Research On Evolutionary Multi-Objective Optimization Algorithms

Multi-objective optimization problems(MOPs)widely exist in scientific research,industrial production,financial investment and other fields.In this type of problem,multiple objectives should be optimized simultaneously,and there is an inevitable conflict between these objectives.This conflict means that one objective cannot be improved without the deterioration of any other conflicting objective.Therefore,there is no unique solution for this MOP to make all the objectives reaching the optimal simultaneously.Instead,it should use the Pareto optimal solutions to balance the performance of all objectives.An evolutionary algorithm(EA)is a subset of evolutionary computing in artificial intelligence.It is inspired by the evolutionary mechanism of natural organisms and iteratively searches for optimal solutions by simulating evolutionary processes such as reproduction,mutation,genetic recombination,and natural selection.Because of its solid global searchability with population-based stochastic optimization,EAs have been widely used to solve multi-objective optimization problems.Many studies have shown that EAs can efficiently optimize 2-dimensional and 3-dimensional multi-objective optimization problems,but they are insufficient in solving manyobjective optimization problems greater than three dimensions.Therefore,using a multi-objective evolutionary algorithm(MOEA)to solve many-objective problems has become a hot spot in intelligent optimization.In addition,in the field of intelligent optimization,the research of designing effective multi-objective algorithm solvers according to the characteristics of multi-objective optimization problems in practical applications is also of great practical application value.Therefore,this thesis focuses on designing evolutionary algorithms to solving many-objective problems and real-world optimization problems.The main research works and contributions are as follows:(1)Research a new dominance criterion to improve the convergence ability of the traditional Pareto-based MOEAs in optimizing many-objective optimization problems.The traditional Pareto-based MOEAs mainly use Pareto dominance sorting to converge the population to the Pareto front of problems.Still,the dominance strength of the Pareto-dominance criterion is affected by the dimension of the problem.With the increase of the objective size,the dominance strength of the Pareto dominance criterion decreases exponentially.For this challenge,the thesis proposes an angle dominance criterion,which first constructs an angle vector for each solution in the population and then compares the angle vectors.The thesis also proves that the Pareto completeness of the angle dominance criterion,therefore this criterion can directly integrate into the traditional Pareto-based MOEAs.Experiments show that the angle dominance has good dominance ability in many-objecitve space and can improve the performance of traditional Pareto dominance-based algorithms when solving many-objective optimization problems.(2)Research a diversity maintenance mechanism to balance the convergence and diversity of Pareto-based MOEAs in optimizing many-objective optimization problems.The Pareto-based MOEAs mainly use the diversity maintenance mechanism to maintain the diversity of the population.When Pareto dominance fails in the high-dimensional objective space,the diversity maintenance mechanism becomes the primary selection strategy of the population.The traditional diversity maintenance mechanism prefers solutions in sparse regions,but these solutions generally have poor convergence.Therefore,this mechanism cannot balance the convergence and diversity of the population in the many-objective space.For this challenge,the thesis proposes a diversity maintenance mechanism based on preprocessing and neighbourhood penalty—the preprocessing deletes the dominance resistance solutions far away from the Pareto front,and the neighbourhood penalty selects diverse solutions closing to the Pareto front in the preprocessed solution set.Experiments show that this mechanism can effectively help the Pareto-based algorithm balance the population's convergence and diversity.(3)Research an adaptive reference point update strategy to help the decompositionbased MOEAs optimize the problems with high-dimensional or irregular Pareto fronts.Traditional decomposition-based algorithms mainly use predefined reference points to guide the population to search in the objective space.The current common method for generating a reference point set is the simplex method.This method can generate a set of uniform reference points in the hyperplane through a combination arrangement.This reference point set is suitable for solving the problems with low-dimensional regular Pareto fronts but cannot solve the problems with high-dimensional or irregular Pareto fronts.The reason is that the generated reference points are located in a regular plane and have a “dimensional crisis” in the number.For this challenge,the thesis proposes an adaptive reference point update strategy to help the decomposition algorithm optimize these problems with high-dimensional or irregular Pareto fronts.The adaptive weight update process mainly includes four steps: deleting invalid reference points,adding sparse solutions,generating additional reference points corresponding to sparse solutions,and fine-tuning the reference points.Experiments show that the adaptive reference point update strategy can improve the performance of traditional decomposition-based MOEAs in optimizing the problems with high-dimensional and irregular Pareto fronts.(4)Research a multi-objective evolutionary algorithm to improve the exploration ability of reinforcement learning in self-play training.In the self-play training,the agent chooses its historical model as the opponent to play the game each time and uses the empirical sample data generated in the game to learn.Since the agent obtains the policy for its historical model after each reinforcement learning training,it isn't easy to explore during the training process.For this challenge,the thesis proposes a multi-objective evolutionary reinforcement learning algorithm that uses the random process of an evolutionary algorithm to improve the ability of reinforcement learning to explore diverse behaviours in self-game training.At the same time,the thesis also constructs a two-objective optimization problem so that agents of equal level and different styles do not dominate each other in the objective space.Experiments in the classic table tennis game Pong and the commercial role-playing game Justice Online show that the multi-objective evolutionary reinforcement learning model can significantly improve the level of the agent.