基于云理论的差分进化算法改进及应用研究
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摘要
差分进化(Differential Evolution, DE)作为目前最优秀的进化优化算法之一，是进化计算、智能优化技术方面的研究热点，已成功应用于车间调度、数字信号处理、模式识别、机器智能、化工、医学等诸多实际工程领域并取得了良好的应用效果。然而，DE和其他进化算法一样，在对复杂优化问题进行求解时仍不可避免地存在多样性不足、易陷入局部最优、后期收敛速度慢、控制参数难以设定等问题。此外标准DE算法的结构设计是用来解决无约束、单目标的优化问题，不可直接用于求解约束多目标优化问题，在一定程度上限制了算法的应用范围。
本课题从理论和应用两方面对DE算法进行了深入研究。从理论角度出发，首先针对DE算法存在的不足，在算法的交叉操作以及变异操作方面进行了深入研究和大量实验仿真工作，一方面提出了新的基于种群多样性的交叉概率因子CR自适应调整策略，有效提高了算法进化后期种群多样性，避免算法陷入局部最优；另一方面，提出新的变异策略，利用优秀解个体提供搜索方向性信息，避免差分向量中个体随机选择带来的搜索盲目性。上述两方面改进构成一种新的p-ADE算法，经仿真实验表明能有效提高全局最优解精度，加快算法收敛速度并增强DE算法的鲁棒性，其相关性能指标优于目前国内外较为先进的DEGL、JADE、jDE、CLPSO等全局最优化算法。其次，本课题首次将云理论思想引入到DE算法中，提出了云差分进化算法——CDE算法，首先结合上述基于种群多样性进行CR参数自适应调整的思想，利用云模型具有随机性和稳定倾向性的特点，提出新的基于云模型的CR自适应调整方法，在保证种群多样性的同时又提高了算法的收敛速度；其次对于复杂优化问题，单靠CR自适应调整策略来扩大种群多样性已难以满足算法对种群多样性的要求，为避免陷入局部最优，利用正、反正态云发生器级联对每个个体进行单维扰动，进一步改善种群分布提高种群多样性。在典型测试函数上的仿真结果表明，本文提出的CDE能在算法进化过程中有效改善种群多样性，克服算法易陷入局部最优的缺点，收敛精度得到明显提高，并加快了算法的收敛速度，在解决复杂优化问题时优势明显。
从应用角度出发，将云差分进化算法分别应用于约束多目标优化以及城市干线双向交通信号协调优化控制的求解中。对于约束多目标问题，首先采用本文提出的CDE算法作为约束多目标算法的进化策略，并提出新的变异策略，利用优秀可行解和不可行解的方向信息增强算法对解的探索能力；其次，采用建立外部种群分别存储可行解和不可行解的方式处理约束条件，并对已有可行解集的更新方法进行改进，有效提高解集的分布性。在CTP类测试函数上的仿真结果显示，相对于现有约束多目标优化算法，本文算法能够获得更优的Pareto解集分布性和收敛效果。对于城市干线双向信号协调优化控制，直接应用本文提出的CDE算法进行求解，通过与目前性能最好的基于多种群免疫算法的协调优化控制方法对比，实验结果表明，新控制方法在收敛精度、速度和鲁棒性上均具有明显优势，可以为交通干线系统提供更优的相位差，有效减少干线直行交通流的平均延误，提高城市主干道交通通行能力。
Differential Evolution (DE) is one of the current best evolutionary algorithms, which hasbecome the research hotspot in many fields such as evolutionary computing and intelligentoptimization. At present, DE has successfully been applied to diverse domains of science andengineering, such as signal processing, neural network optimization, pattern recognition,machine intelligence, chemical engineering and medical science. However, almost all of theevolutionary algorithms, including DE, still suffer from the problems of prematureconvergence, slow convergence rate and difficult parameter setting, especially in optimizingcomplex optimization problems. In addition, the standard DE algorithm can't be used directlyto solve the multi-objective optimization problems (MOPs) and this shortcoming limits thescope of application of DE to some extent.
The article studies DE from theory and application aspects. In theory, firstly, accordingto the insufficiency of DE, the structure and key steps of the algorithm, including mutationand crossover, are deeply investigated and a series of numerical experiments are made in thispaper. For one thing, a new division method of population diversity is proposed, based onwhich a novel adaptive adjustment strategy of parameter CR is presented to improve thepopulation diversity and to avoid sticking at local optima. For another, a new DE mutationstrategy is designed, in which best solutions are utilized to guide the search directionsynchronously, avoiding the search blindness brought by the random selection of individualsin difference vector. So a new modified p-ADE algorithm is presented. Experimental resultsdemonstrate the improved DE can effectively improve the global search ability of DE andoutperform several state-of-the-art optimization algorithms in terms of the main performanceindexes, such as DEGL, JADE, jDE and CLPSO. Secondly, cloud theory is creativelyintroduced to the DE algorithm to construct a new DE version, called CDE. Firstly, a noveladaptive adjustment strategy of parameter CR is proposed based on cloud model, whichcombines the presented adaptive adjustment stratage of parameter CR based on populationdiversity with the characterisitics of stability and randomness of DE. Secondly, CDE utilizes theconnection of positive and inverse normal cloud generators to produce one-dimensionalperturbations to each individual so as to improve population diversity and avoid sticking atlocal optima. Experimental results on benchmark functions demonstrate that CDE can effectively improve the population diversity of DE, avoid sticking at local optima and speedup the convergence rate.
In application, CDE is used to solve the constrained multi-objective optimization andurban traffic signal coordination control problems. For the constrained multi-objectiveoptimization problems, firstly, CDE is utilized as the evolutionary strategy, parameter CR isadjusted adaptively by positive normal cloud generator and a novel mutation strategy isproposed, in which the excellent feasible and infeasible solutions are utilized to improveexploration ability. Secondly, external populations are constructed to store feasible solutionsand infeasible solutions respectively to handle constraint conditions, the update method offeasible solution set is improved to distribution of solution set effectively. Experimentalresults on CTP test functions demonstrate that CMODE can achieve better diversity of Paretosolutions and convergence performance. For urban traffic signal coordination control, CDEalgorithm is introduced to optimize urban route two-way traffic signals. The new methodbased on CDE is compared with current best coordination control method based onmulti-colony immune algorithm. Experimental results prove the superiority of CDE onconvergence accuracy, speed and robustness, it could provide the more excellent phasedifference for traffic artery, decrease average delays in straight-going traffic flow and improvecapacity of urban road traffic.
本课题从理论和应用两方面对DE算法进行了深入研究。从理论角度出发，首先针对DE算法存在的不足，在算法的交叉操作以及变异操作方面进行了深入研究和大量实验仿真工作，一方面提出了新的基于种群多样性的交叉概率因子CR自适应调整策略，有效提高了算法进化后期种群多样性，避免算法陷入局部最优；另一方面，提出新的变异策略，利用优秀解个体提供搜索方向性信息，避免差分向量中个体随机选择带来的搜索盲目性。上述两方面改进构成一种新的p-ADE算法，经仿真实验表明能有效提高全局最优解精度，加快算法收敛速度并增强DE算法的鲁棒性，其相关性能指标优于目前国内外较为先进的DEGL、JADE、jDE、CLPSO等全局最优化算法。其次，本课题首次将云理论思想引入到DE算法中，提出了云差分进化算法——CDE算法，首先结合上述基于种群多样性进行CR参数自适应调整的思想，利用云模型具有随机性和稳定倾向性的特点，提出新的基于云模型的CR自适应调整方法，在保证种群多样性的同时又提高了算法的收敛速度；其次对于复杂优化问题，单靠CR自适应调整策略来扩大种群多样性已难以满足算法对种群多样性的要求，为避免陷入局部最优，利用正、反正态云发生器级联对每个个体进行单维扰动，进一步改善种群分布提高种群多样性。在典型测试函数上的仿真结果表明，本文提出的CDE能在算法进化过程中有效改善种群多样性，克服算法易陷入局部最优的缺点，收敛精度得到明显提高，并加快了算法的收敛速度，在解决复杂优化问题时优势明显。
从应用角度出发，将云差分进化算法分别应用于约束多目标优化以及城市干线双向交通信号协调优化控制的求解中。对于约束多目标问题，首先采用本文提出的CDE算法作为约束多目标算法的进化策略，并提出新的变异策略，利用优秀可行解和不可行解的方向信息增强算法对解的探索能力；其次，采用建立外部种群分别存储可行解和不可行解的方式处理约束条件，并对已有可行解集的更新方法进行改进，有效提高解集的分布性。在CTP类测试函数上的仿真结果显示，相对于现有约束多目标优化算法，本文算法能够获得更优的Pareto解集分布性和收敛效果。对于城市干线双向信号协调优化控制，直接应用本文提出的CDE算法进行求解，通过与目前性能最好的基于多种群免疫算法的协调优化控制方法对比，实验结果表明，新控制方法在收敛精度、速度和鲁棒性上均具有明显优势，可以为交通干线系统提供更优的相位差，有效减少干线直行交通流的平均延误，提高城市主干道交通通行能力。
Differential Evolution (DE) is one of the current best evolutionary algorithms, which hasbecome the research hotspot in many fields such as evolutionary computing and intelligentoptimization. At present, DE has successfully been applied to diverse domains of science andengineering, such as signal processing, neural network optimization, pattern recognition,machine intelligence, chemical engineering and medical science. However, almost all of theevolutionary algorithms, including DE, still suffer from the problems of prematureconvergence, slow convergence rate and difficult parameter setting, especially in optimizingcomplex optimization problems. In addition, the standard DE algorithm can't be used directlyto solve the multi-objective optimization problems (MOPs) and this shortcoming limits thescope of application of DE to some extent.
The article studies DE from theory and application aspects. In theory, firstly, accordingto the insufficiency of DE, the structure and key steps of the algorithm, including mutationand crossover, are deeply investigated and a series of numerical experiments are made in thispaper. For one thing, a new division method of population diversity is proposed, based onwhich a novel adaptive adjustment strategy of parameter CR is presented to improve thepopulation diversity and to avoid sticking at local optima. For another, a new DE mutationstrategy is designed, in which best solutions are utilized to guide the search directionsynchronously, avoiding the search blindness brought by the random selection of individualsin difference vector. So a new modified p-ADE algorithm is presented. Experimental resultsdemonstrate the improved DE can effectively improve the global search ability of DE andoutperform several state-of-the-art optimization algorithms in terms of the main performanceindexes, such as DEGL, JADE, jDE and CLPSO. Secondly, cloud theory is creativelyintroduced to the DE algorithm to construct a new DE version, called CDE. Firstly, a noveladaptive adjustment strategy of parameter CR is proposed based on cloud model, whichcombines the presented adaptive adjustment stratage of parameter CR based on populationdiversity with the characterisitics of stability and randomness of DE. Secondly, CDE utilizes theconnection of positive and inverse normal cloud generators to produce one-dimensionalperturbations to each individual so as to improve population diversity and avoid sticking atlocal optima. Experimental results on benchmark functions demonstrate that CDE can effectively improve the population diversity of DE, avoid sticking at local optima and speedup the convergence rate.
In application, CDE is used to solve the constrained multi-objective optimization andurban traffic signal coordination control problems. For the constrained multi-objectiveoptimization problems, firstly, CDE is utilized as the evolutionary strategy, parameter CR isadjusted adaptively by positive normal cloud generator and a novel mutation strategy isproposed, in which the excellent feasible and infeasible solutions are utilized to improveexploration ability. Secondly, external populations are constructed to store feasible solutionsand infeasible solutions respectively to handle constraint conditions, the update method offeasible solution set is improved to distribution of solution set effectively. Experimentalresults on CTP test functions demonstrate that CMODE can achieve better diversity of Paretosolutions and convergence performance. For urban traffic signal coordination control, CDEalgorithm is introduced to optimize urban route two-way traffic signals. The new methodbased on CDE is compared with current best coordination control method based onmulti-colony immune algorithm. Experimental results prove the superiority of CDE onconvergence accuracy, speed and robustness, it could provide the more excellent phasedifference for traffic artery, decrease average delays in straight-going traffic flow and improvecapacity of urban road traffic.
引文
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