Meta-heuristic Optimization Algorithms For Real-valued Optimization Problems With Their Applications

Many real-world problems can be abstracted as real-valued optimization problems,so solving these optimization problems has turned out to be a hot reserach topic and many solutions have emerged.Among these solutions metaheuristic optimization algorithms are a new type of algorithms different from traditional optimization algorithms,which are easy to implement,flexible and general.Consequently they are suitable for solving complex real-valued optimization problems where traditional optimization algorithms fail.However,the metaheuristic optimization algorithm still suffers from prematureness,slow convergence,sensitive to control parameters,and then difficulty in effectively solving large-scale problems,which seriously affects the performance of these algorithms and limits their development in various real-world applications.In order to solve complex real-valued optimization problems more efficiently,this thesis presents a theoretical framework based on the dynamic dimensional search algorithm of the metaheuristic optimization algorithm,and carries out a series of algorithm designs and analysis,as well as their applications on a specific problem.Specifically,the main research of this paper is as follows.(1)Theoretical study on dynamic dimensional search algorithms.We first conduct an in-depth study on the dynamic dimensional search(DDS)algorithm,establish a basic framework for this type of algorithms,describe the operation mechanism of the search process,and analyze the performance of control parameters and variational operators;then we make the first attempt to use martingale theory in Markov chain analysis to establish the Markov chain analysis model of the dynamic dimensional search algorithm.The strategy transforms the optimal fitness function process into the supermartingale by treating the optimal process of the DDS algorithm as the optimal fitness function process.Therefore,the convergence of the dynamic dimensional search algorithm is thus easily proved and a general convergence framework for dynamic dimensional search algorithms is then determined.(2)To explore metaheuristic optimization algorithms for large-scale real-valued optimization problems.Based on the dynamic dimensional search algorithm in the metaheuristic optimization algorithm,we deeply explore and study the neighborhood search control mechanism and control parameters for the algorithm to deal with the large-scale real-valued optimization problem.Two variants of the dynamic dimensional search algorithm for large-scale real-valued optimization problems are proposed based on the variational operator and variational probability of the algorithm and numerical experiments confirm that these two variants have significant advantages over the dynamic dimensional search algorithm and the rest of the metaheuristic optimization algorithms in terms of accuracy,convergence speed and scalability.(3)To investigate efficient and easy-to-use metaheuristic optimization algorithms.First,we propose a chaotic dynamic dimensional search algorithm using three strategies: chaotic initialization,a new Gaussian variational operator,and chaotic search for solving global optimization problems in order to address the shortcomings of the improved algorithm easily trapped in local optimum.The chaotic initialization enhances the exploration ability of the algorithm,the new Gaussian variational operator improves the solution accuracy and convergence speed of the algorithm,and the chaotic search gives the algorithm the ability to jump out of the local optimum.Then,we demonstrate that the solution accuracy and convergence speed of the chaotic dynamic dimensional search algorithm are significantly improved by testing on three benchmark test sets in the field of real-valued optimization,which shows that the three improvement strategies effectively enhance the exploration and development of the algorithm.Finally,we also analyze the role of the three strategies in the search process through numerical experiments.(4)Improved dynamic dimensional search algorithms with applications.In the context of optimal scheduling of a group of terrace reservoirs,this thesis establishes a mathematical model for optimal scheduling of single-objective power generation in a group of terrace reservoirs.We employ the classical penalty function method to deal with the complex constraints in the model and then take the group of terrace reservoirs in the Qingjiang River basin as the research object to apply the chaotic dynamic dimensional search algorithm in order to solve the optimization and scheduling model.Finally,we study each scheduling scheme in detail to provide technical support and data support for the optimal scheduling of power generation in the Qingjiang River basin,and this provides a new idea to solve the optimal scheduling of power generation in other basins of a group of terrace reservoirs.