A Decomposition Method Based on Random Objective Division for MOEA/D in Many-Objective Optimization

With the number increase of optimization objectives, the selection pressure begins to decrease, and the performance of multi-objective evolutionary algorithms becomes gradually inefficient. A decomposition method based on random objective division (ROD) is proposed in this paper for MOEA/D optimizing many-objective problems. We abbreviate MOEA/D using ROD decomposition as MOEA/D-ROD for easy expression. MOEA/D-ROD adopts a random objective partitioning method transforming a many-objective problem into multiple multi-objective problems. Furthermore, each multi-objective problem utilizes the assigned decomposition method to transform itself into multiple single-objective optimization problems for collaborative optimization. Therefore, different decomposition methods can be combined at the same time to balance diversity and convergence of the algorithm. Three sets of experiments are carried out on two sets of scalable problems DTLZ 1 - 4 and WFG 1 - 9, with the number of objectives from 3-8, 10 and 15. The experimental results verify the effectiveness of the proposed ROD decomposition method in solving those many-objective optimization problems.

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

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

[3]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[4]  Ye Tian,et al.  A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

[5]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[6]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[7]  Ying Tan,et al.  A New Selection Strategy for Decomposition-based Evolutionary Many-Objective Optimization , 2019, 2019 IEEE Congress on Evolutionary Computation (CEC).

[8]  Quan-Ke Pan,et al.  Hybrid Artificial Bee Colony Algorithm for a Parallel Batching Distributed Flow-Shop Problem With Deteriorating Jobs , 2020, IEEE Transactions on Cybernetics.

[9]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[10]  Kay Chen Tan,et al.  Decomposition based dominance relationship for evolutionary many-objective algorithm , 2017, 2017 IEEE Symposium Series on Computational Intelligence (SSCI).

[11]  Xin Yao,et al.  Stochastic Ranking Algorithm for Many-Objective Optimization Based on Multiple Indicators , 2016, IEEE Transactions on Evolutionary Computation.

[12]  Yuren Zhou,et al.  A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[13]  Carlos A. Coello Coello,et al.  Using the Averaged Hausdorff Distance as a Performance Measure in Evolutionary Multiobjective Optimization , 2012, IEEE Transactions on Evolutionary Computation.

[14]  Hai-Lin Liu,et al.  An Evolutionary Multi- and Many-Objective Optimization Algorithm Based on ISDE + and Region Decomposition , 2018, 2018 14th International Conference on Computational Intelligence and Security (CIS).

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

[16]  Heike Trautmann,et al.  On the properties of the R2 indicator , 2012, GECCO '12.

[17]  Xin Liu,et al.  A Distributed Parallel Cooperative Coevolutionary Multiobjective Evolutionary Algorithm for Large-Scale Optimization , 2017, IEEE Transactions on Industrial Informatics.

[18]  Hong Liu,et al.  An Enhanced Multi-objective Group Search Optimizer Based on Multi-producer and Crossover Operator , 2017, J. Inf. Sci. Eng..

[19]  Hong Liu,et al.  A study on a cooperative character modeling based on an improved NSGA II , 2015, Multimedia Tools and Applications.

[20]  Dipti Srinivasan,et al.  A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition , 2017, IEEE Transactions on Evolutionary Computation.

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

[22]  Hong Liu,et al.  Crowd evacuation simulation approach based on navigation knowledge and two-layer control mechanism , 2018, Inf. Sci..

[23]  Andries Petrus Engelbrecht,et al.  A Cooperative approach to particle swarm optimization , 2004, IEEE Transactions on Evolutionary Computation.

[24]  Jouni Lampinen,et al.  Ranking-Dominance and Many-Objective Optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[25]  Hong Li,et al.  MOEA/D + uniform design: A new version of MOEA/D for optimization problems with many objectives , 2013, Comput. Oper. Res..

[26]  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.

[27]  Carlos A. Coello Coello,et al.  A new multi-objective evolutionary algorithm based on a performance assessment indicator , 2012, GECCO.

[28]  Jun-qing Li,et al.  A hybrid multi-objective artificial bee colony algorithm for flexible task scheduling problems in cloud computing system , 2019, Cluster Computing.

[29]  Nicola Beume,et al.  An EMO Algorithm Using the Hypervolume Measure as Selection Criterion , 2005, EMO.

[30]  Tobias Friedrich,et al.  Approximating the volume of unions and intersections of high-dimensional geometric objects , 2008, Comput. Geom..

[31]  Bo Zhang,et al.  Balancing Convergence and Diversity in Decomposition-Based Many-Objective Optimizers , 2016, IEEE Transactions on Evolutionary Computation.

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

[33]  Hong Liu,et al.  A path planning approach for crowd evacuation in buildings based on improved artificial bee colony algorithm , 2018, Appl. Soft Comput..

[34]  Athanasios V. Vasilakos,et al.  Vector coevolving particle swarm optimization algorithm , 2017, Inf. Sci..

[35]  Qingfu Zhang,et al.  An evolutionary many-objective optimisation algorithm with adaptive region decomposition , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[36]  Shengxiang Yang,et al.  Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization , 2014, IEEE Transactions on Evolutionary Computation.

[37]  Slim Bechikh,et al.  A New Decomposition-Based NSGA-II for Many-Objective Optimization , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[38]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[39]  Jing Sun,et al.  Interval Multiobjective Optimization With Memetic Algorithms , 2020, IEEE Transactions on Cybernetics.

[40]  Yuren Zhou,et al.  Evolutionary Many-Objective Optimization Based on Dynamical Decomposition , 2019, IEEE Transactions on Evolutionary Computation.

[41]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[42]  Carlos A. Coello Coello,et al.  Improved Metaheuristic Based on the R2 Indicator for Many-Objective Optimization , 2015, GECCO.

[43]  Shengxiang Yang,et al.  A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[44]  Tapabrata Ray,et al.  A Decomposition-Based Evolutionary Algorithm for Many Objective Optimization , 2015, IEEE Transactions on Evolutionary Computation.

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

[46]  Qingfu Zhang,et al.  Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems , 2014, IEEE Transactions on Evolutionary Computation.

[47]  Yaochu Jin,et al.  A Many-Objective Evolutionary Algorithm Using A One-by-One Selection Strategy , 2017, IEEE Transactions on Cybernetics.

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

[49]  Xin Liu,et al.  3-D Multiobjective Deployment of an Industrial Wireless Sensor Network for Maritime Applications Utilizing a Distributed Parallel Algorithm , 2018, IEEE Transactions on Industrial Informatics.

[50]  Qingfu Zhang,et al.  Evolutionary Many-Objective Optimization Based on Adversarial Decomposition , 2017, IEEE Transactions on Cybernetics.

[51]  Peng Duan,et al.  Efficient multi-objective algorithm for the lot-streaming hybrid flowshop with variable sub-lots , 2020, Swarm Evol. Comput..

[52]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[53]  G. Rudolph.  Evolutionary Search under Partially Ordered Fitness Sets , 2001 .

[54]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[55]  Shengxiang Yang,et al.  Bi-goal evolution for many-objective optimization problems , 2015, Artif. Intell..

[56]  Xin Liu,et al.  Multiobjective recommendation optimization via utilizing distributed parallel algorithm , 2018, Future Gener. Comput. Syst..

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

[58]  Qingfu Zhang,et al.  Matching-Based Selection With Incomplete Lists for Decomposition Multiobjective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[59]  Aimin Zhou,et al.  Preselection via Classification: A Case Study on Evolutionary Multiobjective Optimization , 2017, Inf. Sci..

[60]  Hisao Ishibuchi,et al.  Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems , 2013, EMO.