1. College of Artificial Intelligence, Key Lab of Intelligent Data Information Processing & Control of Hebei Province,
Tangshan University, Tangshan, Hebei 063000, China
2. Yanshan University, Qinhuangdao, Hebei 066004, China
3. Kailuan General Hospital, Tangshan, Hebei 063000, China
4. Tangshan Normal University, Tangshan, Hebei 063000, China
Abstract：To solve the problem that the particle swarm optimization algorithm is easy to fall into the local optimum.A multi-objective optimization algorithm based on the combination of particle swarm optimization and clustering method is proposed.The algorithm is based on the method of reference vector decomposition, and the global optimal solution is updated through the clustering optimization particle strategy.First, the particles are clustered by each uniformly distributed reference vector to promote the diversity of particles. A particle with the smallest aggregation function fitness value is selected from each cluster in order to balance convergence and diversity.The global optimal solution and the individual optimal solution are dynamically updated, and the population is guided to be evenly distributed near the Pareto front.It is compared with the four particle swarm multi-objective optimization algorithms through simulation experiments.Experimental results show that the proposed algorithm obtains 20 IGD optimal values on 27 selected benchmark problems.
Yang J M, Hao J J, Sun H, et al. A Many-objective Evolutionary Algorithm Based on Knee Point and Region Division［J］. Acta Metrologica Sinica, 2021, 42 (8):1068-1075.
［2］
Tian Y, Liu R C, Zhang X Y, et al. A Multipopulation Evolutionary Algorithm for Solving Large-Scale Multimodal Multiobjective Optimization Problems［J］. IEEE Transactions on Evolutionary Computation, 2021, 25 (3):405-418.
Zhao Z W, Hou H Y, Wang W Z, et al. Many-objective Load Distribution for Cold Rolling Based on Reference Point and Differential Mutation Strategy［J］. Acta Metrologica Sinica, 2017, 38 (6): 730-734.
［5］
Wang Z J, Zhan Z H, Kwong S, et al. Adaptive Granularity Learning Distributed Particle Swarm Optimization for Large-Scale Optimization［J］. Ieee Transactions on Cybernetics, 2021, 51 (3): 1175-1188.
Zhao Z W, Liu Y, Xiong Z J, et al. Many-objective Evolutionary Algorithm Based on Multi-subpopulation and Density Estimation for Load Distribution of Cold Rolling ［J］. Acta Metrologica Sinica, 2022, 43(1):65-71.
Nguyen B H, Xue B, Andreae P, et al. A New Binary Particle Swarm Optimization Approach: Momentum and Dynamic Balance Between Exploration and Exploitation［J］. IEEE Transactions on Cybernetics, 2021, 51(2): 589-603.
［11］
Kamel M A, Yu X, Zhang Y M. Real-Time Fault-Tolerant Formation Control of Multiple WMRs Based on Hybrid GA-PSO Algorithm［J］. IEEE Transactions on Automation Science and Engineering, 2021, 18(3):1263-1276.
［13］
Li L, Chang L, Gu T L, Sheng W, et al. On the Norm of Dominant Difference for Many-Objective Particle Swarm Optimization［J］. IEEE Transactions on Cybernetics, 2021, 51(4):2055-2067.
［14］
Deb K, Jain H. An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints ［J］. IEEE Transactions on Evolutionary Computation, 2014, 18(4):577-601.
［4］
Qin S F, Sun C L, Jin Y C, et al. Large-Scale Evolutionary Multiobjective Optimization Assisted by Directed Sampling［J］. IEEE Transactions on Evolutionary Computation, 2021, 25(4):724-738.
［7］
Zhan D W, Xing H L. A Fast Kriging-Assisted Evolutionary Algorithm Based on Incremental Learning［J］. IEEE Transactions on Evolutionary Computation, 2021, 25 (5):941-955.
［12］
Liu W B, Wang Z D, Yuan Y, et al. A Novel Sigmoid-Function-Based Adaptive Weighted Particle Swarm Optimizer［J］. IEEE Transactions on Cybernetics, 2021, 51(2):1085-1093.
［16］
Deb K, Goyal M. A Combined Genetic Adaptive Search (GeneAS) for Engineering Design ［J］. Journal of Computer Science and Informatics, 1996, 26(4):30-45.
［17］
Huband S, Hingston P, Barone L, et al. A review of multiobjective test problems and a scalable test problem toolkit ［J］. IEEE Transactions on Evolutionary Computation, 2006, 10(5):477-506.
［19］
Wang Z J, He G F, Du W H, et al. Application of Parameter Optimized Variational Mode Decomposition Method in Fault Diagnosis of Gearbox［J］. IEEE Access, 2019, 7:44871-44882.
［22］
Li B D, Tang K, Li J L, et al. Stochastic Ranking Algorithm for Many-Objective Optimization Based on Multiple Indicators［J］. IEEE Transactions on Evolutionary Computation, 2016, 20 (6):924-938.
Liu B, Liu Z R, Zhao Z B, et al. Research on Multi population Multi-objective Particle Swarm Optimization Algorithm Based on Velocity Communication ［J］. Acta Metrologica Sinica, 2020, 41(8):1002-1011.
［10］
Liu Y Y, Xi J L, Bai H F, et al. A General Robot Inverse Kinematics Solution Method Based on Improved PSO Algorithm［J］. IEEE Access, 2021, 9:32341-32350.
［15］
Agrawal R B, Deb K. Simulated Binary Crossover for Continuous Search Space ［J］. Complex Systems, 2000, 9(3):115-148.
［20］
Moghaddam A, Alizadeh A, Faridhosseini A, et al. Water distribution networks optimization using GA, SMPSO, and SHGAPSO algorithms based on engineering approach: a real case study［J］. Desalination and Water Treatment, 2020, 193:321-334.
［18］
Lin Q Z, Li J Q, Du Z H, et al. A novel multi-objective particle swarm optimization with multiple search strategies［J］. European Journal of Operational Research, 2015, 247(3):732-744.
［21］
Al M N, Petrovski A, Mccall J. (DMOPSO)-M-2:MOPSO Based on Decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces［J］. Evolutionary Computation, 2014, 22(1):47-77.
2023, Vol. 44 
