Probabilistic Model Based Evolutionary Algorithm With Applications In Complex Settings

Evolutionary algorithm has been widely used in robot control,logistics path planning,aircraft structure design,biomedical research and other fields due to its excellent solving ability,strong adaptability and easy implementation.According to different ways of search method,evolutionary algorithm can be divided into nature-inspired evolutionary algorithm and probabilistic model based evolutionary algorithm.The nature-inspired evolutionary algorithm is developed on the basis of coevolutionary theory,but its diversity and convergence are poor.To solve these problems,the probabilistic model based evolutionary algorithm can explore decision space by learning and sampling of probabilistic model,so it has stronger global search ability and faster convergence speed than the nature-inspired evolutionary algorithm.As an important part of probabilistic model based evolutionary algorithm,sampling has an important impact on the convergence speed and the quality of the solution,but the sampling model has not been deeply studied.Moreover,aiming at the problems of poor diversity and premature convergence of nature-inspired evolutionary algorithm,we use the probabilistic model based evolutionary algorithm to design the eigen coordinate system to improve the performance of the algorithm.In addition,because the sampling model and search mechanism of probabilistic model based evolutionary algorithm have good characteristics,applying them to multiobjective multitasking optimization algorithm can improve the efficiency of knowledge transfer.Based on the above considerations,the innovative work of this paper includes the following four parts:1.As a classical probabilistic model based evolutionary algorithm,the estimation of distribution algorithm is prone to poor diversity and premature convergence.To solve these problems,an efficient mixture sampling model is designed by using uniform sampling method,orthogonal method and mirrored sampling method,which can explore promising regions.Moreover,the theoretical analysis of efficient mixture sampling model indicated that the model can achieve good diversity and convergence at the same time.Finally,an efficient mixture sampling model for Gaussian estimation of distribution algorithm is proposed.Experimental results on the single objective optimization problems show that the proposed algorithm has better diversity and faster convergence speed than the current estimation of distribution algorithm.2.The nature-inspired evolutionary algorithm uses a fixed original coordinate system to search,which will not be able to effectively match different function landscapes,resulting in the algorithm easily falling into local optimum and appear premature convergence.To solve these issues,this paper proposes an adaptive framework to select the coordinate systems.In this framework,the eigen coordinate system is constructed by a covariance matrix in the probabilistic model based evolutionary algorithm,which can match different function landscapes.In particular,using both the original coordinate system and the eigen coordinate system can achieve better performance than using a single coordinate system.Therefore,the selection process of two coordinate systems is defined as a Markov decision process and is controlled by reinforcement learning algorithm.In addition,the proposed framework is applied to three classical nature-inspired evolutionary algorithms,i.e.,differential evolution,particle swarm optimization,and teaching-learning-based optimization.Experimental results on the single objective optimization problems indicate that the proposed framework can significantly improve the performance of nature-inspired evolutionary algorithms.3.Multiobjective multitasking optimization is a new research topic in the field of evolutionary computation,which can solve multiple tasks simultaneously to improve the convergence speed and the quality of each task by knowledge transfer across tasks.However,the core problem is how to select valuable solutions from the source tasks to help the target tasks,and it has not been well solved.Inspired by the sampling model of probabilistic model based evolutionary algorithm,a multiobjective multitasking optimization algorithm based on positive knowledge transfer mechanism is proposed.Firstly,the cheap surrogate model is employed to evaluate the solutions of each task according to the density probability.Moreover,a diversity measuring method is presented to measure the diversity of solutions in each task and obtain the diversity indicators.In addition,the density probability and diversity indicator are combined to obtain comprehensive indicator.Finally,the selection strategy of transferred solutions is designed to find valuable solutions with good diversity based on the comprehensive indicator,which can improve the efficiency of knowledge transfer.Experimental results on multiobjective multitasking optimization problems demonstrate that the proposed algorithm is efficient and competitive.4.Although many multiobjective multitasking optimization algorithm have been proposed,a core problem,designing an efficient transfer strategy,has been scarcely explored.Inspired by the search mechanism of probabilistic model based evolutionary algorithm,this paper designs a multiobjective multitasking optimization algorithm based on multidirectional prediction method.Firstly,the population is divided into multiple classes by the binary clustering method,and the representative point of each class is calculated.Then,the representative points are used to generated multiple prediction directions.Afterward,the adaptive mutation strength is designed according to the improvement degree of each class.Finally,the predictive transferred solutions are generated by the prediction directions and mutation strengths,which can achieve efficient knowledge transfer.Experimental results on multiobjective multitasking optimization problems show that the proposed algorithm can obtain better results.