On The Behavior And Improvements Of The Hypervolume-based Emoas

In the field of Evolutionary Multi-objective Optimization(EMO),the research on the hypervolume-based EMOAs become more and more active,for that they are intuitive and easy to understand.However,due to the heavy computation load of calculating the exact hypervolume values,some researchers have proposed the hypervolume approximation methods in order to reduce the computation load.Besides,it has been reported that the reference point specification in SMS-EMOA(i.e.,one of the hypervolume-based EMOAs)strongly influences the distribution of the solution set on some special shapes of Pareto front of multi-objective optimization problems(MOPs).In this thesis,we further examine the effect of the reference point specification on both the exact hypervolume-based EMOAs(i.e.,SMS-EMOA and FV-MOEA)and the hypervolume approximation-based EMOAs(i.e.,HypE and R2HCA-EMOA).Not only 3-objective MOPs but also 5-,8-and 10-objective many-objective optimization problems(MaOPs)are considered.Different shapes of Pareto front(i.e.,linear against non-linear and triangular against inverted-triangular)are considered.In our experiments,we show the common behaviors of the hypervolume-based(and hypervolume approximation-based)EMOAs on various MOPs(and MaOPs).The results suggest that the reference point specification is an important issue for the hypervolume-based EMOA design.We also analyse the particular behavior of each EMOA.The poor diversity of solutions by HypE and the insensitivity of the position of the reference point in R2HCA-EMOA are shown and illustrated.Based on the behavioral experiments and analyses,some improvements for hypervolume-based EMOAs are made.First,we propose a weak convergence detection-based dynamic reference point specification mechanism,which shows good performance on both MOPs and MaOPs.Second,we proposed a new direction vector generation mechanism based on uniform mechanism for R2HCA-EMOA.By appropriately choosing the parameter in this mechanism,better performance is obtained than the original uniform mechanism and the state-of-the-art random mechanism(i.e.,the mechanism used by the researcher who proposed R2HCA-EMOA).