【作者】 李静；

【导师】 陈尚云；

【作者基本信息】 西南交通大学 ， 应用数学， 2022， 硕士

【摘要】 无论是在科学研究还是社会实践中,都存在涉及多个目标的优化问题,我们在解决这类问题时,往往期望各个目标均能达到最优,但在实际问题的求解过程中,多目标优化问题中的各个目标可能是相互制约的,因此需要对这些目标进行平衡。解决多目标优化问题的传统方法是引入参数将其转化为单目标优化问题,然后对其进行求解。但这类方法由于缺乏先验知识通常很难确定参数值,存在一定的局限性,求解效率相对较低。粒子群算法作为群智能优化算法的一个重要分支,为解决多目标优化问题供了新的思路。针对高维度、具备复杂非线性特征的多目标优化问题,粒子群算法将各个目标进行综合考量,在粒子搜寻及更新过程中出了大量具有挑战性的研究课题,进一步拓展了多目标优化问题的研究。本文针对多目标优化问题,以标准粒子群算法框架为基础,结合ε-Pareto支配、角度偏好、突变及三类归档集等优化手段,出了两种改进的优化算法,在MATLAB上进行了仿真实验,并且将改进的算法应用于具体实例中进行验证及对比实验,结果证明了这两种算法的可行性和有效性。具体内容和创新点可以概括如下:(1)将拥挤度判定、突变操作、偏好信息加入到多目标粒子群算法,出了基于角度偏好的ε-Pareto支配的多目标粒子群算法(AP-εPSO);并在AP-εPSO算法的基础上将归档集又更新为三类归档集,同时引入了高斯混沌突变,出了基于角度偏好和三归档集的多目标粒子群算法(AP-TPSO);最终将两种改进的优化算法在MATLAB上进行了仿真实验。(2)将AP-εPSO和AP-TPSO算法分别与出租车合乘定价模型相结合,在具体的多目标优化问题上进行验证及对比实验。更多还原

【Abstract】 Whether in scientific research or social practice,there are optimization problems involving multiple objectives.When solving such problems,we often expect that all the objective can be optimal.However,in the process of solving practical problems,each goal of the multi-objective optimization problem may be mutually constrained,so we need to balance these objectives.The traditional method to solve the multi-objective optimization problem is to introduce parameters to transform it into a single objective optimization problem,and then solve it.However,due to the lack of prior knowledge,this kind of method is usually difficult to determine the parameter value,and has certain limitations,so the efficiency is relatively low.Particle swarm optimization(PSO)is an important branch of swarm intelligence optimization algorithm.It provides a new way to solve the multi-objective optimization problem.Aiming at the multi-objective optimization problem with high dimension and complex nonlinear characteristics,particle swarm algorithm comprehensively considers each objective,and proposes a large number of challenging research topics in the process of particle search and update,which further expands the research of multi-objective optimization problem.In this paper,based on the multi-objective optimization problem,the standard particle swarm optimization framework is used.By means of ε-Pareto domination,angle preference,mutation and three types of archive sets,two kinds of improved optimization algorithms are proposed.Simulation experiments are carried out on MATLAB,and the improved algorithms are applied to specific examples for verification and comparison experiments.The results show that the two algorithms are feasible and effective.The specific content and innovations can be summarized as follows:(1)The congestion degree determination,mutation operation and preference information are added to the multi-objective particle swarm algorithm,and the multi-objective particle swarm algorithm based on angle preference and ε-Pareto(AP-ε PSO)is proposed.On the basis of the AP-ε PSO algorithm,the archive set is updated into three types of archive sets,and Gaussian chaotic mutation is introduced,and the multi-objective particle swarm algorithm based on angle preference and three archive sets(AP-TPSO)is proposed.Finally,the two improved optimization algorithms are simulated on MATLAB.(2)The AP-ε PSO and AP-TPSO algorithms are combined with the Co-taxi pricing model respectively,to verify and compare on the specific multi-objective optimization problem.更多还原