Research On Fast Construction Approach Of Pareto Non-dominated Solution Set On High-dimensional Multi-objective Problem

The approachs to solve multi-objective problem can be divided into two major categories: goal transformation approach and Pareto non-dominated solution.The goal transformation approach is mainly to convert the multi-objective function into single-objective problem through linear weighting and other approach,and constructing the Pareto non-dominated solution set provides a better solution space.There are few studies on efficient non-dominated solution set construction approachs in the previous studies.For the multi-objective problem in the big data era,existing construction approachs are very inefficient.For the multi-objective problem of high-dimensional and large-scale solution space,this thesis studies effective and fast constructing approach of non-dominated solution set to further improves the efficiency of multi-objective decision-making.Firstly,the related definitions and properties of non-dominated solutions are studied.The related definitions and existing theorems of non-dominated solutions are given.Construction theorem of non-dominated solution set proposed,including ordering theorem,dominating theorem,eliminating theorem,and determining theorem.Secondly,the typical non-dominated solution set constructing approachs are studied.Its design idea,construction principle and process are introduced,and the compute time complexity is analyzed.Based on this,Gradual Target Eliminating Algorithm(GTEA)is proposed to constructing non-dominated solution set.The ordered feasible solution set that do not containing objective optimal solutions is constructed,the ordering rules of feasible solution set and the search rules of non-dominated solutions are designed.Analyze the computing time complexity of the algorithm in different situations and prove the completeness and correctness of the algorithm.The time performance test of the algorithm is performed through the classic high-dimensional multi-objective test function,and compared with the existing non-dominated solution set construction approach.The experimental test algorithm time performance influencing factors and the distribution of the non-dominated solution set that constructed by GTEA,and based on experimental results from multiple Analyze the temporal performance of the algorithm.According to the experimental results,the time performance of the algorithm is analyzed from different perspectivesThe experimental results show that the proposed algorithm can construct non-dominated solution set quickly and efficiently.The computing time complexity is lower than NTCM that proposed in the latest researched,and the computational performance is better.When the feasible solution space is large and the number of optimization objectives is large,it has significant advantages over other approachs.