objective evolutionary algorithm based on Minimum Spanning Tree , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[2]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[3]  Liaquat Hossain,et al.  An efficient multiobjective evolutionary algorithm for community detection in social networks , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

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

[5]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

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

[7]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

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

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

[10]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

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

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

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

[14]  Carlos A. Coello Coello,et al.  A Micro-Genetic Algorithm for Multiobjective Optimization , 2001, EMO.

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

[16]  Jinhua Zheng,et al.  Strategies based on polar coordinates to keep diversity in multi-objective genetic algorithm , 2005, 2005 IEEE Congress on Evolutionary Computation.

[17]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[18]  Jinhua Zheng,et al.  Spread Assessment for Evolutionary Multi-Objective Optimization , 2009, EMO.

[19]  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.

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

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

[22]  David A. Van Veldhuizen,et al.  Evolutionary Computation and Convergence to a Pareto Front , 1998 .

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

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