Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Nondominated sorting (NDS), which divides a population into several nondomination levels (NDLs), is a basic step in many evolutionary multiobjective optimization (EMO) algorithms. It has been widely studied in a generational evolution model, where the environmental selection is performed after generating a whole population of offspring. However, in a steady-state evolution model, where a population is updated right after the generation of a new candidate, the NDS can be extremely time consuming. This is especially severe when the number of objectives and population size become large. In this paper, we propose an efficient NDL update method to reduce the cost for maintaining the NDL structure in steady-state EMO. Instead of performing the NDS from scratch, our method only updates the NDLs of a limited number of solutions by extracting the knowledge from the current NDL structure. Notice that our NDL update method is performed twice at each iteration. One is after the reproduction, the other is after the environmental selection. Extensive experiments fully demonstrate that, comparing to the other five state-of-the-art NDS methods, our proposed method avoids a significant amount of unnecessary comparisons, not only in the synthetic data sets, but also in some real optimization scenarios. Last but not least, we find that our proposed method is also useful for the generational evolution model.

[1]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints , 2014, IEEE Transactions on Evolutionary Computation.

[2]  Maxim Buzdalov,et al.  Fast Implementation of the Steady-State NSGA-II Algorithm for Two Dimensions Based on Incremental Non-Dominated Sorting , 2015, GECCO.

[3]  Jinhua Zheng,et al.  Achieving balance between proximity and diversity in multi-objective evolutionary algorithm , 2012, Inf. Sci..

[4]  Ye Tian,et al.  An Efficient Approach to Nondominated Sorting for Evolutionary Multiobjective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[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]  Maxim Buzdalov,et al.  Various Degrees of Steadiness in NSGA-II and Their Influence on the Quality of Results , 2015, GECCO.

[7]  Nikhil R. Pal,et al.  ASMiGA: An Archive-Based Steady-State Micro Genetic Algorithm , 2015, IEEE Transactions on Cybernetics.

[8]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[9]  Qingfu Zhang,et al.  Decomposition-Based Multiobjective Evolutionary Algorithm With an Ensemble of Neighborhood Sizes , 2012, IEEE Transactions on Evolutionary Computation.

[10]  Antonio J. Nebro,et al.  jMetal: A Java framework for multi-objective optimization , 2011, Adv. Eng. Softw..

[11]  Eckart Zitzler,et al.  HypE: An Algorithm for Fast Hypervolume-Based Many-Objective Optimization , 2011, Evolutionary Computation.

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

[13]  Eckart Zitzler,et al.  Indicator-Based Selection in Multiobjective Search , 2004, PPSN.

[14]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

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

[16]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[17]  Antonio J. Nebro,et al.  On the Effect of Applying a Steady-State Selection Scheme in the Multi-Objective Genetic Algorithm NSGA-II , 2009, Nature-Inspired Algorithms for Optimisation.

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

[19]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[20]  Kim-Fung Man,et al.  Learning paradigm based on jumping genes: A general framework for enhancing exploration in evolutionary multiobjective optimization , 2013, Inf. Sci..

[21]  Kent McClymont,et al.  Deductive Sort and Climbing Sort: New Methods for Non-Dominated Sorting , 2012, Evolutionary Computation.

[22]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[23]  Jon Louis Bentley,et al.  Multidimensional binary search trees used for associative searching , 1975, CACM.

[24]  Nikhil R. Pal,et al.  A Multiobjective Genetic Programming-Based Ensemble for Simultaneous Feature Selection and Classification , 2016, IEEE Transactions on Cybernetics.

[25]  Xin Yao,et al.  Corner Sort for Pareto-Based Many-Objective Optimization , 2014, IEEE Transactions on Cybernetics.

[26]  Hisao Ishibuchi,et al.  Evolutionary many-objective optimization: A short review , 2008, 2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence).

[27]  Qingfu Zhang,et al.  Adaptive Operator Selection With Bandits for a Multiobjective Evolutionary Algorithm Based on Decomposition , 2014, IEEE Transactions on Evolutionary Computation.

[28]  Qingfu Zhang,et al.  An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition , 2015, IEEE Transactions on Evolutionary Computation.

[29]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

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

[31]  Enrique Alba,et al.  On the Effect of the Steady-State Selection Scheme in Multi-Objective Genetic Algorithms , 2009, EMO.

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

[33]  Kalyanmoy Deb,et al.  A dual-population paradigm for evolutionary multiobjective optimization , 2015, Inf. Sci..