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Multi-objective optimization Pareto set non-inferiority stratification method based on subspace statistics

A multi-objective optimization and subspace technology, applied in computing, genetic modeling, data processing applications, etc., can solve problems such as time-consuming and low real-time algorithm performance, and achieve the effect of saving non-inferior layering time.

Inactive Publication Date: 2014-03-26
NO 709 RES INST OF CHINA SHIPBUILDING IND CORP
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Problems solved by technology

[0005] The present invention aims at the shortcomings of the existing evolutionary algorithm Pareto set non-inferiority stratification that needs to traverse all individuals in the population and takes too much time to cause the algorithm's real-time performance is not strong, provides a multi-objective optimization Pareto set non-inferior stratification method, This method divides the subspace of the multi-dimensional space to perform fast non-inferior stratification of the Pareto set of multi-objective optimization, which can improve the efficiency of the optimization algorithm

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  • Multi-objective optimization Pareto set non-inferiority stratification method based on subspace statistics
  • Multi-objective optimization Pareto set non-inferiority stratification method based on subspace statistics
  • Multi-objective optimization Pareto set non-inferiority stratification method based on subspace statistics

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Embodiment Construction

[0027] The present invention is a kind of multi-objective optimization Pareto hierarchical method based on subspace statistics, and its specific steps are as follows:

[0028] (1) Multi-dimensional space structure

[0029] Suppose the objective function for optimization is g i (i=1,2,...,m), where m is the number of objective functions, and its standardization method is:

[0030]

[0031] Using the normalized objective function f i (i=1,2,...,m) form an m-dimensional space V, and the i-th dimension corresponds to the objective function value f i , then the spatial range corresponding to the i-th dimension is [min(f i ),max(f i )].

[0032] (2) Subspace division and determination of equipotential distribution boundary

[0033] Divide the multi-dimensional space constructed in step (1) into subspaces, and the size of the divided subspaces is determined according to the population size; let the population size be N, and the number of segments in each dimension is q is ...

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Abstract

A multi-objective optimization Pareto set non-inferiority stratification method based on subspace statistics comprises the following steps: (1) constructing multidimensional space, (2) performing subspace division and equipotential distribution sector determination, (3) performing population-individual subspace mapping, (4) performing dominant individual statistics on subspaces, (5) calculating individual ranks, and (6) performing Pareto set non-inferiority stratification. The multi-objective optimization Pareto set non-inferiority stratification method has the advantages that it is not necessary that global traversal is performed on each individual in a population in a set to count the number of the dominant individuals; after high-dimensional solution space is discretized into the subspaces, the whole space can be divided into a dominant subspace set, an equivalently dominant subspace set and an inferior subspace set according to each subspace; all the individuals only need to be counted at a time according to the dominant subspaces or the inferior subspaces of equipotential distribution sectors, so that fast Pareto set non-inferiority stratification is achieved. In this way, the method provides a basis for real-time and quasi real-time engineering application of the evolutionary multi-objective optimization algorithm.

Description

technical field [0001] The present invention relates to a fast non-inferior layering method based on subspace statistics in the field of intelligent optimization algorithms, specifically a Pareto set non-inferior layering method for multi-objective optimization problems, applicable to multi-objective optimization problems Pareto set solution individual non-inferiority stratification, including multi-objective genetic algorithm, multi-objective particle swarm algorithm and other non-inferiority stratification in evolutionary Pareto set multi-objective optimization algorithm, and can be extended to other Pareto set multi-objective optimization question. Background technique [0002] Multi-objective optimization problem MOP (Multi-objective Optimization Problem) refers to the optimization problem of multiple objective functions on the feasible domain of the solution. Many optimization problems in scientific research and engineering practice can be attributed to multi-objective ...

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Application Information

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IPC IPC(8): G06Q10/04G06N3/12
Inventor 李伦吴汉宝黄友澎胡忠辉
Owner NO 709 RES INST OF CHINA SHIPBUILDING IND CORP
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