基于密度聚类的多目标粒子群优化算法
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摘要
提出了一种基于密度聚类的领导粒子选择策略的多目标粒子群优化算法。首先,将粒子进行分类;然后,对外部档案采用改进的循环拥挤距离排序,并将高斯变异引入到进化种群,在保持具有全局搜索能力的同时,也避免了陷入局部最优。对WFG系列测试函数的仿真结果表明,与经典多目标优化算法相比,本文算法在解的收敛性和多样性等方面有显著的提升。
Aiming at the leader particle selection problem, we present a multi-objective particle swarm optimization algorithm based on density clustering, termed as DN-MOPSO. Firstly, the particles composed of evolutionary population and external archive are divided into several classes by using density clustering technique in decision variable space. And then, the particles in the evolutionary population select their respective global leader particles according to the classification results so as to achieve the balance between global search capabilities and local search capabilities. Moreover, when the non-dominated solutions exceed the maximum limit, the improved circular crowed distance will be utilized to sort the external archive so that the obtained solution set can be well the distributed.In addition, the Gauss mutation operator mechanism is introduced into the iterative process to ensure the proposed algorithm jumping out of premature and promote the search capacities. Finally, the proposed DN-MOPSO algorithm is tested on several WFG benchmarks functions and compared with some classic multi-objective optimization algorithms.Simulation results show that DN-MOPSO algorithm can achieve better approximation to the optimal Pareto front and get well-spread Pareto solutions. Moreover, this strategy in this paper can not only enlarge the search scope of the DNMOPSO algorithm, but also improve the search accuracy, meanwhile, maintain the diversity of non-dominated solution.Therefore, the convergence and diversity of the solutions obtained by DN-MOPSO algorithm are significantly improved. These simulation results also indicate that DN-MOPSO algorithm is highly feasible and competitive for solving multi-objective optimization problems.
Aiming at the leader particle selection problem, we present a multi-objective particle swarm optimization algorithm based on density clustering, termed as DN-MOPSO. Firstly, the particles composed of evolutionary population and external archive are divided into several classes by using density clustering technique in decision variable space. And then, the particles in the evolutionary population select their respective global leader particles according to the classification results so as to achieve the balance between global search capabilities and local search capabilities. Moreover, when the non-dominated solutions exceed the maximum limit, the improved circular crowed distance will be utilized to sort the external archive so that the obtained solution set can be well the distributed.In addition, the Gauss mutation operator mechanism is introduced into the iterative process to ensure the proposed algorithm jumping out of premature and promote the search capacities. Finally, the proposed DN-MOPSO algorithm is tested on several WFG benchmarks functions and compared with some classic multi-objective optimization algorithms.Simulation results show that DN-MOPSO algorithm can achieve better approximation to the optimal Pareto front and get well-spread Pareto solutions. Moreover, this strategy in this paper can not only enlarge the search scope of the DNMOPSO algorithm, but also improve the search accuracy, meanwhile, maintain the diversity of non-dominated solution.Therefore, the convergence and diversity of the solutions obtained by DN-MOPSO algorithm are significantly improved. These simulation results also indicate that DN-MOPSO algorithm is highly feasible and competitive for solving multi-objective optimization problems.
引文
[1]KENNEDY J,EBERHART R.Particle swarm optimization[C]//IEEE International Conference on Neural Networks.USA:IEEE,2002:1942-1948.
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[14]KNOWLES J,CORNE D.On metrics for comparing nondominated sets[C]//Proceedings of the 2002 Congress on Evolutionary Computation.USA:IEEE,2002:711-716.
[15]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.
[16]汤彬,王学武,薛立卡,等.双焊接机器人避障路径规划[J].华东理工大学学报(自然科学版),2017,43(3):417-424.
[2]COELLO C A C,LECHUGA M S.MOPSO:A proposal for multiple objective particle swarm optimization[C]//Proceedings of the 2002 Congress on Evolutionary Computation.USA:IEEE,2002:1051-1056.
[3]ZITZLER E,DEB K,THIELE L.Comparison of multiobjective evolutionary algorithms:Empirical results[J].Evolutionary Computation,2014,8(2):173-195.
[4]TRIPATHI P K,BANDYOPADHYAY S,PAL S K.Multiobjective particle swarm optimization with time variant inertia and acceleration coefficients[J].Information Sciences,2007,177(22):5033-5049.
[5]PULIDO G T,COELLO C A C.Using clustering techniques to improve the performance of a multi-objective particle swarm optimizer[C]//Genetic and Evolutionary Computation.Berlin Heidelberg:Springer,2004:225-237.
[6]PENG G,FANG Y,CHAI D,et al.Multi-objective particle swarm optimization algorithm based on sharing-learning and Cauchy mutation[C]//Control Conference.USA:IEEE,2016:9155-9160.
[7]王学武,薛立卡,顾幸生.三态协调搜索多目标粒子群优化算法[J].控制与决策,2015,30(11):1945-1952.
[8]TSAI C F,YAO C.Enhancement of data clustering using TSS-DBSCAN approach for data mining[C]//International Conference on Machine Learning and Cybernetics.USA:IEEE,2017:535-540.
[9]罗辞勇,陈民铀,张聪誉,等.采用循环拥挤排序策略的改进NSGA-Ⅱ算法[J].控制与决策,2010,25(2):227-231.
[10]SAHA D,BANERJEE S,JANA N D.Multi-objective particle swarm optimization based on adaptive mutation[C]//Third International Conference on Computer,Communication,Control and Information Technology.USA:IEEE,2015:1-5.
[11]ZHANG Q,LI H.MOEA/D:A multiobjective evolutionary algorithm based on decomposition[J].IEEE Transactions on Evolutionary Computation,2007,11(6):712-731.
[12]DEB K,PRATAP A,AGARWAL S,et al.A fast and elitist multiobjective genetic algorithm:NSGA-Ⅱ[J].IEEETransactions on Evolutionary Computation,2002,6(2):182-197.
[13]ZITZLER E,THIELE L,LAUMANNS M,et al.Performance assessment of multi-objective optimizers:An analysis and review[J].IEEE Transactions on Evolutionary Computation,2003,7(2):117-132.
[14]KNOWLES J,CORNE D.On metrics for comparing nondominated sets[C]//Proceedings of the 2002 Congress on Evolutionary Computation.USA:IEEE,2002:711-716.
[15]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.
[16]汤彬,王学武,薛立卡,等.双焊接机器人避障路径规划[J].华东理工大学学报(自然科学版),2017,43(3):417-424.