Knee Region Evolution Algorithm For Multi-modal And Multi-objective Optimization

In the present research,there are many evolutionary algorithms to solve the multi-objective optimization problem in order to obtain the optimal Pareto Front with uniform distribution.At the same time,many scholars are concerned about the selection of the final solution set.However,there are few researches on the Pareto Sets that affect the optimal Pareto Front distribution.And the selection of the final solution sets into the search process of evolutionary algorithm is not very high concern.When the optimal Pareto Set and the optimal Pareto Front are analyzed at the same time,there will be a phenomenon that more than two subsets correspond to the same Pareto front.This phenomenon is called a multi-modal multi-objective optimization problem.In order to solve this kind of problem,we need to balance the attention of the objective space and the decision space in the search process.In addition,most of the researches on the final solution set are based on the optimal Pareto frontier obtained after optimization to give the user the most appropriate solution,but this may cause large errors.In order to reduce the error,we can embed the problem of solution set selection in the process of algorithm search,so that each update will be improved.In summary,this thesis proposes a multi-modal multi-objective optimization algorithm based on the knee region.During each evolution,the knee region is selected to preferentially enter the next generation.Not only can increase the selection pressure of the algorithm at the later stage of the search,but also can accelerate the convergence of the algorithm,and it can also provide users with an appropriate solution after the optimization is completed.At the same time,the algorithm adopts niche strategy to provide high-quality parent population for population optimization.And use the special crowding distance as the third selection mechanism in environment selection to solve the multi-modal characteristics in the optimization problem and provide as many alternative solutions as possible for decision makers.In addition,this thesis constructs some test functions for the multi-modal multi-objective optimization problem of the knee region point/knee region.Three different methods for finding knee points were embedded in multi-modal multi-objective optimization algorithms for comparison and analysis.Finally,in order to significantly analyze the pros and cons of the algorithm,this thesis proposes two performance indicators to evaluate the pros and cons of the knee region.The main research contents of this thesis are as follows:Firstly,the background and significance of the multi-modal multi-objective optimization problem are introduced,and the role of determining the knee point/knee region and the status of the test function for the knee point/knee region are explained in detail.Based on this,a multi-modal multi-objective optimization algorithm based on knee region is proposed and three methods of determining knee points and one method of knee region are introduced.Secondly,the process of constructing the knee point/knee region test function is described in detail.Then,according to the characteristics of the knee points,several basic knee point functions are proposed.The characteristics of symmetry,differentiability,bias and so on are considered comprehensively in combination with the determination method of knee region.Thirdly,three different methods for identifying knee points in the knee region are embedded into different multi-modal multi-objective optimization algorithms for experimental testing.Then,we made a comparative analysis with the newly proposed performance index of knee region.Finally,the content of this thesis is summarized.And the shortcomings and deficiencies of the current work are analyzed,and the future research directions are prospected.