人工蜂群算法及其应用的研究
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摘要
如何设计有效的算法,求解科学研究和工程实践中遇到的大量优化问题,一直是众多领域研究的热点.近年来,进化算法在求解不连续、不可微、多峰等复杂优化问题上表现出色,受到了国内外研究人员的广泛关注.目前,进化算法已经在许多领域得到了十分广泛的应用.
人工蜂群算法(Artifcial Bee Colony Algorithm,简称为ABC)是进化算法的一个分支,它主要模拟蜂群的智能采蜜行为.由于该算法具有结构简单、易于实现、参数较少等特点,一经提出便受到众多学者的关注和研究.然而,目前关于人工蜂群算法的研究与应用还处于初级阶段,尚有很多问题有待解决.例如,与其他进化算法类似,标准ABC算法也存在收敛速度慢、对过于复杂的问题可能搜索不到最优解、计算精度不高等问题.针对这些问题,本文以提高算法的通用性、高效性和鲁棒性为主要目标,提出了几种改进的人工蜂群算法,主要工作如下:
1.针对人工蜂群算法的搜索方程探索能力强,开发能力弱的特点,受差分进化算法变异方程的启发,提出了两个新算法ABC/best/1和ABC/best/2.这两个算法的搜索方程只在最优位置附近产生新的候选解,从而提高了算法的开发能力.通过26个测试函数的仿真实验,结果表明ABC/best/1和ABC/best/2性能要优于其他两个人工蜂群算法.
2.为了进一步提高算法的开发能力,提出了一个新的搜索方程.通过该搜索方程产生的候选解不仅围绕在最优解附近,并且搜索方向受最优解的引导,从而大大地提高了算法的开发能力.进一步,为了充分利用和平衡标准ABC搜索方程和所提出搜索方程的探索能力和开发能力,通过引入选择概率进而提出了一个新的人工蜂群算法(MABC).通过28个测试函数的仿真实验,结果表明所提的算法性能优于其他几种比较算法.
3.提出了一个新的ABC改进版本(简称为EABC).在这个算法里,根据采蜜蜂和观察蜂在搜索过程中的侧重点不同,提出了两个不同的搜索方程分别被采蜜蜂和观察蜂用来产生新的候选解.从整体上看,新算法更注重于挖掘问题的特征信息.最后,通过48个测试函数的仿真实验,结果表明EABC性能优于,或至少可与标准的或改进的人工蜂群算法、差分进化算法和粒子优化算法相媲美.同时, EABC在高维测试函数上也表现出了优越的性能.
4.首先,受遗传算法杂交算子的启发,通过设计一个新的搜索方程产生候选解,进而提出一种新的人工蜂群算法(简称为CABC)以提高算法的搜索性能.进一步,为了充分利用搜索空间中的有用信息,通过正交设计构造一个正交学习策略.由于正交学习策略利用了正交设计小样本特性,它可以产生更有前途的候选解.接着,结合正交学习策略提出了一种提高人工蜂群算法搜索性能的通用框架,得到了三种新颖的算法(分别记为OABC、OGABC和OCABC).对22个测试函数的仿真实验,结果验证了新搜索方程和正交学习策略的有效性.通过与几个具有代表性的进化算法比较结果表明,所提出的算法显著地提高了人工蜂群算法的性能.
5.为了解决混沌系统控制与同步问题,提出一种改进的人工蜂群算法(简称为IABC).该算法在ABC/best/1和ABC/rand/1的基础上,引入参数M以提高它们的搜索能力.进一步,为了充分利用这两个搜索方程的优点,克服它们的缺点,按照一定的概率引入这两个搜索方程来产生候选解.以典型He′non Map系统为例进行仿真,验证了IABC算法的有效性与稳定性.
How to design an efcient algorithm to solve the problems in various scientifc andengineering felds is essential in science and real applications. Recently, evolutionary al-gorithms (EAs) have shown considerable success in solving optimization problems charac-terized as nonconvex, discontinuous, nondiferentiable, and so on and attracted more andmore attention in recent years. At present, EAs have been broadly applied to diversifedfelds and the research fruits of EAs have already permeated into many disciplines.
Artifcial bee colony algorithm (ABC), which belongs to the family of EAs, is basedon simulating the foraging behavior of the honeybee swarm. Due to its simplicity, easeof implementation and few parameters, ABC has captured much attention and has beenapplied to solve many practical optimization problems since its invention. However, atpresent, the research and application on artifcial bee colony algorithm is still in primitivestage. There are still many problems to be studied and solved. For example, similar toother EAs, ABC also faces up to the poor convergence and the low calculating accuracyin solving complex optimization problems. To address these concerning issues, someimproved ABCs for global optimization are proposed in the dissertation for the majorpurpose of increasing the universality, efciency and robustness. The main contributionsand original ideals included in the dissertation are summarized as follows:
1. There is still an insufciency in the ABC regarding its solution search equation,which is good at exploration but poor at exploitation. Inspired by diferential evolution(DE), we propose two modifed ABCs (denoted as ABC/best/1and ABC/best/2), whichare based on that each bee searches only around the best solution of the previous iterationin order to improve the exploitation. Experiments are conducted on a set of26benchmarkfunctions. The results demonstrate good performance of ABC/best in solving complexnumerical optimization problems when compared with two ABC based algorithms.
2. In order to further improve the exploitation of the algorithm, a novel solutionsearch equation is proposed. In the new search equation, the generated candidate solu-tion is not only around the best solution, but also its search direction is guided by thebest solution, which results in the strong exploitation. Then, to make full use of and bal-ance the exploration of the solution search equation of ABC and the exploitation of theproposed solution search equation, we introduce a selective probability and get the newsearch mechanism (MABC). Experiments are conducted on a set of28benchmark func-tions. The results demonstrate good performance of MABC in solving complex numerical optimization problems when compared with the others algorithms.
3. A novel ABC method is presented called as EABC to improve the performanceof ABC. In this method, according to diferent emphases of employed bees and onlookersin the search process, two new search equations for solution update of employed bees andonlookers respectively are proposed to balance exploration and exploitation. Overall, thenew version puts more emphasis on exploiting the domain-specifc knowledge. Finally,simulation results show that EABC is better than, or at least comparable to, other classicor modifed ABC, diferential evolution and particle swarm optimization algorithms fromthe literature in terms of convergence performance for a set of48benchmark functions.EABC also shows promising results for relatively high dimensional problems.
4. Inspired by the crossover of genetic algorithm, we frst propose an improvedABC method called as CABC where a modifed search equation is applied to generatea candidate solution to improve the search ability of ABC. Furthermore, we use theorthogonal experimental design (OED) to form an orthogonal learning (OL) strategy forvariant ABCs to discover more useful information from the search experiences. Owing toOED’s good character of sampling a small number of well representative combinations fortesting, the OL strategy can construct a more promising and efcient candidate solution.In this paper, the OL strategy is applied to three versions of ABC, i.e., the standardABC, global-best-guided ABC (GABC), and CABC, which yields OABC, OGABC, andOCABC, respectively. The experimental results on a set of22benchmark functionsdemonstrate the efectiveness and efciency of the modifed search equation and the OLstrategy. The comparisons with some other ABCs and several state-of-the-art algorithmsshow that the proposed algorithms signifcantly improve the performance of ABC.
5. To solve the control and synchronization problems of chaotic dynamical systems,we propose an improved ABC (IABC). In IABC, a parameter M is applied to ABC/rand/1and ABC/best/1. Then, in order to take advantage of them and avoid the shortages ofthem, we use a selective probability to control the frequency of introducing ABC/rand/1and ABC/best/1and get a new search mechanism. Numerical simulation based on He′nonMap and comparisons with some typical existing algorithms demonstrate the efectivenessand robustness of the proposed approach.
人工蜂群算法(Artifcial Bee Colony Algorithm,简称为ABC)是进化算法的一个分支,它主要模拟蜂群的智能采蜜行为.由于该算法具有结构简单、易于实现、参数较少等特点,一经提出便受到众多学者的关注和研究.然而,目前关于人工蜂群算法的研究与应用还处于初级阶段,尚有很多问题有待解决.例如,与其他进化算法类似,标准ABC算法也存在收敛速度慢、对过于复杂的问题可能搜索不到最优解、计算精度不高等问题.针对这些问题,本文以提高算法的通用性、高效性和鲁棒性为主要目标,提出了几种改进的人工蜂群算法,主要工作如下:
1.针对人工蜂群算法的搜索方程探索能力强,开发能力弱的特点,受差分进化算法变异方程的启发,提出了两个新算法ABC/best/1和ABC/best/2.这两个算法的搜索方程只在最优位置附近产生新的候选解,从而提高了算法的开发能力.通过26个测试函数的仿真实验,结果表明ABC/best/1和ABC/best/2性能要优于其他两个人工蜂群算法.
2.为了进一步提高算法的开发能力,提出了一个新的搜索方程.通过该搜索方程产生的候选解不仅围绕在最优解附近,并且搜索方向受最优解的引导,从而大大地提高了算法的开发能力.进一步,为了充分利用和平衡标准ABC搜索方程和所提出搜索方程的探索能力和开发能力,通过引入选择概率进而提出了一个新的人工蜂群算法(MABC).通过28个测试函数的仿真实验,结果表明所提的算法性能优于其他几种比较算法.
3.提出了一个新的ABC改进版本(简称为EABC).在这个算法里,根据采蜜蜂和观察蜂在搜索过程中的侧重点不同,提出了两个不同的搜索方程分别被采蜜蜂和观察蜂用来产生新的候选解.从整体上看,新算法更注重于挖掘问题的特征信息.最后,通过48个测试函数的仿真实验,结果表明EABC性能优于,或至少可与标准的或改进的人工蜂群算法、差分进化算法和粒子优化算法相媲美.同时, EABC在高维测试函数上也表现出了优越的性能.
4.首先,受遗传算法杂交算子的启发,通过设计一个新的搜索方程产生候选解,进而提出一种新的人工蜂群算法(简称为CABC)以提高算法的搜索性能.进一步,为了充分利用搜索空间中的有用信息,通过正交设计构造一个正交学习策略.由于正交学习策略利用了正交设计小样本特性,它可以产生更有前途的候选解.接着,结合正交学习策略提出了一种提高人工蜂群算法搜索性能的通用框架,得到了三种新颖的算法(分别记为OABC、OGABC和OCABC).对22个测试函数的仿真实验,结果验证了新搜索方程和正交学习策略的有效性.通过与几个具有代表性的进化算法比较结果表明,所提出的算法显著地提高了人工蜂群算法的性能.
5.为了解决混沌系统控制与同步问题,提出一种改进的人工蜂群算法(简称为IABC).该算法在ABC/best/1和ABC/rand/1的基础上,引入参数M以提高它们的搜索能力.进一步,为了充分利用这两个搜索方程的优点,克服它们的缺点,按照一定的概率引入这两个搜索方程来产生候选解.以典型He′non Map系统为例进行仿真,验证了IABC算法的有效性与稳定性.
How to design an efcient algorithm to solve the problems in various scientifc andengineering felds is essential in science and real applications. Recently, evolutionary al-gorithms (EAs) have shown considerable success in solving optimization problems charac-terized as nonconvex, discontinuous, nondiferentiable, and so on and attracted more andmore attention in recent years. At present, EAs have been broadly applied to diversifedfelds and the research fruits of EAs have already permeated into many disciplines.
Artifcial bee colony algorithm (ABC), which belongs to the family of EAs, is basedon simulating the foraging behavior of the honeybee swarm. Due to its simplicity, easeof implementation and few parameters, ABC has captured much attention and has beenapplied to solve many practical optimization problems since its invention. However, atpresent, the research and application on artifcial bee colony algorithm is still in primitivestage. There are still many problems to be studied and solved. For example, similar toother EAs, ABC also faces up to the poor convergence and the low calculating accuracyin solving complex optimization problems. To address these concerning issues, someimproved ABCs for global optimization are proposed in the dissertation for the majorpurpose of increasing the universality, efciency and robustness. The main contributionsand original ideals included in the dissertation are summarized as follows:
1. There is still an insufciency in the ABC regarding its solution search equation,which is good at exploration but poor at exploitation. Inspired by diferential evolution(DE), we propose two modifed ABCs (denoted as ABC/best/1and ABC/best/2), whichare based on that each bee searches only around the best solution of the previous iterationin order to improve the exploitation. Experiments are conducted on a set of26benchmarkfunctions. The results demonstrate good performance of ABC/best in solving complexnumerical optimization problems when compared with two ABC based algorithms.
2. In order to further improve the exploitation of the algorithm, a novel solutionsearch equation is proposed. In the new search equation, the generated candidate solu-tion is not only around the best solution, but also its search direction is guided by thebest solution, which results in the strong exploitation. Then, to make full use of and bal-ance the exploration of the solution search equation of ABC and the exploitation of theproposed solution search equation, we introduce a selective probability and get the newsearch mechanism (MABC). Experiments are conducted on a set of28benchmark func-tions. The results demonstrate good performance of MABC in solving complex numerical optimization problems when compared with the others algorithms.
3. A novel ABC method is presented called as EABC to improve the performanceof ABC. In this method, according to diferent emphases of employed bees and onlookersin the search process, two new search equations for solution update of employed bees andonlookers respectively are proposed to balance exploration and exploitation. Overall, thenew version puts more emphasis on exploiting the domain-specifc knowledge. Finally,simulation results show that EABC is better than, or at least comparable to, other classicor modifed ABC, diferential evolution and particle swarm optimization algorithms fromthe literature in terms of convergence performance for a set of48benchmark functions.EABC also shows promising results for relatively high dimensional problems.
4. Inspired by the crossover of genetic algorithm, we frst propose an improvedABC method called as CABC where a modifed search equation is applied to generatea candidate solution to improve the search ability of ABC. Furthermore, we use theorthogonal experimental design (OED) to form an orthogonal learning (OL) strategy forvariant ABCs to discover more useful information from the search experiences. Owing toOED’s good character of sampling a small number of well representative combinations fortesting, the OL strategy can construct a more promising and efcient candidate solution.In this paper, the OL strategy is applied to three versions of ABC, i.e., the standardABC, global-best-guided ABC (GABC), and CABC, which yields OABC, OGABC, andOCABC, respectively. The experimental results on a set of22benchmark functionsdemonstrate the efectiveness and efciency of the modifed search equation and the OLstrategy. The comparisons with some other ABCs and several state-of-the-art algorithmsshow that the proposed algorithms signifcantly improve the performance of ABC.
5. To solve the control and synchronization problems of chaotic dynamical systems,we propose an improved ABC (IABC). In IABC, a parameter M is applied to ABC/rand/1and ABC/best/1. Then, in order to take advantage of them and avoid the shortages ofthem, we use a selective probability to control the frequency of introducing ABC/rand/1and ABC/best/1and get a new search mechanism. Numerical simulation based on He′nonMap and comparisons with some typical existing algorithms demonstrate the efectivenessand robustness of the proposed approach.
引文
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