细菌觅食优化算法的改进及应用研究
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摘要
在实际生产和生活中,优化无处不在,力学中的优化问题也比比皆是,尤其是在工程力学中,许多问题都伴随着反问题。而反问题的求解,一般是利用建立泛函求极小值的方法,这就需要用到优化算法。传统的优化方法总有着计算效率低和局部搜索的局限性。随着人类生存空间的扩大,实际工程中的力学问题越来越复杂,传统的优化算法已不再满足求解精度和效率的要求,因此,对高效的智能优化方法的需求日益迫切。近年来,遗传算法、蚁群算法、粒子群算法等智能优化方法正逐渐被应用于力学中包括反问题在内的各类优化问题。细菌觅食优化算法(BFO)是近些年来发展起来的,基于大肠杆菌觅食行为模型的一种新型智能算法。它具有对初值和参数选择不敏感、鲁棒性强、简单易于实现,以及并行处理和全局搜索等优点。
由于对BFO算法的研究尚处于起步阶段,BFO的应用还不够深入且它在应用过程中也存在精度不够高、收敛速度不够快的缺点,尤其是在多峰问题寻优时难以找到全部最优解。因此,分析、研究和改进BFO算法以及拓展、深入其应用,对生产、生活中各个领域的优化问题求解都具有十分重要的意义。为此,本文着重从BFO算法的改进和应用方面进行了研究。主要研究工作如下：
(1)针对BFO易早熟和收敛速度慢等缺陷,本文对标准BFO算法的操作进行了三项改进：在趋向操作中,通过赋予细菌灵敏度的概念来改变细菌的游动步长；在复制操作中,嵌入分布估计思想；在迁徙操作中,提出自适应迁徙概率,进而提出了一种较全面的细菌觅食优化改进算法——分布估计细菌觅食优化算法(EDA-BFO),显著提高了算法的运行效率和求解质量,为解决复杂寻优问题提供了有效方法。通过函数优化测试验证,表明该算法是可行和有效的,编码后适用于解决高维复杂工程的相应优化问题。
(2)针对BFO在多峰问题寻优时难以找到全部最优解及精度不高的问题,提出了一种基于小生境技术的细菌觅食算法(NBFO)。该算法避免了因聚集行为不当而导致的细菌在非全局极值点处大量聚集的局限性,维护了群体的多样性,并提高了算法的全局搜索能力。典型多峰值测试函数的求解试验表明：小生境细菌觅食优化算法有更强的全局搜索能力和更高的收敛速度,能够高效地寻找到多个全局最优值,是一种寻优能力、效率和可靠性更高的优化算法,其综合性能比标准细菌觅食算法有显著提高。
(3)针对标准BFO算法的收敛速度不够快的缺点,考虑到遗传算法具有大范围快速搜索能力,本文将遗传算法和细菌觅食算法相结合,提出了遗传-细菌觅食混合优化算法(GA-BFO算法)。函数的优化测试结果表明,对于复杂的多维函数优化问题,GA-BFO混合算法无论在时间效率上还是在求解精度上,均优于两个单一算法,获得了优化性能和时间性能的双赢。
(4)针对标准BFO算法的全局收敛能力不如PSO的情形,将PSO算法作为一个变异算子引入BFO算法的聚集操作中,提出一种混合的粒子群-细菌觅食优化算法(PSO-BFO),充分发挥BFO算法的局部搜索能力和PSO算法的全局搜索能力,令两个单一算法相互取长补短、优势互补。函数的优化测试结果表明,对于复杂的多维函数优化问题,PSO-BFO混合算法是有效的,且在全局收敛可靠性和收敛速度方面明显地优于BFO和PSO算法这两个单一算法。
(5)由于EDA-BFO算法具有较强的全局搜索能力,同时具有较高的精度、模型简单、计算复杂度低、不易陷入局部最优解等优点,本文在BP神经网络的训练中嵌入EDA-BFO算法的复制和迁徙操作,提出了一种改进的BP神经网络模型(BFO-BP神经网络模型),用它来优化神经网络连接权值。为检验所提出的改进模型的优越性,将BFO-BP神经网络模型和BP神经网络模型同时应用于力学经典反问题——复合材料的损伤定位的数值仿真研究,并将两种模型的研究结果进行了对比。仿真结果表明：BFO-BP神经网络模型的损伤定位识别精度比BP神经网络模型的损伤定位识别精度高；在处理具有不确定信息的损伤定位领域中,BFO-BP神经网络模型具有良好的发展前景。
(6)混沌系统参数辨识在对参数未知、参数不匹配等混沌系统的控制和同步中占有相当重要的地位,但目前的研究还比较薄弱,方法不多。本文提出了基于BFO的动力系统参数辨识的具体算法,为了检验BFO进行动力学系统参数辨识的有效性和可行性,分别对Lorenz和Chen无噪声的混沌系统和有噪声的混沌系统进行计算机数值仿真研究。结果表明BFO算法能有效地辨识无噪声混沌系统的参数,此外,BFO算法在添加了白噪声的混沌系统参数辨识中,相对PSO算法和GA算法而言,仍具有更高的辨识精度和更强的抗噪声能力。
Optimization is involved in every aspect of production and practical-life activities as well as Mechanics. Especially, in the field of engineering mechanics, plenty problems come along with the inverse problems. Optimization algorithms are often used in the general way of solving inverse problems--establishing functional along with minimization process. The weakness of the traditional optimization algorithm is the limitations of lower computing efficiency and local searching techniques. Mechanics problems in the practical engineering is becoming more and more sophisticated and complicated which makes tradition algorithm incompatible with the demand of the accuracy and efficiency. Therefore, it is urgent to develop new intelligent algorithm that is more efficient than ever. In recent years, intelligent optimization method such as genetic algorithm, ant colony optimization, particle swarm optimization etc. are wildly applied in the inverse problems of mechanics. Bacterial Foraging Optimization (BFO) is one of the new intelligent optimization methods that are based on the simulation of the foraging of Escherichia coli. The advantage of BFO is the insensitivity of parameter choosing, robustness, parallel computing and easily global searching.
Researches of BFO remain initiation, and during the superficial application the weakness of relatively low accuracy and rate of convergence is discovered. Especially coping with the multi-model function optimization problems, it is difficult for BFO to discover all the optimal solutions at once. Therefore, it is highly important to thoroughly apply the BFO into the living and production, analyze and improve the original algorithm of BFO. This thesis focus mainly on the melioration and application of BFO and the major works are listed below:
(1) To remove the defects of prematurity and low rate of convergence,3modifications were added to the standard BFO:In the Chemotaxis process, change the step length of the bacterial with the bacterial sensitivities; During the process of swarming process, attach each bacterial the probability of adaptive migration, and generate a more comprehensive improved algorithm:Estimated Distribution Algorithm of BFO (EDA-BFO), which can ameliorate the computing efficiency and solution quality significantly and might provide an effective way of solving complex optimization problems. After applied to the test functions, EDA-BFO is proved to be feasible and effective, and can be coded to solve high-dimensional optimization problems in practical engineering.
(2) As for the low accuracy of finding out all optimal solutions with multi-method functions, Niched Bacterial Foraging Optimization is performed. Niched techniques can relatively avoid bacteria's chemotaxis, which may lead to gathering in the non-global extreme point, maintain the divergence of the bacterial and thus improve the capability of global searching. With the simulated optimization experiment with typical test functions, NBFO can generate a better searching ability globally and higher rate of convergence. NBFO is able to tracing multiple optimal solutions with higher accuracy and rate of convergence; its overall performance is significantly enhanced than the standard algorithm.
(3) For the weakness of low rate of convergence, and considering the genetic algorithm is able to search in large scale, a hybrid algorithm of GA and BFO (GA-BFO) is given in this thesis. Being applied to sophisticated high-dimensional test functions, both higher time-efficiency and solution accuracy is obtained.
(4) Considering the global convergence rate of BFO has no competence with PSO, an improvement of handling PSO as a mutation operator is given to combine the two algorithms--PSO and BFO in order to give full play of the ability for searching locally with BFO and globally with PSO. The mixed algorithm (PSO-BFO) is able to make the best of both optimization method and is proved to be effective after testing on the practical functions for its reliability of global convergence and rate of convergence, which are obviously more prominent than standard BFO or PSO.
(5) Due to the better global searching ability of EDA-BFO, as well as the merit of high accuracy, simple modeling, low complexity of computing and unable of sinking into local extreme point, the operation of reproduction and swarming process is inserted into the standard BP network training, then an ameliorated BP network modal (BFO-BP) is generated, with optimized network connection weight. BFO-BP is applied into the simulation research of a classical inverse problem in mechanic--locating damage of compound material and the result is compared with control. Results say:BFO-BP's location of damage is highly accurate than the other, therefore BFO-BP network model possess potential in the field of locating damage of unknown.
(6) Chaos system parameter identification plays a major role in the control and synchronism of chaos system, which contains unknown or unmatched parameters. Research on this field is superficial with no effective method. This thesis put forward a specific algorithm of identifying parameters of dynamical systems based on BFO in order to examine the validity and feasibility of BFO in PID of dynamical system. In practical research, numerical simulation of Lorenz&Chen non-noise chaos system and noise chaos systems are studied. Results show that BFO algorithm can effectively distinguish the parameters in the chaos systems without noise; meanwhile, BFO also has a superior ability of accurate identification of parameters in the chaos systems with white noise than PSO and GA.
由于对BFO算法的研究尚处于起步阶段,BFO的应用还不够深入且它在应用过程中也存在精度不够高、收敛速度不够快的缺点,尤其是在多峰问题寻优时难以找到全部最优解。因此,分析、研究和改进BFO算法以及拓展、深入其应用,对生产、生活中各个领域的优化问题求解都具有十分重要的意义。为此,本文着重从BFO算法的改进和应用方面进行了研究。主要研究工作如下：
(1)针对BFO易早熟和收敛速度慢等缺陷,本文对标准BFO算法的操作进行了三项改进：在趋向操作中,通过赋予细菌灵敏度的概念来改变细菌的游动步长；在复制操作中,嵌入分布估计思想；在迁徙操作中,提出自适应迁徙概率,进而提出了一种较全面的细菌觅食优化改进算法——分布估计细菌觅食优化算法(EDA-BFO),显著提高了算法的运行效率和求解质量,为解决复杂寻优问题提供了有效方法。通过函数优化测试验证,表明该算法是可行和有效的,编码后适用于解决高维复杂工程的相应优化问题。
(2)针对BFO在多峰问题寻优时难以找到全部最优解及精度不高的问题,提出了一种基于小生境技术的细菌觅食算法(NBFO)。该算法避免了因聚集行为不当而导致的细菌在非全局极值点处大量聚集的局限性,维护了群体的多样性,并提高了算法的全局搜索能力。典型多峰值测试函数的求解试验表明：小生境细菌觅食优化算法有更强的全局搜索能力和更高的收敛速度,能够高效地寻找到多个全局最优值,是一种寻优能力、效率和可靠性更高的优化算法,其综合性能比标准细菌觅食算法有显著提高。
(3)针对标准BFO算法的收敛速度不够快的缺点,考虑到遗传算法具有大范围快速搜索能力,本文将遗传算法和细菌觅食算法相结合,提出了遗传-细菌觅食混合优化算法(GA-BFO算法)。函数的优化测试结果表明,对于复杂的多维函数优化问题,GA-BFO混合算法无论在时间效率上还是在求解精度上,均优于两个单一算法,获得了优化性能和时间性能的双赢。
(4)针对标准BFO算法的全局收敛能力不如PSO的情形,将PSO算法作为一个变异算子引入BFO算法的聚集操作中,提出一种混合的粒子群-细菌觅食优化算法(PSO-BFO),充分发挥BFO算法的局部搜索能力和PSO算法的全局搜索能力,令两个单一算法相互取长补短、优势互补。函数的优化测试结果表明,对于复杂的多维函数优化问题,PSO-BFO混合算法是有效的,且在全局收敛可靠性和收敛速度方面明显地优于BFO和PSO算法这两个单一算法。
(5)由于EDA-BFO算法具有较强的全局搜索能力,同时具有较高的精度、模型简单、计算复杂度低、不易陷入局部最优解等优点,本文在BP神经网络的训练中嵌入EDA-BFO算法的复制和迁徙操作,提出了一种改进的BP神经网络模型(BFO-BP神经网络模型),用它来优化神经网络连接权值。为检验所提出的改进模型的优越性,将BFO-BP神经网络模型和BP神经网络模型同时应用于力学经典反问题——复合材料的损伤定位的数值仿真研究,并将两种模型的研究结果进行了对比。仿真结果表明：BFO-BP神经网络模型的损伤定位识别精度比BP神经网络模型的损伤定位识别精度高；在处理具有不确定信息的损伤定位领域中,BFO-BP神经网络模型具有良好的发展前景。
(6)混沌系统参数辨识在对参数未知、参数不匹配等混沌系统的控制和同步中占有相当重要的地位,但目前的研究还比较薄弱,方法不多。本文提出了基于BFO的动力系统参数辨识的具体算法,为了检验BFO进行动力学系统参数辨识的有效性和可行性,分别对Lorenz和Chen无噪声的混沌系统和有噪声的混沌系统进行计算机数值仿真研究。结果表明BFO算法能有效地辨识无噪声混沌系统的参数,此外,BFO算法在添加了白噪声的混沌系统参数辨识中,相对PSO算法和GA算法而言,仍具有更高的辨识精度和更强的抗噪声能力。
Optimization is involved in every aspect of production and practical-life activities as well as Mechanics. Especially, in the field of engineering mechanics, plenty problems come along with the inverse problems. Optimization algorithms are often used in the general way of solving inverse problems--establishing functional along with minimization process. The weakness of the traditional optimization algorithm is the limitations of lower computing efficiency and local searching techniques. Mechanics problems in the practical engineering is becoming more and more sophisticated and complicated which makes tradition algorithm incompatible with the demand of the accuracy and efficiency. Therefore, it is urgent to develop new intelligent algorithm that is more efficient than ever. In recent years, intelligent optimization method such as genetic algorithm, ant colony optimization, particle swarm optimization etc. are wildly applied in the inverse problems of mechanics. Bacterial Foraging Optimization (BFO) is one of the new intelligent optimization methods that are based on the simulation of the foraging of Escherichia coli. The advantage of BFO is the insensitivity of parameter choosing, robustness, parallel computing and easily global searching.
Researches of BFO remain initiation, and during the superficial application the weakness of relatively low accuracy and rate of convergence is discovered. Especially coping with the multi-model function optimization problems, it is difficult for BFO to discover all the optimal solutions at once. Therefore, it is highly important to thoroughly apply the BFO into the living and production, analyze and improve the original algorithm of BFO. This thesis focus mainly on the melioration and application of BFO and the major works are listed below:
(1) To remove the defects of prematurity and low rate of convergence,3modifications were added to the standard BFO:In the Chemotaxis process, change the step length of the bacterial with the bacterial sensitivities; During the process of swarming process, attach each bacterial the probability of adaptive migration, and generate a more comprehensive improved algorithm:Estimated Distribution Algorithm of BFO (EDA-BFO), which can ameliorate the computing efficiency and solution quality significantly and might provide an effective way of solving complex optimization problems. After applied to the test functions, EDA-BFO is proved to be feasible and effective, and can be coded to solve high-dimensional optimization problems in practical engineering.
(2) As for the low accuracy of finding out all optimal solutions with multi-method functions, Niched Bacterial Foraging Optimization is performed. Niched techniques can relatively avoid bacteria's chemotaxis, which may lead to gathering in the non-global extreme point, maintain the divergence of the bacterial and thus improve the capability of global searching. With the simulated optimization experiment with typical test functions, NBFO can generate a better searching ability globally and higher rate of convergence. NBFO is able to tracing multiple optimal solutions with higher accuracy and rate of convergence; its overall performance is significantly enhanced than the standard algorithm.
(3) For the weakness of low rate of convergence, and considering the genetic algorithm is able to search in large scale, a hybrid algorithm of GA and BFO (GA-BFO) is given in this thesis. Being applied to sophisticated high-dimensional test functions, both higher time-efficiency and solution accuracy is obtained.
(4) Considering the global convergence rate of BFO has no competence with PSO, an improvement of handling PSO as a mutation operator is given to combine the two algorithms--PSO and BFO in order to give full play of the ability for searching locally with BFO and globally with PSO. The mixed algorithm (PSO-BFO) is able to make the best of both optimization method and is proved to be effective after testing on the practical functions for its reliability of global convergence and rate of convergence, which are obviously more prominent than standard BFO or PSO.
(5) Due to the better global searching ability of EDA-BFO, as well as the merit of high accuracy, simple modeling, low complexity of computing and unable of sinking into local extreme point, the operation of reproduction and swarming process is inserted into the standard BP network training, then an ameliorated BP network modal (BFO-BP) is generated, with optimized network connection weight. BFO-BP is applied into the simulation research of a classical inverse problem in mechanic--locating damage of compound material and the result is compared with control. Results say:BFO-BP's location of damage is highly accurate than the other, therefore BFO-BP network model possess potential in the field of locating damage of unknown.
(6) Chaos system parameter identification plays a major role in the control and synchronism of chaos system, which contains unknown or unmatched parameters. Research on this field is superficial with no effective method. This thesis put forward a specific algorithm of identifying parameters of dynamical systems based on BFO in order to examine the validity and feasibility of BFO in PID of dynamical system. In practical research, numerical simulation of Lorenz&Chen non-noise chaos system and noise chaos systems are studied. Results show that BFO algorithm can effectively distinguish the parameters in the chaos systems without noise; meanwhile, BFO also has a superior ability of accurate identification of parameters in the chaos systems with white noise than PSO and GA.
引文
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