混合粒子群协同优化算法及其应用研究
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摘要
在科学技术研究中，很多计算问题都可以归结为具有非线性和多峰特性目标函数的全局优化问题，高效求得此类问题的全局最优解一直是优化计算领域的研究方向。粒子群优化(Particle Swarms Optimization，PSO)算法是应用于求解此类问题的一种有效方法，与其它优化算法相比，它的优点突出。虽然PSO算法在很多问题中已得到成功应用，但仍存在早熟收敛导致的局部收敛速度慢，计算精度不高等问题，进一步提高PSO算法的计算性能已是当前研究的热点。
本文在深入研究粒子群优化算法的基础上，从提升其计算性能入手，提出了若干改进的粒子群优化算法，相应得到了较高的优化性能；在算法混合思想指导下，重点提出了两种混合粒子群协同优化算法，取得了更为全面的计算性能。并成功应用优化算法精确、高效地解决了氧化铝生产工艺过程的物料平衡计算难题。论文主要包括如下研究内容：
综合表述了PSO算法产生背景及其国内外研究与应用现状，并对标准PSO算法结构特性和计算过程进行必要分析。
论文以提高粒子在解空间中的探索能力来提升PSO算法的全局收敛性能，定义了平稳度和聚集度的概念，提出了三种改进的粒子群优化算法。①基于空间变异的粒子群优化算法(SM-PSO)。在最优解的搜索过程中，根据群体适应度变化情况，通过自适应调整搜索空间来提高粒子群的局部寻优效率和全局寻优性能，以提高搜索速度和成功率。其中证明了算法收敛性。②具有加速因子的粒子群优化算法(AF-PSO)。根据粒子的运动轨迹，对粒子的速度进行动态调整，从而通过改进粒子的空间探索能力来提高算法的收敛速度。其中对算法的收敛性进行了证明，并给出了有关参数选取的指导性原则。③具有随机变异特性的改进型粒子群算法(AM-PSO)。该算法克服了标准粒子群算法后续迭代过程速度慢且易陷入局部最优解的缺点。在迭代过程中，粒子的变异概率取决于粒子的适应度值以及当前所有粒子的聚集度和平稳度，通过变异，粒子可有效地探索新的空间领域，从而可以有效地避免陷入局部最优解。通过大量实验仿真以及在激光焊接质量检测中的实际工程应用对三种改进方法分别进行了性能对比分析与讨论。
对于复杂的优化问题，算法在解空间中的探测和开发能力往往单靠某一种算法在整体计算性能上很难得到全面有效利用与平衡，从而影响算法的整体求解精度和效率。对此，本文提出并实现了由粒子群优化算法作主导框架，将其它优化算法中某些优良计算特性与机制融入其中的两种混合粒子群协同优化算法(SASM-PSCO和CSM-PSCO)。它们既保留了粒子群优化算法原有的优点，其不足之处则被其它算法的优点所弥补，诸如模拟退火法中具有的突跳性，单纯形算法的快速收敛性，混沌运动的强随机性和遍历性等。仿真测试及工程应用结果表明，两种混合粒子群协同优化算法具有较为全面的优化计算整体性能。文中讨论了各种被引入的优化算法与粒子群优化算法的融合方法与步骤问题，并给出了混合粒子群协同优化算法的收敛性定理证明。
在简要分析和讨论拜耳法氧化铝生产的基本原理和生产工艺流程基础上，针对实际工程应用中不同的生产工艺给出了拜耳法物料平衡计算的三种数学模型，将复杂的工程计算问题抽象成非线性多目标优化的数学问题，用前述各种优化算法进行计算，均取得了很好的应用结果，其中两种混合型优化算法的计算性能较之改进型优化算法更为全面。
最后，对粒子群优化算法的发展方向进行了展望。
In science and technology research, a lot of computing problems can be formulated as a global optimization problem of the objective function with nonlinear and multi-peak characteristics. How to solve a global solution of these problems is one of the most important topics in optimization. Recently, particle swarm optimization (PSO) algorithm is one of the most powerful methods for solving such problems, compared with other optimization algorithms, its advantages highlighted. Although PSO has gained much attention and wide applications in different fields, there are still slower local convergence and lower computational accuracy problem caused by premature convergence, and how to improve the globally convergence ability has been the main research direction so far.
In this paper, based on in-depth study of particle swarm optimization algorithm, from start to upgrade its computing performance, a number of improved particle swarm optimization algorithms were given, the corresponding measure has been higher results; Under the guidance of thought of the hybrid algorithm, hybrid particle swarm cooperative optimization algorithms were proposed and achieved very good computing performance and results. The difficult problems of the material balance computation in the alumina production process were solved accurately and efficiently. Several points are included in this paper as follows:
The origin and background of PSO were introduced, and the current research and application situations were summarized deeply, and then structural characteristics and calculation process of the standard PSO algorithm were carried out the necessary analysis of the process.
It is reasonable that improving exploration ability can make particles explore solution space more efficiently in order to improve PSO global performance, the concepts of the gathering degree and the steady degree were defined, then three different improved PSO algorithms were proposed. First is a novel particle swarm optimization algorithm based on adaptive space mutation (SM-PSO). During the searching process, the convergence speed and globally convergence ability is greatly improved by the adaptive space mutation based on the variance of the population's fitness, the convergence theorem of the algorithm is proved. Second is a particle swarm optimization algorithm with accelerating factor (AF-PSO). The particle can dynamically adjust flying velocity according to flying direction at the different iterations, and effectively escapes from local optimum solution according to the gathering degree and the steady degree, and finally attains global optimum solution, and then the convergence and parameter selection of the algorithm are analyzed and discussed deeply. Third is a novel particle swarm optimization with stochastic mutation (AM-PSO). The mutation probability of the current particle is determined by the mean of all the particle's fitness, the gathering degree and the steady degree, the exploration ability is efficiently improved by the mutation, and the probability of falling into local optimum is greatly decreased. Experimental results and practical application in quality monitoring of laser welding process show the new methods have faster convergence speed and higher globally convergence ability than the standard PSO.
For complex optimization problems, the abilities of exploration and exploitation of algorithm often cannot be utilized and balanced effectively by depending solely on one method, thus influence solving overall precision and efficiency of the algorithm. Based on the main framework of particle swarm optimization algorithm, we proposed two hybrid particle swarm cooperative optimization algorithms in combination with certain excellent characteristics and mechanisms of other optimization algorithms. They retain the original advantages of particle swarm optimization, the disadvantages were offset by the merits of other algorithms, such as sudden jump characteristics of simulated annealing, fast convergence of the simplex algorithm, and randomness and ergodicity of the strong chaotic motion. Simulation testing and engineering application results show that hybrid particle swarm cooperative optimization algorithms have a more comprehensive optimization performance. The paper discusses the methods and steps of the integration problem of other algorithms and particle swarm optimization, and the convergence theorems of hybrid algorithms were proved.
Based on the in-depth analysis and discussion the technological process and the basic principles of the alumina production process in Bayer, three mathematical models of Bayer material balance computation were proposed for practical engineering applications in different production technology, complex engineering computing problems were first converted into non-linear multi-objective optimization problems, and the above optimization algorithms were applied to solve them and achieved excellent results. The results also show that two hybrid optimization algorithms have more comprehensive computing performance than the improved optimization algorithms.
Finally, the whole research contents were summarized, particle swarm optimization algorithm was prospected for the direction of development in future.
本文在深入研究粒子群优化算法的基础上，从提升其计算性能入手，提出了若干改进的粒子群优化算法，相应得到了较高的优化性能；在算法混合思想指导下，重点提出了两种混合粒子群协同优化算法，取得了更为全面的计算性能。并成功应用优化算法精确、高效地解决了氧化铝生产工艺过程的物料平衡计算难题。论文主要包括如下研究内容：
综合表述了PSO算法产生背景及其国内外研究与应用现状，并对标准PSO算法结构特性和计算过程进行必要分析。
论文以提高粒子在解空间中的探索能力来提升PSO算法的全局收敛性能，定义了平稳度和聚集度的概念，提出了三种改进的粒子群优化算法。①基于空间变异的粒子群优化算法(SM-PSO)。在最优解的搜索过程中，根据群体适应度变化情况，通过自适应调整搜索空间来提高粒子群的局部寻优效率和全局寻优性能，以提高搜索速度和成功率。其中证明了算法收敛性。②具有加速因子的粒子群优化算法(AF-PSO)。根据粒子的运动轨迹，对粒子的速度进行动态调整，从而通过改进粒子的空间探索能力来提高算法的收敛速度。其中对算法的收敛性进行了证明，并给出了有关参数选取的指导性原则。③具有随机变异特性的改进型粒子群算法(AM-PSO)。该算法克服了标准粒子群算法后续迭代过程速度慢且易陷入局部最优解的缺点。在迭代过程中，粒子的变异概率取决于粒子的适应度值以及当前所有粒子的聚集度和平稳度，通过变异，粒子可有效地探索新的空间领域，从而可以有效地避免陷入局部最优解。通过大量实验仿真以及在激光焊接质量检测中的实际工程应用对三种改进方法分别进行了性能对比分析与讨论。
对于复杂的优化问题，算法在解空间中的探测和开发能力往往单靠某一种算法在整体计算性能上很难得到全面有效利用与平衡，从而影响算法的整体求解精度和效率。对此，本文提出并实现了由粒子群优化算法作主导框架，将其它优化算法中某些优良计算特性与机制融入其中的两种混合粒子群协同优化算法(SASM-PSCO和CSM-PSCO)。它们既保留了粒子群优化算法原有的优点，其不足之处则被其它算法的优点所弥补，诸如模拟退火法中具有的突跳性，单纯形算法的快速收敛性，混沌运动的强随机性和遍历性等。仿真测试及工程应用结果表明，两种混合粒子群协同优化算法具有较为全面的优化计算整体性能。文中讨论了各种被引入的优化算法与粒子群优化算法的融合方法与步骤问题，并给出了混合粒子群协同优化算法的收敛性定理证明。
在简要分析和讨论拜耳法氧化铝生产的基本原理和生产工艺流程基础上，针对实际工程应用中不同的生产工艺给出了拜耳法物料平衡计算的三种数学模型，将复杂的工程计算问题抽象成非线性多目标优化的数学问题，用前述各种优化算法进行计算，均取得了很好的应用结果，其中两种混合型优化算法的计算性能较之改进型优化算法更为全面。
最后，对粒子群优化算法的发展方向进行了展望。
In science and technology research, a lot of computing problems can be formulated as a global optimization problem of the objective function with nonlinear and multi-peak characteristics. How to solve a global solution of these problems is one of the most important topics in optimization. Recently, particle swarm optimization (PSO) algorithm is one of the most powerful methods for solving such problems, compared with other optimization algorithms, its advantages highlighted. Although PSO has gained much attention and wide applications in different fields, there are still slower local convergence and lower computational accuracy problem caused by premature convergence, and how to improve the globally convergence ability has been the main research direction so far.
In this paper, based on in-depth study of particle swarm optimization algorithm, from start to upgrade its computing performance, a number of improved particle swarm optimization algorithms were given, the corresponding measure has been higher results; Under the guidance of thought of the hybrid algorithm, hybrid particle swarm cooperative optimization algorithms were proposed and achieved very good computing performance and results. The difficult problems of the material balance computation in the alumina production process were solved accurately and efficiently. Several points are included in this paper as follows:
The origin and background of PSO were introduced, and the current research and application situations were summarized deeply, and then structural characteristics and calculation process of the standard PSO algorithm were carried out the necessary analysis of the process.
It is reasonable that improving exploration ability can make particles explore solution space more efficiently in order to improve PSO global performance, the concepts of the gathering degree and the steady degree were defined, then three different improved PSO algorithms were proposed. First is a novel particle swarm optimization algorithm based on adaptive space mutation (SM-PSO). During the searching process, the convergence speed and globally convergence ability is greatly improved by the adaptive space mutation based on the variance of the population's fitness, the convergence theorem of the algorithm is proved. Second is a particle swarm optimization algorithm with accelerating factor (AF-PSO). The particle can dynamically adjust flying velocity according to flying direction at the different iterations, and effectively escapes from local optimum solution according to the gathering degree and the steady degree, and finally attains global optimum solution, and then the convergence and parameter selection of the algorithm are analyzed and discussed deeply. Third is a novel particle swarm optimization with stochastic mutation (AM-PSO). The mutation probability of the current particle is determined by the mean of all the particle's fitness, the gathering degree and the steady degree, the exploration ability is efficiently improved by the mutation, and the probability of falling into local optimum is greatly decreased. Experimental results and practical application in quality monitoring of laser welding process show the new methods have faster convergence speed and higher globally convergence ability than the standard PSO.
For complex optimization problems, the abilities of exploration and exploitation of algorithm often cannot be utilized and balanced effectively by depending solely on one method, thus influence solving overall precision and efficiency of the algorithm. Based on the main framework of particle swarm optimization algorithm, we proposed two hybrid particle swarm cooperative optimization algorithms in combination with certain excellent characteristics and mechanisms of other optimization algorithms. They retain the original advantages of particle swarm optimization, the disadvantages were offset by the merits of other algorithms, such as sudden jump characteristics of simulated annealing, fast convergence of the simplex algorithm, and randomness and ergodicity of the strong chaotic motion. Simulation testing and engineering application results show that hybrid particle swarm cooperative optimization algorithms have a more comprehensive optimization performance. The paper discusses the methods and steps of the integration problem of other algorithms and particle swarm optimization, and the convergence theorems of hybrid algorithms were proved.
Based on the in-depth analysis and discussion the technological process and the basic principles of the alumina production process in Bayer, three mathematical models of Bayer material balance computation were proposed for practical engineering applications in different production technology, complex engineering computing problems were first converted into non-linear multi-objective optimization problems, and the above optimization algorithms were applied to solve them and achieved excellent results. The results also show that two hybrid optimization algorithms have more comprehensive computing performance than the improved optimization algorithms.
Finally, the whole research contents were summarized, particle swarm optimization algorithm was prospected for the direction of development in future.
引文
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