张冬梅 龚小胜 戴光明. 基于多重分形主曲线模型多目标演化算法研究[J]. 计算机研究与发展, 2011, 48(9): 1729-1739.
 引用本文: 张冬梅 龚小胜 戴光明. 基于多重分形主曲线模型多目标演化算法研究[J]. 计算机研究与发展, 2011, 48(9): 1729-1739.
Zhang Dongmei, Gong Xiaosheng, and Dai Guangming. Multi-Objective Evolutionary Algorithm for Principal Curve Model Based on Multifractal[J]. Journal of Computer Research and Development, 2011, 48(9): 1729-1739.
 Citation: Zhang Dongmei, Gong Xiaosheng, and Dai Guangming. Multi-Objective Evolutionary Algorithm for Principal Curve Model Based on Multifractal[J]. Journal of Computer Research and Development, 2011, 48(9): 1729-1739.

## Multi-Objective Evolutionary Algorithm for Principal Curve Model Based on Multifractal

• 摘要: 为了克服目前模型多目标演化算法多采用PCA,local PCA等线性建模方法,存在模型拟合效果不理想、对建模参数敏感等问题,提出一种基于多重分形的主曲线模型多目标演化算法(multifractal based principal curve multi-objective evolutionary algorithm, MFPC-MOEA).算法采用主曲线方法对解集分布进行非线性建模,通过建立种群个体分布概率模型,生成目标空间均匀分布的个体,保证优化结果的多样性.另外算法通过多重分形方法分析个体在解集空间中的分布,设计了基于多重分形谱的模型演化多目标算法建模开始评测标准,同时采用多重分形方法评估算法收敛程度,设计相关的演化多目标优化算法停止策略.新算法采用国际公认的ZDT,DTLZ测试函数进行实验验证,并与NSGA-II,MOEA/D,PAES,SPEA2,RM-MEDA经典演化多目标优化算法进行了实验比较.实验结果表明,该算法在HV,SPREAD,IGD,EPSILON性能指标上均有较好的表现.说明通过引入多重分形策略和主曲线建模方法,在一定程度上提高了解的质量,为求解多目标优化问题提供新的思路.

Abstract: Current model-based multi-objective evolutionary algorithms use linear modeling approach such as PCA and local PCA, which has deficiencies that the model fitting result is not satisfactory and is sensitive to modeling parameters. In this paper, a multi-objective evolutionary optimization algorithm based on multifractal principal curve (MFPC-MOEA) is proposed. The algorithm uses principal curve to build nonlinear modeling on the distribution of the solution set and to establish the probability model on the individual distribution of population, which can generate the individuals distributed evenly in the objective space and ensure the diversity of optimization results.The start and stop criteria for the algorithm modeling are two important aspects of modeling multi-objective algorithm. In this paper, we analyze the distribution of individuals in the solution space with multifractal spectrum, and design the start criteria of the modeling for the model of multi-objective evolutionary algorithm, which is used as initial conditions of model. Furthermore, multifractal approach is used for assessing the convergence degree of algorithm, in order to design a stop criteria of the multi-objective evolutionary optimization algorithm. Moreover, we adopt internationally recognized testing functions such as ZDT, DTLZ, etc, to conduct the comparison experiment with NSGA-II, MOEA/D, PAES, SPEA2, MFPC-MOEA and other classical multi-objective evolutionary optimization algorithms. The simulation results show that the proposed algorithm performs better on the performance indicators of HV, SPREAD, IGD and EPSILON, which indicates that through the introduction of multifractal modeling strategy and principal curve method, the quality of solution is improved in a certain extent. A new idea to solve multi-objective optimization problems (MOPs) is provided.

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈