The Study On Many-objective Optimization Algorithms Based On PCA

Many-objective Optimization Problems are a kind of practical optimizationproblems which are common in the real world. Compared to two or three objectivesoptimization problems, the most obvious feature of Many-objective optimizationproblems is more than three objectives. Moreover, with the increase in the number ofobjectives, non-dominated solutions’ number will increase exponentially, which leads topoor performance in the selection and search capacity of optimization algorithms basedon Pareto ranking. So the traditional optimization algorithms are not good enough forsolving Many-objective Optimization Problems. In recent years, the research ofMany-objective optimization algorithms has become a hot spot in optimization field.These researches include mainly two aspects. One aspect is reducing objective number.The other is using a new dominant mechanism to replace the traditional Paretodominant mechanism.This thesis focuses on how to reduce objective dimension and change the dominantmechanism by means of PCA. The contributions in the thesis are as follows:Firstly, in terms of reducing the objective dimension, this thesis proposes analgorithm called COPCA-NSGA-II which improves both redundant objective processand initialization population. In processing redundant objectives, COPCA-NSGA-IIunifies the redundant objectives which come from PCA into a new virtual objectiveinstead of abandoning them, and adds it into non-redundant objective set. In initializingpopulation, some solutions of the set from last NSGA-II are add into the initializationpopulation rather than complete initialization. The experimental results show thatCOPCA-NSGA-II has better convergence and distribution than classicalPCA-NSGA-II.Secondly, in terms of dominant mechanism, this thesis proposes a dominantmechanism based on PCA. During selecting the non-dominated solutions, thePCA-dominant mechanism adopts principal component analysis of objective matrix toget the weight of each objective, multiplies each objective value by its weight and usesthe subtraction of two objective values instead of the traditional way based on Paretodominance. The experiments results show that PCA-dominant mechanism can achievebetter results for the Many-objective optimization problems which have moreobjectives. Thirdly, In order to verify the feasibility of the algorithms in practical application,this thesis applies COPCA-NSGA-II and PCA-dominant mechanism into virtualmachine allocation in cloud computing. The experimental results show that these twoalgorithms can reach a satisfactory solution set in optimizing a simplified model havingfive objectives, which validates the feasibility and effectiveness of the proposedalgorithms in practical applications.