Robust Dynamic Multi-objective Evolutionary Optimization Based On A Novel Robustness Definition

In reality,many actual control and research objects are changing over time or the environment.In order to solve the dynamic multi-objective optimization problems(DMOPs),researchers often use an optimized method of tracking the moving optima in the dynamic environment.That is,when the change of the environment is detected,a new round of multi-objective evolutionary optimization process is triggered,and all or some of the initial populations are predicted by using the previous environmental timevarying historical information.The evolutionary strategy with better diversity is always used to increase population diversity,so that optimal solution can be found near the current real Pareto frontier within a finite time.This kind of re-triggering evolution algorithms often can't find a satisfactory Pareto solution in a dynamic multi-objective optimization problem with complex objective function evaluation or rapid environmental change.To solve this problem,researchers give robust optimal over time(ROOT).This method can find a set of robust Pareto solutions whcich satisfy the robustness threshold and can be used in multiple continuous dynamic environments.However,the existing definition of robust Pareto solution is designed to calculate its robust performance for each individual instead of whole Pareto solutions' front.When the Pareto front in the adjacent dynamic environment has a cross,bump change,or the distribution uniformity changes,the deviation of robustness evaluation could occur with using the existing robustness definition.To solve this,this thesis gives a new definition of robustness,and gives the corresponding robust dynamic multi-objective evolutionary optimization algorithm based on this.Firstly,in order to accurately measure the robust performance of the Pareto solution,we consider the Pareto front as a whole,and use the hyper-volume of the Pareto front to describe the robust performance of the solution.Based on the above definition of robustness,a robust dynamic multi-objective evolutionary optimization algorithm is constructed with MOEA/D algorithm.The simulation results of 9 benchmarks show that this algorithm can find the robust Pareto solutions satisfying the future continuous dynamic environment.In addition,this algorithm can also obtain robustness Pareto solutions under the premise of satisfying the convergence and distribution.Secondly,the new robustness definition based on the hyper-volume can't directly reflect the influence of the evolution of each individual on the overall robust performance of the whole Pareto solution set.In order to bring robust performance into population evolution,this chapter gives the concept of individual contribution to analyze the effect of each individual on the robust performance of the whole Pareto solution set.Furthermore,two models based on the average hyper-volume and the survival time of the fixed-time window are constructed.Based on these two models,the robust performance of Pareto solution set can be described.In addition,three prediction methods are used to estimate the fitness of the Pareto solutions in future dynamic moments.The experimental results of eight test functions show that the proposed algorithm can obtain better solution of robust performance and RPOOT can work better with AR prediction method.Thirdly,the robustness evaluation method based on the individual contribution can successfully lead the evolution of the individual by using the robust performance,but it also have shortcomings in the calculation cost.Thus,the multi-population method is introduced to solve the above problem.Population is divided into multiple subpopulations according to the location in objective space.The results of 8 test functions prove that the robust dynamic multi-objective evolutionary optimization method based on multi-population can not only obtain excellent robust performance,but also can reduce the computational cost.The above research results not only enrich the robust dynamic multi-objective optimization algorithm theory,but also provide a new research direction for solving the dynamic multi-objective optimization problems.