融合粒子群的全局优化混合智能算法研究
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摘要
粒子群优化算法是一种基于种群搜索策略的自适应的随机优化算法,由于其简单易实现,收敛速度快,目前已被广泛应用于神经网络、模糊系统控制、模式识别等多个领域,所以研究和掌握其特性与规律是一个具有理论和应用两个方面重要意义的课题,同时对其应用领域的拓展也有重要的现实意义。
本文在分析基本粒子群优化算法的基础上,对其算法的改进和应用做了较为系统的研究工作。本文的主要研究内容如下:
1、提出了两种改进的粒子群优化算法:非线性递减惯性权重策略的粒子群优化算法和带有种群的平均信息和保持活性策略的粒子群优化算法。数值试验表明,这两种算法的寻优性能都优于基本的PSO算法。
2、针对粒子群优化算法的早熟收敛问题和后期的振荡现象,提出了三种带有变异算子混合的粒子群优化算法:带有指数递减的惯性权重和随机变异的粒子群优化算法、带有随机变异和速度方程改进的粒子群优化算法和带有自适应阀值变异的粒子群优化算法。数值试验表明,这三种改进的算法都具有较强的全局寻优能力。
3、针对约束优化问题,提出了两种混合的粒子群优化算法:基于外点法的求解约束优化问题混合粒子群算法和一种非线性约束优化问题改进的混沌粒子群算法。数值实验表明,这两种新算法都是有效的和稳健的。
4、提出了一种求解0-1非线性规划问题的罚函数-粒子群优化算法。数值试验表明,此算法简单,易于实现,收敛速度快,精度高。
总之,本文对粒子群优化算法的改进及其应用进行了较为全面深入的分析研究,最后对所做工作进行了总结,并提出了进一步研究的方向。
Particle swarm optimization (PSO) is an adaptive stochastic optimization algorithm which based on the population search strategy. PSO has been widely used in neural networks, fuzzy system control, pattern recognition and so on for its simple concept and fast convergence. Therefore, it is significant to study and master the characteristics and rule of PSO in both theory and application areas. In addition, in view of its wide market prospect, it’s also important in practice to extend its application scope.
Basing on the analysis of standard PSO algorithm, this article systematically researches the application and improvement of PSO algorithm. The main work of this thesis is as follows:
1 Two improved PSO algorithms are proposed: one is the PSO algorithm with the strategy of nonlinear decreasing inertia weight, the other is the PSO algorithm with the average information of swarm and keeping active strategy. The experimental results demonstrate that both of the two proposed algorithms are better than the standard PSO algorithm in the ability of global searching.
2 In order to overcome the disadvantage of premature convergence and oscillation in later period, three kinds of hybrid particle swarm optimization algorithms with different mutation operators are proposed: the PSO algorithm with exponent decrease inertia weight and stochastic mutation, improved velocity of the PSO algorithm and adaptive mutation and the PSO algorithm with adaptive threshold mutation. The experimental results demonstrate that these three kinds of improved PSO algorithms are excellent in global searching.
3 For constrained optimization problems, two kinds of hybrid particle swarm optimization algorithms are proposed: the improved particle swarm optimization algorithm based on outside point method for solving constrained optimization problems and the improved chaotic particle swarm algorithm for solving the nonlinear constrained optimization problems. Numerical experiments show that both of the two new algorithms are effective and robust.
4 For solving zero-one nonlinear programming problems, we proposed a penalty function-PSO hybrid algorithm. It is shown in numerical experiments that this algorithm is simple and easy to implement with fast convergence and high accuracy.
In general, the theory and application of PSO are analyzed comprehensively. Finally, the whole research contents are summarized, and further work is given.
本文在分析基本粒子群优化算法的基础上,对其算法的改进和应用做了较为系统的研究工作。本文的主要研究内容如下:
1、提出了两种改进的粒子群优化算法:非线性递减惯性权重策略的粒子群优化算法和带有种群的平均信息和保持活性策略的粒子群优化算法。数值试验表明,这两种算法的寻优性能都优于基本的PSO算法。
2、针对粒子群优化算法的早熟收敛问题和后期的振荡现象,提出了三种带有变异算子混合的粒子群优化算法:带有指数递减的惯性权重和随机变异的粒子群优化算法、带有随机变异和速度方程改进的粒子群优化算法和带有自适应阀值变异的粒子群优化算法。数值试验表明,这三种改进的算法都具有较强的全局寻优能力。
3、针对约束优化问题,提出了两种混合的粒子群优化算法:基于外点法的求解约束优化问题混合粒子群算法和一种非线性约束优化问题改进的混沌粒子群算法。数值实验表明,这两种新算法都是有效的和稳健的。
4、提出了一种求解0-1非线性规划问题的罚函数-粒子群优化算法。数值试验表明,此算法简单,易于实现,收敛速度快,精度高。
总之,本文对粒子群优化算法的改进及其应用进行了较为全面深入的分析研究,最后对所做工作进行了总结,并提出了进一步研究的方向。
Particle swarm optimization (PSO) is an adaptive stochastic optimization algorithm which based on the population search strategy. PSO has been widely used in neural networks, fuzzy system control, pattern recognition and so on for its simple concept and fast convergence. Therefore, it is significant to study and master the characteristics and rule of PSO in both theory and application areas. In addition, in view of its wide market prospect, it’s also important in practice to extend its application scope.
Basing on the analysis of standard PSO algorithm, this article systematically researches the application and improvement of PSO algorithm. The main work of this thesis is as follows:
1 Two improved PSO algorithms are proposed: one is the PSO algorithm with the strategy of nonlinear decreasing inertia weight, the other is the PSO algorithm with the average information of swarm and keeping active strategy. The experimental results demonstrate that both of the two proposed algorithms are better than the standard PSO algorithm in the ability of global searching.
2 In order to overcome the disadvantage of premature convergence and oscillation in later period, three kinds of hybrid particle swarm optimization algorithms with different mutation operators are proposed: the PSO algorithm with exponent decrease inertia weight and stochastic mutation, improved velocity of the PSO algorithm and adaptive mutation and the PSO algorithm with adaptive threshold mutation. The experimental results demonstrate that these three kinds of improved PSO algorithms are excellent in global searching.
3 For constrained optimization problems, two kinds of hybrid particle swarm optimization algorithms are proposed: the improved particle swarm optimization algorithm based on outside point method for solving constrained optimization problems and the improved chaotic particle swarm algorithm for solving the nonlinear constrained optimization problems. Numerical experiments show that both of the two new algorithms are effective and robust.
4 For solving zero-one nonlinear programming problems, we proposed a penalty function-PSO hybrid algorithm. It is shown in numerical experiments that this algorithm is simple and easy to implement with fast convergence and high accuracy.
In general, the theory and application of PSO are analyzed comprehensively. Finally, the whole research contents are summarized, and further work is given.
引文
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[9]张更新,赵辉,王红君,苏君临.基于动态参数的粒子群算法研究[J].天津理工大学学报,2005,21(4):42-44.
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