元胞遗传算法研究及应用
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摘要
由于科技发展的需要，人们不得不面对科学研究和工程领域中的愈来愈复杂的寻优问题，元胞遗传算法提供了一种解决复杂优化问题的途径。元胞遗传算法将遗传操作限制在邻域内进行，减缓了优势个体在群体中的扩散速度，具有更好的全局探索能力，在求解复杂、多极值点优化问题中显示出优越性。然而，邻域内的遗传操作也带来元胞遗传算法收敛速度慢、局部搜索能力弱的问题。目前，元胞遗传算法大多注重元胞自动机邻域结构，缺乏对元胞自动机模拟自然现象的系统研究。为此，本文对元胞遗传算法进行了较为系统完整地研究分析，从不同角度提出几种改进算法，提高了算法全局收敛率及收敛速度，并在工程应用领域做出了新探索。本文研究内容和成果如下：
（1）以选择压力作为分析手段，对标准元胞遗传算法进行定性分析。通过测试具有代表性的函数，从进化过程与计算性能两方面，对元胞遗传算法与标准遗传算法进行对比分析，并分析总结了邻域结构对算法性能的影响。研究表明，在进化过程中，标准元胞遗传算法具有较好的维持群体多样性能力。
（2）对灾变机制元胞遗传算法进行研究，提出基于个体差异的灾变元胞遗传算法。研究不同移民方式下，灾变规模和灾变周期对灾变机制元胞遗传算法选择压力的影响。以精英移民策略为基础，将具有差异的优秀个体植入灾难区域，提高了进化过程中的群体多样性。这种方法在处理多峰、存在局部极值点的优化问题时，提高了算法跳出局部极值点的能力，亦使优化问题的收敛速度和收敛率得到提高。
（3）研究生态密度对生态系统进化的影响规律，提出两种不同演化行为机制的元胞遗传算法。为了进一步维持群体的多样性，从自然界的渐进演化行为出发，提出具有演化规则的元胞遗传算法，以便提高全局搜索能力。基于个体的适应度，以物种间的捕食策略替代自然演化行为，提出具有捕食机制的元胞遗传算法，从而提高局部探索能力。这两种算法的运行效率均优于基本元胞遗传算法。
（4）结合粒子群算法与元胞遗传算法，借鉴粒子群优化中粒子信息交互模式，提出两种不同融合机制的混合元胞遗传算法。根据粒子群概念，构造一个元胞遗传算法的新算子，研究融合粒子群概念的混合元胞遗传算法。为了提高全局搜索能力，将多中心城市策略引入元胞遗传算法，结合粒子群算法，提出多中心城市策略的混合元胞遗传算法。这两种混合元胞遗传算法既能保证优化问题的优化结果，又能提高收敛速度。
（5）考虑夹持元件的局部变形，推导出工件的位置误差分析模型。以最小的工件位置误差为目标，构建夹紧力的优化设计模型，并提出了基于灾变元胞遗传算法的夹紧力优化设计模型求解方法。
with the development of technology, people have to face the more and morecomplicated optimization problems constantly arising in science and engineering, to wichcellular genetic algorithm provides an effective solution. It is an algorithms model thatcombins celluar automata with genetic algorithm. In this algorithm, the genetic operate of acertain individuals is restricted within neighborhood, so it slows down the diffusion speed ofthe good individual. On the one hand, the cellular genetic algorithm can offer us an overallexploitation in sloving problems struck into local optimum, thus increase the globalconvergence, and shows great superiority in coping complexe problem. On the other hand, itsexploiation is poor; it has the poor speed of convering due to running genetic operate withinneighborhood. Apart from this, on the CGA study, great attention of current researchers hasbeen paid to the struct of neighborhood of cellular automata, yet the research of simulatingnatural phenomenon is lacking. This paper gives an overall and systematical research andanalysis on cellular genetic algorithms; several improved algorithms have been presented insolving the new engineering problems. The main content and innovation are as follows:
（1）Based on the current cellular genetic algorithm, by mean of selection pressure,qualitative analysis is conducted. Addopting a number of function typical optium, CGA iscompared with SGA in the aspects of evaluation process and computation performance. CGAcan matains population diversity better than SGA throughout evolutionary process. A severalconclution is achived on neighborhood structure to the influence of the algorithmperformance.
（2）In different way of migration on cellular genetic algorithm with disater, effect ofselection pressure, relevant to the size and period of disasters, is researched. According to theelastic migration strategy, different excellent individual are placed in disater region toimprove population diversity. The experiment results shows that the cellular geneticalgorithms with new migration strategy can improve the optimization accuracy andconvergence rate as well as harbors superiority of exploration and exploitation.
（3）According to different mechanisms of evoluational behavior, two improved celluargentic algorithms are presented. One is cellular genetic algorithms with evlutionary rules,which moniative nature.the other one is cellular genetic algorithms with predator and preymechanism, which mimic the predator-prey model from natural ecology, the evolution rule of cellular genetic algorithm is replaced by predator and prey mechanism. These two algorithmscan be improved from exploitation and exploiration resepectly.
（4）Two hybrid cellular genetic algorithms are present. They are the hybrid cellulargenetic algorithms with PSO and the hybrid cellular genetic algorithms with polycentric cityand PSO. They include comunication that is adopted by PSO, so except the result is moresatisfactory, convergence speed is also increased. Polycentric stagey can play a role inmaintain population diversity.
（5）Considering local fixel deformation, after workpcece position error is determined,optimal model of clamping forces is built. And then, aiming at minimizing the workpceceposition error, a cellular genetic algorithm with disasters is investigated to solve the proposedmodel so that the global optimal clamping forces can be efficiently obtained. This result ofstudy is better than the result of nolinear programming.
（1）以选择压力作为分析手段，对标准元胞遗传算法进行定性分析。通过测试具有代表性的函数，从进化过程与计算性能两方面，对元胞遗传算法与标准遗传算法进行对比分析，并分析总结了邻域结构对算法性能的影响。研究表明，在进化过程中，标准元胞遗传算法具有较好的维持群体多样性能力。
（2）对灾变机制元胞遗传算法进行研究，提出基于个体差异的灾变元胞遗传算法。研究不同移民方式下，灾变规模和灾变周期对灾变机制元胞遗传算法选择压力的影响。以精英移民策略为基础，将具有差异的优秀个体植入灾难区域，提高了进化过程中的群体多样性。这种方法在处理多峰、存在局部极值点的优化问题时，提高了算法跳出局部极值点的能力，亦使优化问题的收敛速度和收敛率得到提高。
（3）研究生态密度对生态系统进化的影响规律，提出两种不同演化行为机制的元胞遗传算法。为了进一步维持群体的多样性，从自然界的渐进演化行为出发，提出具有演化规则的元胞遗传算法，以便提高全局搜索能力。基于个体的适应度，以物种间的捕食策略替代自然演化行为，提出具有捕食机制的元胞遗传算法，从而提高局部探索能力。这两种算法的运行效率均优于基本元胞遗传算法。
（4）结合粒子群算法与元胞遗传算法，借鉴粒子群优化中粒子信息交互模式，提出两种不同融合机制的混合元胞遗传算法。根据粒子群概念，构造一个元胞遗传算法的新算子，研究融合粒子群概念的混合元胞遗传算法。为了提高全局搜索能力，将多中心城市策略引入元胞遗传算法，结合粒子群算法，提出多中心城市策略的混合元胞遗传算法。这两种混合元胞遗传算法既能保证优化问题的优化结果，又能提高收敛速度。
（5）考虑夹持元件的局部变形，推导出工件的位置误差分析模型。以最小的工件位置误差为目标，构建夹紧力的优化设计模型，并提出了基于灾变元胞遗传算法的夹紧力优化设计模型求解方法。
with the development of technology, people have to face the more and morecomplicated optimization problems constantly arising in science and engineering, to wichcellular genetic algorithm provides an effective solution. It is an algorithms model thatcombins celluar automata with genetic algorithm. In this algorithm, the genetic operate of acertain individuals is restricted within neighborhood, so it slows down the diffusion speed ofthe good individual. On the one hand, the cellular genetic algorithm can offer us an overallexploitation in sloving problems struck into local optimum, thus increase the globalconvergence, and shows great superiority in coping complexe problem. On the other hand, itsexploiation is poor; it has the poor speed of convering due to running genetic operate withinneighborhood. Apart from this, on the CGA study, great attention of current researchers hasbeen paid to the struct of neighborhood of cellular automata, yet the research of simulatingnatural phenomenon is lacking. This paper gives an overall and systematical research andanalysis on cellular genetic algorithms; several improved algorithms have been presented insolving the new engineering problems. The main content and innovation are as follows:
（1）Based on the current cellular genetic algorithm, by mean of selection pressure,qualitative analysis is conducted. Addopting a number of function typical optium, CGA iscompared with SGA in the aspects of evaluation process and computation performance. CGAcan matains population diversity better than SGA throughout evolutionary process. A severalconclution is achived on neighborhood structure to the influence of the algorithmperformance.
（2）In different way of migration on cellular genetic algorithm with disater, effect ofselection pressure, relevant to the size and period of disasters, is researched. According to theelastic migration strategy, different excellent individual are placed in disater region toimprove population diversity. The experiment results shows that the cellular geneticalgorithms with new migration strategy can improve the optimization accuracy andconvergence rate as well as harbors superiority of exploration and exploitation.
（3）According to different mechanisms of evoluational behavior, two improved celluargentic algorithms are presented. One is cellular genetic algorithms with evlutionary rules,which moniative nature.the other one is cellular genetic algorithms with predator and preymechanism, which mimic the predator-prey model from natural ecology, the evolution rule of cellular genetic algorithm is replaced by predator and prey mechanism. These two algorithmscan be improved from exploitation and exploiration resepectly.
（4）Two hybrid cellular genetic algorithms are present. They are the hybrid cellulargenetic algorithms with PSO and the hybrid cellular genetic algorithms with polycentric cityand PSO. They include comunication that is adopted by PSO, so except the result is moresatisfactory, convergence speed is also increased. Polycentric stagey can play a role inmaintain population diversity.
（5）Considering local fixel deformation, after workpcece position error is determined,optimal model of clamping forces is built. And then, aiming at minimizing the workpceceposition error, a cellular genetic algorithm with disasters is investigated to solve the proposedmodel so that the global optimal clamping forces can be efficiently obtained. This result ofstudy is better than the result of nolinear programming.
引文
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