Decision Space And Target Space Data Fusion Strategy For Expensive Interval Multi-objective Optimization

In real life and engineering projects,people often encounter the best optimization of multi-objective at the same time in a given area.These objectives often conflict with each other,and these problems are called “multi-objective optimization problems”.From the multi-objective optimization problem have been proposed,evolutionary algorithm has been as the most effective way to solve such problems,but this kind of evolutionary algorithm solves most of the deterministic problems of known optimization functions.The practical engineering optimization problem is different,optimization functions are often unknown,and the evaluation of experimental costs is expensive,the optimization function often contains uncertain variables expressed in the available interval.Summing up the above two questions as "the expensive interval multi-objective optimization ".In this paper,the main improvements are as follows:(1)For the case that the modeling data are not sufficient,an improved NSGA-II algorithm is proposed based on the principal curve modeling for solving the expensive interval multi-objective optimization with unknown objective function.Firstly,the proposed algorithm builds a modified K principal curve using the population data of the manifold distribution in decision space.Secondly,a new offspring is generated through interpolation and extension according to the built K principal curve,and the proposed strategy of offspring generation is more efficient than that of random offspring generation in genetic algorithm.Finally,due to the crowding distance of the objective space can not be obtained,the closest solutions before and after the candidate solution can be found based on the K principal curve model,so the selection of the solutions with same sequence in decision space is realized.Therefore,the NSGA-II is improved.(2)For the case that the modeling data are not sufficient,based on the idea of agent model and data mining,the data fusion strategy of decision space and target space is put forward.Firstly,a kind of modeling strategy of interval function Gaussian process is proposed to replace the objective and constraint function in the objective space.In this model,the relevance and the accuracy of the interval function are taken as theoptimization goal,and multi-objective optimization algorithm is used to get the Gaussian process parameters.And K principal curve models are built based on population data in decision space.Secondly,two kinds of dominance parameter between the candidate solutions is obtained by Gaussian surrogate model and nearest neighbor strategy respectively.Then the fading memory strategy is given that the two kinds of dominance parameters are integrated to get the practical dominance,and the ratio of two dominance parameters are adjusted adaptively with the evolutionary generations.Finally,two kinds of crowding distance between the candidate solutions is obtained by Gaussian surrogate model and K principal curve model strategy respectively.Then the fading memory strategy is given that the two kinds of crowding distance are integrated to get the practical crowding distance.The results of simulation show the validity of this algorithm.