人工蜂群算法的研究与应用
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摘要
人工蜂群算法(Artificial Bee Colony algorithm, ABC)是2005年提出的一种新型群智能优化算法，并广泛应用于人工神经网络训练、滤波器设计、认知无线电和盲信号分离等众多领域，均取得了良好应用效果，使其成为目前最有前景的进化算法之一。然而，与其他进化算法的发展一样，在研究初期，存在大量问题需要研究，例如提高算法在各种优化问题上的求解性能、拓展算法的应用范围等。
本课题为完善ABC算法的理论体系，针对算法存在的问题，从理论和应用两方面对其进行深入研究。在理论研究方面，针对各种典型优化问题展开研究，一方面，改进ABC算法内在运行机制，力图提高算法在高维复杂单目标优化、二目标优化以及约束多目标优化问题上的求解性能；另一方面，尝试引入其他机制，使算法能够处理多峰函数优化和高维多目标优化问题，并取得令人较为满意的效果。在实际应用方面，将ABC算法应用到面向三维感知的无线多媒体传感器网络的全目标覆盖问题中，取得了良好效果。具体如下：
第一，针对ABC算法在求解复杂单目标函数优化问题时仍存在易陷入局部最优、收敛速度慢等问题，对其内在运行机制进行深入研究：为尽量避免算法陷入局部最优，为跟随蜂设计新的概率选择模型代替原有较为贪婪的较优个体选择方式，并设计反向学习变异策略代替侦察蜂行为；为在保证种群多样性的同时尽量提高收敛速度，在跟随蜂和引领蜂的搜索中加入方向性搜索信息，设计新的搜索策略，综合以上改进提出一种改进人工蜂群算法。实验仿真结果表明该改进算法性能优于现有四种算法。
第二，针对ABC算法目前尚不能处理多峰优化问题，通过大量实验研究，结合小生境技术，尝试提出一种小生境人工蜂群算法。一方面，为使算法尽可能多的搜索到多峰函数的极值解，做如下四方面工作：1、改进原有的小生境模型，增强算法对各个峰的辨识能力；2、建立新的引领蜂个体保留方式、利用排挤机制确定迭代种群，使算法不止收敛于单个最优峰，增强算法集聚于各个峰的能力；3、改进跟随蜂在选择较优蜜源时原有的较为贪婪的选择方式，扩大种群多样性；4、建立外部种群记录搜索过程中的已得极值解，避免搜索造成峰值点丢失的情况。另一方面，为尽量提高搜索精度，改进原有依靠个体适应度值判断个体优劣的评判标准，结合小生境技术在峰内判断个体优劣，加强个体在峰内的搜索。仿真结果表明该算法能较为准确地识别各个峰。
第三，针对现有基于ABC算法的二目标优化算法的收敛性和分布性有待提高的问题，以NSGA-II作为二目标算法的主体框架、ABC执行进化操作，提出二目标人工蜂群算法。主要改进措施包括：1、设计新的精英种群确定方式，改善最优解集的分布性；2、根据二目标的特点，设计新的搜索策略，加快算法收敛到最优Pareto前沿的速度。标准测试函数上的实验结果显示，该算法能够稳定有效地找到Pareto最优解集并同时保证良好分布性，其相关性能指标超过国内外多个先进二目标进化算法。
第四，针对目前ABC算法尚无法解决高维多目标优化问题的情况，尝试提出一种以ABC执行主体进化策略的高维多目标算法。首先，将高维多目标问题转化成单目标问题，加大收敛动力；其次，根据高维多目标问题的特点，改进跟随蜂选择较优个体时较为贪婪的选择方式，为侦察蜂设计新的搜索策略，加强对非支配解的探索能力；最后，提出新的分布性维护方法，避免解集覆盖不完整、分布不均匀。实验证实该算法收敛性和分布性效果良好，且解集覆盖范围广。
第五，针对现有基于ABC算法的约束多目标算法性能较差的问题，采用建立外部种群分别存储优秀可行解和不可行解的方式处理约束条件，利用ABC算法执行进化操作，并借助优秀可行解和不可行解的方向性引导信息增强算法对解的探索能力，建立新的搜索方式，提出基于ABC算法的约束多目标算法。在CTP类测试函数上的仿真结果显示，相对于现有几种约束多目标优化算法，本课题提出的约束多目标算法能够获得更优的分布性和收敛性效果。
第六，为解决面向三维感知的多媒体传感器网络的全目标覆盖问题，提出基于人工蜂群算法的通用全目标覆盖算法：一方面，改进现有的三维感知模型，并通过公式推导得到最优仰俯角的计算公式，利用改进ABC算法进行求解；另一方面，建立偏向角调配方案的数学模型以降低算法复杂度，并改进ABC算法实现偏向角的最优调配。实验仿真结果表明该算法能够有效解决全目标覆盖问题。
Artificial Bee Colony algorithm (ABC) proposed in2005is one of the current bestevolutionary algorithms, which has become the research hotspot in many fields such asevolutionary computing and intelligent optimization. At present, ABC has successfully beenapplied to diverse domains of science and engineering, such as neural network optimization,filter design, cognitive radio, and blind signal separation. However, almost all of theevolutionary algorithms, including ABC, still suffer from the problems of prematureconvergence, slow convergence rate and difficult parameter setting, especially in optimizinghigh-dimensional complex optimization problems. In addition, the standard ABC algorithmcan't be used directly to solve the multimodal function optimization problems and thisshortcoming limits the scope of application of ABC to some extent.
According to the insufficiency of ABC, it is deeply investigated from theory andapplication aspects in this paper. In theory, according to a series of optimization problems,including high-dimensional complex single objective optimization problem, multimodalfunction optimization, two objective optimization problem, many objective optimizationproblem and constrained multi-objective optimization problems, the structure and key steps ofthe algorithm are improved to improve its optimal performance in every optimization problem.In application, the improved ABC algorithm is applied successfully to solve a frontiercoverage-all targets problem for directional sensor networks based on three-dimensionalperception, Concrete contents is as follows.
Firstly, according to ABC still suffer from the problems of premature convergence, slowconvergence rate and slow convergence speed at a later time in optimizing high-dimensionalcomplex single objective optimization problem, the inherent operation mechanism of ABCare deeply investigated. An improved artificial bee colony algorithm was proposed to improvethe optimization performance. Concrete improvement measures in the improved ABCalgorithm include:1、considering the method of choosing the excellent individual ofemployed bees is too greedy, a new probability choice model is proposed to increasepopulation diversity;2、A new searching method is designed, in which the better individualsare utilized to guide the search direction synchronously, to ensure the population diversity andimprove convergence speed;3、considering the parameter of controlling the behavior of the scout bees is difficult to set and has a greater impact on the algorithm, the new searchingmodel of scouts is proposed. Experimental results show that the proposed algorithmoutperform several state-of-the-art optimization algorithms in terms of the main performanceindexes.
Secondly, in order to improve multimodal evolutionary algorithms, a niche artificial beecolony algorithm is proposed combining ABC and the niche technology based on a lot ofexperiments. On the one hand, the traditional niche model is improved to increase populationdiversity and enhance the capacity of identifying every peak. On the other hand, according tomultimodal optimization problems, concrete improvement measures in NABC include:1、considering the method of choosing the excellent individual of employed bees is too greedy, anew probability choice model is proposed to increase population diversity;2、the traditionalevaluation criteria of judging superiority and inferiority individual depending on individualfitness value is improved, a new evaluation method combining the niche technology isproposed to strengthen the searching ability of individuals in every peak;3、in order to avoidthe phenomenon of losing the peak points because of population diversity deficiency, theexternal population is established to record the acquired peak points. Experimental resultsshow that the proposed algorithm can identify each peak accurately.
Thirdly, in order to improve the performance of convergence and distribution ofmulti-objective evolutionary algorithms, a multi-objective optimization algorithm based onartificial bee colony algorithm is proposed, in which NSGA-II is taken as the main frameworkof two targets evolutionary algorithm and evolutionary operation is implemented by ABC.Concrete improvement measures in the proposed algorithm include:1、the method ofascertaining elite population is designed to improve the distribution of the optimal solutionsets;2、according to characteristic of two targets optimization problems, new searchingmethod is designed to accelerate the converges speed to the optimal Pareto front.Experimental results on ZDT show that, the proposed algorithm can get Pareto optimalsolutions effectively with good distribution performance, all of its performance indexes arebetter than or at least comparable to several existing state-of-the-art MOEAs.
Fourthly, in order to improve the performance of many objective evolutionary algorithms,a many objective evolutionary algorithm based on artificial bee colony algorithm is proposedin this paper. Concrete improvement measures in the proposed algorithm include:1、many objective optimization problem is transformed to single objective optimization problem toincrease the power of convergence;2、 according to characteristic of many objectiveoptimization problems, new searching method is designed to form an improved ABC, andevolutionary operation is implemented by an improved ABC;3、a new diversity maintenancemethod is established to improve distributivity performance. Experimental results show that,the proposed algorithm can get Pareto optimal solutions effectively with good distribution andconvergence performance and with a wide coverage area.
Fifthly, considering that the performance of constrained multi-objective evolutionaryalgorithms, a constrained multi-objective optimization algorithm based on ABC is proposedin this paper. Concrete improvement measures in the proposed algorithm include:firstly,external populations are constructed to store feasible solutions and infeasible solutionsrespectively to handle constraint conditions, the update method of feasible solution set isimproved to distribution of solution set effectively. Secondly, ABC is utilized as theevolutionary strategy, new searching strategy is proposed, in which the excellent feasible andinfeasible solutions are utilized to improve exploration ability. Experimental results on CTPtest functions demonstrate that the proposed algorithm can achieve better diversity of Paretosolutions and convergence performance than or at least comparable to several existingstate-of-the-art CMOEAs.
Sixthly, in order to solve coverage-all targets for wireless directional sensor networksbased on three-dimensional perception model, a universal coverage-all targets algorithm isproposed. On the one hand, the present three-dimensional perception model is improved, andthe calculation formula of the optimal elevation angle is derivate by deep mathematicalanalysis, which is solved by an improved ABC. On the other hand, the mathematical model ofallocation scheme of deviation angle is established to reduce the complexity, and which issolved by an improved ABC. Experimental results show that this algorithm can solvecoverage-all targets efficiently.
本课题为完善ABC算法的理论体系，针对算法存在的问题，从理论和应用两方面对其进行深入研究。在理论研究方面，针对各种典型优化问题展开研究，一方面，改进ABC算法内在运行机制，力图提高算法在高维复杂单目标优化、二目标优化以及约束多目标优化问题上的求解性能；另一方面，尝试引入其他机制，使算法能够处理多峰函数优化和高维多目标优化问题，并取得令人较为满意的效果。在实际应用方面，将ABC算法应用到面向三维感知的无线多媒体传感器网络的全目标覆盖问题中，取得了良好效果。具体如下：
第一，针对ABC算法在求解复杂单目标函数优化问题时仍存在易陷入局部最优、收敛速度慢等问题，对其内在运行机制进行深入研究：为尽量避免算法陷入局部最优，为跟随蜂设计新的概率选择模型代替原有较为贪婪的较优个体选择方式，并设计反向学习变异策略代替侦察蜂行为；为在保证种群多样性的同时尽量提高收敛速度，在跟随蜂和引领蜂的搜索中加入方向性搜索信息，设计新的搜索策略，综合以上改进提出一种改进人工蜂群算法。实验仿真结果表明该改进算法性能优于现有四种算法。
第二，针对ABC算法目前尚不能处理多峰优化问题，通过大量实验研究，结合小生境技术，尝试提出一种小生境人工蜂群算法。一方面，为使算法尽可能多的搜索到多峰函数的极值解，做如下四方面工作：1、改进原有的小生境模型，增强算法对各个峰的辨识能力；2、建立新的引领蜂个体保留方式、利用排挤机制确定迭代种群，使算法不止收敛于单个最优峰，增强算法集聚于各个峰的能力；3、改进跟随蜂在选择较优蜜源时原有的较为贪婪的选择方式，扩大种群多样性；4、建立外部种群记录搜索过程中的已得极值解，避免搜索造成峰值点丢失的情况。另一方面，为尽量提高搜索精度，改进原有依靠个体适应度值判断个体优劣的评判标准，结合小生境技术在峰内判断个体优劣，加强个体在峰内的搜索。仿真结果表明该算法能较为准确地识别各个峰。
第三，针对现有基于ABC算法的二目标优化算法的收敛性和分布性有待提高的问题，以NSGA-II作为二目标算法的主体框架、ABC执行进化操作，提出二目标人工蜂群算法。主要改进措施包括：1、设计新的精英种群确定方式，改善最优解集的分布性；2、根据二目标的特点，设计新的搜索策略，加快算法收敛到最优Pareto前沿的速度。标准测试函数上的实验结果显示，该算法能够稳定有效地找到Pareto最优解集并同时保证良好分布性，其相关性能指标超过国内外多个先进二目标进化算法。
第四，针对目前ABC算法尚无法解决高维多目标优化问题的情况，尝试提出一种以ABC执行主体进化策略的高维多目标算法。首先，将高维多目标问题转化成单目标问题，加大收敛动力；其次，根据高维多目标问题的特点，改进跟随蜂选择较优个体时较为贪婪的选择方式，为侦察蜂设计新的搜索策略，加强对非支配解的探索能力；最后，提出新的分布性维护方法，避免解集覆盖不完整、分布不均匀。实验证实该算法收敛性和分布性效果良好，且解集覆盖范围广。
第五，针对现有基于ABC算法的约束多目标算法性能较差的问题，采用建立外部种群分别存储优秀可行解和不可行解的方式处理约束条件，利用ABC算法执行进化操作，并借助优秀可行解和不可行解的方向性引导信息增强算法对解的探索能力，建立新的搜索方式，提出基于ABC算法的约束多目标算法。在CTP类测试函数上的仿真结果显示，相对于现有几种约束多目标优化算法，本课题提出的约束多目标算法能够获得更优的分布性和收敛性效果。
第六，为解决面向三维感知的多媒体传感器网络的全目标覆盖问题，提出基于人工蜂群算法的通用全目标覆盖算法：一方面，改进现有的三维感知模型，并通过公式推导得到最优仰俯角的计算公式，利用改进ABC算法进行求解；另一方面，建立偏向角调配方案的数学模型以降低算法复杂度，并改进ABC算法实现偏向角的最优调配。实验仿真结果表明该算法能够有效解决全目标覆盖问题。
Artificial Bee Colony algorithm (ABC) proposed in2005is one of the current bestevolutionary algorithms, which has become the research hotspot in many fields such asevolutionary computing and intelligent optimization. At present, ABC has successfully beenapplied to diverse domains of science and engineering, such as neural network optimization,filter design, cognitive radio, and blind signal separation. However, almost all of theevolutionary algorithms, including ABC, still suffer from the problems of prematureconvergence, slow convergence rate and difficult parameter setting, especially in optimizinghigh-dimensional complex optimization problems. In addition, the standard ABC algorithmcan't be used directly to solve the multimodal function optimization problems and thisshortcoming limits the scope of application of ABC to some extent.
According to the insufficiency of ABC, it is deeply investigated from theory andapplication aspects in this paper. In theory, according to a series of optimization problems,including high-dimensional complex single objective optimization problem, multimodalfunction optimization, two objective optimization problem, many objective optimizationproblem and constrained multi-objective optimization problems, the structure and key steps ofthe algorithm are improved to improve its optimal performance in every optimization problem.In application, the improved ABC algorithm is applied successfully to solve a frontiercoverage-all targets problem for directional sensor networks based on three-dimensionalperception, Concrete contents is as follows.
Firstly, according to ABC still suffer from the problems of premature convergence, slowconvergence rate and slow convergence speed at a later time in optimizing high-dimensionalcomplex single objective optimization problem, the inherent operation mechanism of ABCare deeply investigated. An improved artificial bee colony algorithm was proposed to improvethe optimization performance. Concrete improvement measures in the improved ABCalgorithm include:1、considering the method of choosing the excellent individual ofemployed bees is too greedy, a new probability choice model is proposed to increasepopulation diversity;2、A new searching method is designed, in which the better individualsare utilized to guide the search direction synchronously, to ensure the population diversity andimprove convergence speed;3、considering the parameter of controlling the behavior of the scout bees is difficult to set and has a greater impact on the algorithm, the new searchingmodel of scouts is proposed. Experimental results show that the proposed algorithmoutperform several state-of-the-art optimization algorithms in terms of the main performanceindexes.
Secondly, in order to improve multimodal evolutionary algorithms, a niche artificial beecolony algorithm is proposed combining ABC and the niche technology based on a lot ofexperiments. On the one hand, the traditional niche model is improved to increase populationdiversity and enhance the capacity of identifying every peak. On the other hand, according tomultimodal optimization problems, concrete improvement measures in NABC include:1、considering the method of choosing the excellent individual of employed bees is too greedy, anew probability choice model is proposed to increase population diversity;2、the traditionalevaluation criteria of judging superiority and inferiority individual depending on individualfitness value is improved, a new evaluation method combining the niche technology isproposed to strengthen the searching ability of individuals in every peak;3、in order to avoidthe phenomenon of losing the peak points because of population diversity deficiency, theexternal population is established to record the acquired peak points. Experimental resultsshow that the proposed algorithm can identify each peak accurately.
Thirdly, in order to improve the performance of convergence and distribution ofmulti-objective evolutionary algorithms, a multi-objective optimization algorithm based onartificial bee colony algorithm is proposed, in which NSGA-II is taken as the main frameworkof two targets evolutionary algorithm and evolutionary operation is implemented by ABC.Concrete improvement measures in the proposed algorithm include:1、the method ofascertaining elite population is designed to improve the distribution of the optimal solutionsets;2、according to characteristic of two targets optimization problems, new searchingmethod is designed to accelerate the converges speed to the optimal Pareto front.Experimental results on ZDT show that, the proposed algorithm can get Pareto optimalsolutions effectively with good distribution performance, all of its performance indexes arebetter than or at least comparable to several existing state-of-the-art MOEAs.
Fourthly, in order to improve the performance of many objective evolutionary algorithms,a many objective evolutionary algorithm based on artificial bee colony algorithm is proposedin this paper. Concrete improvement measures in the proposed algorithm include:1、many objective optimization problem is transformed to single objective optimization problem toincrease the power of convergence;2、 according to characteristic of many objectiveoptimization problems, new searching method is designed to form an improved ABC, andevolutionary operation is implemented by an improved ABC;3、a new diversity maintenancemethod is established to improve distributivity performance. Experimental results show that,the proposed algorithm can get Pareto optimal solutions effectively with good distribution andconvergence performance and with a wide coverage area.
Fifthly, considering that the performance of constrained multi-objective evolutionaryalgorithms, a constrained multi-objective optimization algorithm based on ABC is proposedin this paper. Concrete improvement measures in the proposed algorithm include:firstly,external populations are constructed to store feasible solutions and infeasible solutionsrespectively to handle constraint conditions, the update method of feasible solution set isimproved to distribution of solution set effectively. Secondly, ABC is utilized as theevolutionary strategy, new searching strategy is proposed, in which the excellent feasible andinfeasible solutions are utilized to improve exploration ability. Experimental results on CTPtest functions demonstrate that the proposed algorithm can achieve better diversity of Paretosolutions and convergence performance than or at least comparable to several existingstate-of-the-art CMOEAs.
Sixthly, in order to solve coverage-all targets for wireless directional sensor networksbased on three-dimensional perception model, a universal coverage-all targets algorithm isproposed. On the one hand, the present three-dimensional perception model is improved, andthe calculation formula of the optimal elevation angle is derivate by deep mathematicalanalysis, which is solved by an improved ABC. On the other hand, the mathematical model ofallocation scheme of deviation angle is established to reduce the complexity, and which issolved by an improved ABC. Experimental results show that this algorithm can solvecoverage-all targets efficiently.
引文
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