| Multi-objective problem is one class of problems that often encountered in scientific research and engineering applications. It typically consists of multiple conflicting sub-goals, to find the best design to meet all these goals, it is necessary to solve multi-objective and multi-constrained optimization problem, namely multi-objective optimization problem (MOPs). a solution can get one or a few goals better, other goals may be poor. Multi-objective optimization for the purpose of seeking for multi-objective optimization problem, a group of non-dominated solution set or Pareto set.Genetic Algorithm(GA) is a population evolution based on self-organizing, self-learning heuristic search algorithm. Each individual in the population are feasible solutions to optimization problems, and individual survival of the fittest in the population from generation to generation to ensure algorithm evolution towards the optimal direction. This optimization process is very much in line with the optimization problem in particular, the requirements of the multi-objective optimization problem. Especially applied to the multi-objective optimization theory, the multi-objective optimization evolution algorithm has been booming in the Pareto dominant mechanism. However, encountered in the current research work on high-dimensional multiobjective optimization problem to the slow convergence model for multi-objective optimization convergence criteria for design is far from being perfect.Designing new dominant mechanism in order to judge the merits of the relationship between individuals in the population from a view of more fair and reasonable point. Especially in solving many-dimensional multiobjective optimization problem, pressure is not enough, lead to the choice of algorithm based on Pareto dominant mechanism leading to the convergence speed is slow or even stagnation. Therefore, a new dominant mechanism in high-dimensional multiobjective optimization problems received more and more the concern of scholars. Consider individual goals to adapt to the value of size, the merits of individual number of targets, as well as decision-making preferences of the decision-makers to design a new multi-objective dominant mechanism. The dominant mechanism in the theoretical study and practical application have achieved very significant results.Multifractal is used to study the Play distribution of collection(interested in the elements, objects, individuals) or the theory of the distribution measure. Excavation work in the multifractal theory in these laws, also known as the singularity law mining. The distribution of singularity refers to the collection of field measure showing the apparent aggregation or energy in a region before the outbreak of the state. This singularity is usually multi-fractal collection of field area to be divided and separate fractal analysis to describe the characteristics of the entire data field, through the analysis of dimensions and singularity data. Multifractal approach applied to the search space singularity analysis of evolutionary multi-objective optimization algorithm will find the following law. The singularity of individual distribution, populations of individuals at some point or showing the characteristics of the manifold of a dimension, and with the depth of the algorithm to optimize the degree of non-inferior solution manifold and individual singularity exponent is basically stable. Therefore, study design multifractal method is introduced to the multi-objective optimization evolution algorithm, through the design the multifractal assess the population distribution of the convergence method, to assess the population distribution of the singularity,this research work is based on the above research to solve many-dimensional multiobjective optimization algorithm with OE improvement strategies and DZ new dominant mechanism. These methods are discussed from the perspective of a new dominant mechanism to improve the effectiveness of existing algorithms based on orthogonal E dominant strategy. Presented in the summary of the current dominant theory on the basis of a scalable the DZ dominant mechanism for this dominant mechanism to get through the relationship between the various dominant mechanisms. In order to more effectively high dimensional multiobjective optimization problem is solved. This paper also proposed on the basis of these work-based multifractal master curve model multi-objective evolutionary algorithm (MFPC-MOEA). The algorithm uses the multifractal singularity of the individual distribution of the population to be evaluated in order to design a new type of modeling evaluation criteria. Population modeling and then using the master curve, master curve modeling method compared to other linear modeling approach, the model is more accurate, the modeling process is relatively simple. Combining the method with a heuristic search algorithm and model of evolution multi-objective optimization algorithm on the Pareto solution set manifold to grasp, to ensure the superiority of the algorithm to multi-objective optimization problem solving and innovative algorithm design.In the numerical experiments section, based on the multi-objective optimization algorithm and commonly used test sets. In this paper the OE improvement strategies and DZ dominant mechanism for the large number of numerical test analysis. Simulation of many-dimensional optimization solution set there are some difficulties, so the algorithm starting from the analysis of test functions from the distance parameters and positional parameters, the distance parameter of the algorithm to optimize the results of convergence and to determine the convergence of the algorithm for statistical analysis, analysis results show that these improvement strategy and the dominant mechanism to some extent, improved before the algorithm had a significant effect. MFPC-MOEA algorithm is also numerical experiments part of its performance conducted a comprehensive analysis, the comparison algorithm on a simulation of the target space is difficult to distinguish with the naked eye the pros and cons, so the paper the use of statistical performance indicators (HV, EPSILON, SPREAD) mean and variance of the data, by comparing the MFPC-MOEA model multi-objective optimization algorithm on the basis of the modeling work of the master curve reflects the model of the advantages of multi-objective optimization algorithm. Opportunities multifractal modeling assessment methods, accurate assessment of the introduction timing of the master curve was built. MFPC-MOEA and the RM-the MEDA algorithm comparison of MFPC-MOEA algorithm to maintain the advantage of the evolution of policy search. That MFPC-MOEA algorithm not only is the Innovative ideas, but also the test proved it is a good algorithm. |
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