P系统优化算法及应用研究
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摘要
P系统(膜计算)是一种从生物细胞、组织和器官的结构与功能中抽象出来的新的并行分布式计算模型。受生物细胞结构及其它生命活动的启发,基于已有的研究成果,本文对P系统优化算法及应用进行了深入的研究。本文的主要研究成果如下：
(1)提出了一种嵌套式膜结构P系统优化算法。该算法采用嵌套式膜结构,各层膜内的对象在交流规则的作用下由内向外进化,设计了自噬规则、自适应变异规则以及部分迁移规则使得算法能够随着优化进程进行动态调整对象集分布、改善算法的全局搜索性能。通过对典型无约束测试函数的寻优计算,验证了该算法具有收敛速度快,精度高等优点。将该算法用于求解质子交换膜燃料电池建模的参数估计问题,结果表明所建模型能有效反映实际系统的非线性特性。
(2)提出了一种具有扩张收缩膜结构的混合P系统优化算法。该算法的P系统膜结构采用扩张和收缩机制来增强算法的全局勘探和局部开采能力,所设计的实数量子更新规则通过利用当前进程中的最优个体对其余个体进行引导,以提高算法的收敛速度。通过对典型测试函数的寻优计算表明该算法较DNA-GA和GA有更高的搜索效率和精度。将该算法用于求解炼油厂FCCU反应-再生过程模型参数估计问题,结果验证了所提算法的有效性。
(3)提出了一种DNA分子操作的P系统优化算法。该算法采用嵌套式膜结构和已有的交流、选择等规则,结合DNA重排规则和重组规则,设计易位、复制、反转、交叉等规则来提高对象集的多样性,增强算法的抗欺骗能力。DNA定点诱变规则中的动态互补变异机制和可变增益使得算法的全局勘探和局部搜索随着搜索进程的继续而动态变化,提高了算法的可靠性和搜索精度。通过对典型测试函数的寻优计算验证了该算法的有效性。将该算法用于具有多峰误差表面特性的ⅡR数字滤波器设计,结果表明该算法得到的滤波器的频幅响应更加接近理想状态。
(4)提出了一种基于Box密度分配策略的多目标P系统优化算法。该算法采用动态膜结构和选择、交流、交叉、自适应变异规则；基于Pareto支配关系和Box密度分配策略对目标空问中拥挤度大的区域内对象进行引导,使得算法最终所得到的多目标Pareto解集在非支配边界上分布更加均匀。通过对典型多目标优化函数进行寻优求解,结果验证了该算法的最终非支配解集达到或接近真实Pareto前沿,而且分布相对均匀,可有效地用于求解多目标优化问题。
P systems (also known as membrane computing) are presented originally as a distributed and parallel computational model that is abstracted from the structure and functioning of living cells, tissues or organs. Based on the fruits of existing membrane computing, inspired by the cells'structure and other behaviors of life, this dissertation discusses series of methodologies and their applications in addressing the process modeling and parameter estimation problems which possess great nonlinearity and deception. The contributions and innovations of this dissertation are as follows:
(1) A P systems based optimization algorithm with nested membrane structure is proposed. In this algorithm, the nested membrane and new rules such as autophagy rule, adaptive mutation rule and partial migration rule are designed to help algorithm to adjust its population distribution with procedure, avoid premature and to improve the algorithm's global convergence performance. Studies on some typical unconstrained benchmark functions indicate that the proposed algorithm possess great reliability, fast convergence speed and searching accuracy. The algorithm is also used to solve the parameter estimation problems of proton exchange membrane fuel cell modeling, and the results show that those models established by the proposed method can reflect the nonlinear external dynamic property of the practical systems.
(2) A P systems based hybrid optimization algorithm with expansion and contraction mechanism (PHOA) is proposed. In PHOA, the expansion of the search space makes the proposed algorithm realize exploration and the dynamic contraction of search space makes it realize exploitation. The real-coded quantum update rules make full use of the current best solution and guide the rest mutating toward the potential global optimum, which accelerate the algorithm's convergence speed. Studies on some benchmark functions show that the proposed scheme outperforms DNA based genetic algorithm (DNA-GA) and standard genetic algorithm (SGA) both in search efficiency and accuracy. With the parameters obtained by this algorithm, the discrete transfer function matrix model of FCCU reactor-regenerator in an oil refinery is established. The results validate the effectiveness of the proposed approach.
(3) DNA molecular operation based P systems optimization algorithm (DNA-PSOA) is proposed. Combining with the nested membrane structure and the traditional communication rule and selection rule, the proposed DNA rearrangement and recombination rules are designed to improve the distribution of object set and strengthened the algorithm's abilities of anti-premature. The dynamic complementary mutation mechanism and variable gain in site-directed mutagenesis rule make this algorithm realize dynamic shift from exploration and exploitation in the whole processes. Numerical experiments validate the effectiveness of the proposed algorithm. Then the algorithm is applied to design the llR digital filters that possess multimodal error surface property. The results and comparison with others show that the proposed method can obtain better filters with close-to-ideal amplitude responses.
(4) A box-density-distribution-strategy based multi-objective P systems optimization algorithm (Box-MPSOA) is proposed. In the framework of P systems, the dynamic membrane structure is adopted to changing in the number of targets in multi-objective optimization problems. The rules such as selecting, communication, crossover and adaptive mutation used in the Box-MPSOA make the algorithm converge faster. Based on Pareto domination, box-density-distributing-strategy redistribute the individuals which are located in the high-density box, so that the distribution of final Pareto solution set will be more uniform on the nondominated solution set front. Benchmark multi-objective optimization problems are tested to validate the proposed algorithm. Simulation results show that the final non-dominated solution set obtained by Box-MPSOA reaches or is close to the true Pareto front with good diversity. It can be concluded that the proposed algorithm is capable to solve the multi-objective optimization problems efficiently.
(1)提出了一种嵌套式膜结构P系统优化算法。该算法采用嵌套式膜结构,各层膜内的对象在交流规则的作用下由内向外进化,设计了自噬规则、自适应变异规则以及部分迁移规则使得算法能够随着优化进程进行动态调整对象集分布、改善算法的全局搜索性能。通过对典型无约束测试函数的寻优计算,验证了该算法具有收敛速度快,精度高等优点。将该算法用于求解质子交换膜燃料电池建模的参数估计问题,结果表明所建模型能有效反映实际系统的非线性特性。
(2)提出了一种具有扩张收缩膜结构的混合P系统优化算法。该算法的P系统膜结构采用扩张和收缩机制来增强算法的全局勘探和局部开采能力,所设计的实数量子更新规则通过利用当前进程中的最优个体对其余个体进行引导,以提高算法的收敛速度。通过对典型测试函数的寻优计算表明该算法较DNA-GA和GA有更高的搜索效率和精度。将该算法用于求解炼油厂FCCU反应-再生过程模型参数估计问题,结果验证了所提算法的有效性。
(3)提出了一种DNA分子操作的P系统优化算法。该算法采用嵌套式膜结构和已有的交流、选择等规则,结合DNA重排规则和重组规则,设计易位、复制、反转、交叉等规则来提高对象集的多样性,增强算法的抗欺骗能力。DNA定点诱变规则中的动态互补变异机制和可变增益使得算法的全局勘探和局部搜索随着搜索进程的继续而动态变化,提高了算法的可靠性和搜索精度。通过对典型测试函数的寻优计算验证了该算法的有效性。将该算法用于具有多峰误差表面特性的ⅡR数字滤波器设计,结果表明该算法得到的滤波器的频幅响应更加接近理想状态。
(4)提出了一种基于Box密度分配策略的多目标P系统优化算法。该算法采用动态膜结构和选择、交流、交叉、自适应变异规则；基于Pareto支配关系和Box密度分配策略对目标空问中拥挤度大的区域内对象进行引导,使得算法最终所得到的多目标Pareto解集在非支配边界上分布更加均匀。通过对典型多目标优化函数进行寻优求解,结果验证了该算法的最终非支配解集达到或接近真实Pareto前沿,而且分布相对均匀,可有效地用于求解多目标优化问题。
P systems (also known as membrane computing) are presented originally as a distributed and parallel computational model that is abstracted from the structure and functioning of living cells, tissues or organs. Based on the fruits of existing membrane computing, inspired by the cells'structure and other behaviors of life, this dissertation discusses series of methodologies and their applications in addressing the process modeling and parameter estimation problems which possess great nonlinearity and deception. The contributions and innovations of this dissertation are as follows:
(1) A P systems based optimization algorithm with nested membrane structure is proposed. In this algorithm, the nested membrane and new rules such as autophagy rule, adaptive mutation rule and partial migration rule are designed to help algorithm to adjust its population distribution with procedure, avoid premature and to improve the algorithm's global convergence performance. Studies on some typical unconstrained benchmark functions indicate that the proposed algorithm possess great reliability, fast convergence speed and searching accuracy. The algorithm is also used to solve the parameter estimation problems of proton exchange membrane fuel cell modeling, and the results show that those models established by the proposed method can reflect the nonlinear external dynamic property of the practical systems.
(2) A P systems based hybrid optimization algorithm with expansion and contraction mechanism (PHOA) is proposed. In PHOA, the expansion of the search space makes the proposed algorithm realize exploration and the dynamic contraction of search space makes it realize exploitation. The real-coded quantum update rules make full use of the current best solution and guide the rest mutating toward the potential global optimum, which accelerate the algorithm's convergence speed. Studies on some benchmark functions show that the proposed scheme outperforms DNA based genetic algorithm (DNA-GA) and standard genetic algorithm (SGA) both in search efficiency and accuracy. With the parameters obtained by this algorithm, the discrete transfer function matrix model of FCCU reactor-regenerator in an oil refinery is established. The results validate the effectiveness of the proposed approach.
(3) DNA molecular operation based P systems optimization algorithm (DNA-PSOA) is proposed. Combining with the nested membrane structure and the traditional communication rule and selection rule, the proposed DNA rearrangement and recombination rules are designed to improve the distribution of object set and strengthened the algorithm's abilities of anti-premature. The dynamic complementary mutation mechanism and variable gain in site-directed mutagenesis rule make this algorithm realize dynamic shift from exploration and exploitation in the whole processes. Numerical experiments validate the effectiveness of the proposed algorithm. Then the algorithm is applied to design the llR digital filters that possess multimodal error surface property. The results and comparison with others show that the proposed method can obtain better filters with close-to-ideal amplitude responses.
(4) A box-density-distribution-strategy based multi-objective P systems optimization algorithm (Box-MPSOA) is proposed. In the framework of P systems, the dynamic membrane structure is adopted to changing in the number of targets in multi-objective optimization problems. The rules such as selecting, communication, crossover and adaptive mutation used in the Box-MPSOA make the algorithm converge faster. Based on Pareto domination, box-density-distributing-strategy redistribute the individuals which are located in the high-density box, so that the distribution of final Pareto solution set will be more uniform on the nondominated solution set front. Benchmark multi-objective optimization problems are tested to validate the proposed algorithm. Simulation results show that the final non-dominated solution set obtained by Box-MPSOA reaches or is close to the true Pareto front with good diversity. It can be concluded that the proposed algorithm is capable to solve the multi-objective optimization problems efficiently.
引文
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