求解优化问题的改进粒子群算法研究

发布时间：2018-01-14 13:30

本文关键词：求解优化问题的改进粒子群算法研究　出处：《北方民族大学》2017年硕士论文　论文类型：学位论文

【摘要】：粒子群优化(PSO)算法由于原理简单、易实现、调控参数少及收敛性能好等优点,并且能够有效解决不连续、不可微的优化问题,已经成为智能优化领域的研究热点;但PSO算法存在收敛速度慢、精度低及不易跳出局部寻优等缺点.本文提出了粒子的最近等值粒子和最优反方向概念,并且对无约束连续优化问题、混合整数问题和多目标优化问题提出了相应的改进算法.首先,简述了优化问题的相关概念、研究现状和求解方法,阐述了目前常见的群智能优化算法及研究状况,主要对粒子群优化算法的相关原理进行了分析.其次,提出了粒子的最近等值粒子,并在此基础上提出了等高随机替换策略,运用简化粒子群算法进行更新,加快了粒子寻优能力;同时对适应值最差的一部分粒子,采用了最优随机反方向搜索策略以利于跳出局部最优.对不同类型的测试函数,仿真实验表明,两种策略的融合使得算法在寻优速度和精度方面上有极大的提高.再次,针对混合整数优化问题,提出了多维惯性权重的改进方法,使得粒子群算法中的每个粒子都可以有选择的对自身上代速度进行学习;同时采用线性递减步长搜索策略,平衡了整数变量的全局和局部搜索能力;采用混沌策略对品质最差的部分粒子进行变异,从而保证了种群多样性.实验数据验证了改进策略的有效性.最后,针对多目标优化问题,提出了多维自适应的惯性权重.同时引入了拥挤熵策略进行外部档案的维护和更新,并对算法中距离最优粒子较远的部分粒子采取混沌变异策略,从而保证了种群多样性.比较实验数据证实了算法的可行性和有效性.
[Abstract]:Particle Swarm Optimization (PSO) algorithm has the advantages of simple principle, easy implementation, less control parameters and good convergence performance, and it can effectively solve the problem of discontinuous and non-differentiable optimization. It has become the research hotspot in the field of intelligent optimization. However, the PSO algorithm has the disadvantages of slow convergence, low precision and difficulty to jump out of the local optimization. In this paper, the concepts of the nearest equivalent particle and the optimal inverse direction of particles are proposed, and the unconstrained continuous optimization problem is also discussed. The corresponding improved algorithms for mixed integer problem and multi-objective optimization problem are proposed. Firstly, the related concepts, research status and solution methods of the optimization problem are briefly described. This paper describes the current common swarm intelligence optimization algorithm and its research status, mainly analyzes the relevant principles of particle swarm optimization algorithm. Secondly, the recent equivalent particles of particles are proposed. On the basis of this, a random substitution strategy of equal height is proposed, and the simplified particle swarm optimization algorithm is used to update the algorithm, which accelerates the ability of particle optimization. At the same time, for some particles with the worst fitness, the optimal random reverse direction search strategy is used to jump out of the local optimum. The simulation results for different types of test functions show that. The fusion of the two strategies greatly improves the speed and accuracy of the algorithm. Thirdly, for the mixed integer optimization problem, an improved method of multi-dimension inertia weight is proposed. Each particle in the particle swarm optimization algorithm can be selected to learn the previous generation speed. At the same time, the global and local search ability of integer variables is balanced by linear decreasing step size search strategy. Chaos strategy is used to mutate some of the worst-quality particles so as to ensure the diversity of the population. The experimental data verify the effectiveness of the improved strategy. Finally, the multi-objective optimization problem is addressed. A multidimensional adaptive inertial weight is proposed, and the congestion entropy strategy is introduced to maintain and update the external files, and chaos mutation strategy is adopted for some particles which are far away from the optimal particles in the algorithm. Thus, the diversity of the population is guaranteed, and the feasibility and effectiveness of the algorithm are verified by comparing the experimental data.
【学位授予单位】：北方民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP18

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