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

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.