混合免疫优化理论与算法及其应用研究
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摘要
在科学研究和工程实践中广泛存在着优化问题，因而开展优化问题的研究具有重要的理论意义和应用价值。模拟生物免疫系统智能信息处理机制的免疫优化算法具有自组织、多样性好、鲁棒性强等优点，适宜于优化问题的求解。然而依靠单一模式的优化算法难以满足具有强非线性、不确定性、时变等特征的复杂优化问题的性能要求。混合免疫优化算法为复杂优化问题的求解提供了新的思路和有效的途径，同时也是优化理论与算法研究的发展方向之一。
本文借鉴免疫系统的机理并结合其它优化算法开展混合免疫优化理论与算法及其应用的研究。针对组合优化和数值优化问题，本文从机制模型、算法设计、理论分析、性能测试、算法比较等方面进行系统研究，通过仿真实验验证了混合免疫优化算法的有效性；将所研究的混合免疫优化算法应用于复杂离散混沌系统滑模优化控制中，取得了良好的控制效果。论文的主要研究成果与创新如下：
(1)针对组合优化问题，利用免疫克隆选择算法和蚁群算法的各自优势，提出一种基于串联混合方式的优化算法：结合抗体小窗口局部搜索算法的克隆选择和蚁群融合算法(ACLA)。在蚁群算法中引入混沌扰动能在一定程度上避免早熟、停滞；克隆扩增、免疫基因等算子的操作能加快克隆选择算法的收敛速度；局部搜索算法的应用，能有效提高ACLA算法的搜索效率。针对旅行商问题的实验结果表明，该混合算法在收敛速度与求解精度上均取得了较好的效果。
(2)针对组合优化问题，融合协同进化算法、免疫克隆选择算法的各自优势，构造了一种基于多子种群免疫进化的两层框架模型，在此模型的基础上提出一种基于竞争-合作的分层协同进化免疫算法(HCIA)。HCIA算法通过对若干个子种群进行局部最优免疫优势、基于竞争的克隆扩增等低层免疫操作和高层遗传操作，增强优秀抗体实现亲和度成熟的机会，提高了抗体群分布的多样性，使其在深度搜索和广度寻优之间取得了平衡。通过典型组合优化问题——旅行商问题的实验仿真结果表明，HCIA算法具有可靠的全局收敛性及较快的收敛速度。
(3)针对函数全局优化问题，融合免疫算法的多样性机理、粒子群的信息共享及协同进化思想，提出基于两层模型的多子种群粒子群免疫协同进化算法(MAPCPSOI)。MAPCPSOI算法首先通过对若干个子种群进行具有协同合作特征的低层自适应多态杂交粒子群操作，改善了子种群的多样性，有效抑制了收敛过程中的早熟停滞现象；然后通过具有协同竞争特征的高层免疫克隆选择操作，显著地提高了全局寻优能力，进一步提高了收敛精度。函数优化的仿真结果表明：与其他改进微粒群算法相比，MAPCPSOI算法具有更快的收敛速度和更高的求解精度，尤其适合超高维函数及其它复杂函数的优化问题求解。
(4)针对多模态函数优化问题，提出融合Powell法的粒子群优化算法(IPSO-P)及免疫云粒子群优化算法(PPSO)这两种算法。IPSO-P算法将粒子群优化算法的全局搜索能力与Powell法的强局部寻优能力有机地结合起来，在保证求解速度、尽可能找到全部极值点的同时提高了解的精确性。而在PPSO算法中，通过引入基于云模型的云变异算子提高了种群的多样性，利用小波变异克隆选择算法对云变异粒子群优化算法搜索到的较优解进行局部搜索以进一步提高解的精度。仿真实验表明这两种新混合算法的有效性。
(5)将免疫云粒子群优化算法(PPSO)应用于离散混沌系统滑模优化控制中，提出一种基于PPSO算法的神经滑模等效控制方法。该方法通过将BP神经网络的输出作为滑模等效控制的切换部分的系数，有效克服了传统滑模等效控制的抖振现象；利用PPSO算法对神经滑模控制器的参数进行全局优化，提高了离散混沌系统的控制品质。实验仿真表明，该方法无需了解离散混沌系统精确模型，具有响应速度快、控制精度高以及抗干扰能力强的优点。
As optimization problems exist widely in scientific research and engineeringpractice, research on optimization problems is of great theoretical significance andpractical value. With characters of self-organization, good diversity and strongrobustness, immune optimization algorithm simulating intelligent informationprocessing mechanism of biological immune system is suit for solving optimizationproblems. Since optimization problems are becoming more and more complex, it ishard to meet the performance requirements of complex optimization problems withfeatures of strong nonlinearity, uncertainty and time variation only by a singleoptimization method. Hybrid immune optimization algorithm not only can offer newidea and effective way for this kind of problem but also is a direction of thedevelopment of optimization theory and algorithms.
Inspired by the mechamism of immune system, research on Theories andAlgorithms of Hybrid Immune Optimization and its applications is carried through bycombining with other optimization algorithms in this dissertation. Aiming atcombinatorial optimization problem and numerical optimization problem, a systematicstudy of this dissertation is launched on mechanism model, algorithm design, theoryanalysis, performance testing and algorithm comparison. The performance of hybridimmune optimization algorithm is confirmed through the simulation experiments.Hybrid immune optimization algorithm is used to sliding mode optimization control ofcomplex discrete-time chaotic systems, favorable control performance is achieved.The main work can be summarized as follows:
(1) To solve combinatorial optimization problem, utilizing each superiority ofimmune clonal selection algorithm and ant colony algorithm, a serial hybrid algorithm,which combines immune algorithm and ant algorithm with local search algorithmbased on antibody small window (ACLA), is proposed. A mechanism of chaoticdisturbance is introduced into ant colony algorithm to avert precocity and stagnationto a certain extent. In order to improve convergent velocity of clonal selectionalgorithm, the operators of clone expansion and immune gene operation are introducedinto clonal selection algorithm.Through the application of local search algorithm,ACLA can improve searching efficiency. Simulation tests for traveling salesman problem illustrate that ACLA has a remarkable quality of convergent precision and theconvergent velocity.
(2) Aiming at combinatorial optimization problem, combining the respectiveadvantages of co-evolutionary algorithm and immune clonal selection algorithm, atwo-floor model based on multiple-population immune evolution as well asHierarchical Co-evolutionary Immune Algorithm(HCIA) based oncompetition-cooperation is put forward. Multiple subpopulations are operated bybottom floor immune operators such as local optimization immunodominance, clonalexpansion based on competition and top floor genetic operators. Through thoseoperators, excellent antibody affinity maturation and diversity of antibodysubpopulation distribution was enhanced, the balance between in the depth andbreadth of the search-optimizing was acquired. Experimental results for travelingsalesman problem, a typical combinatorial optimization problem, indicate that HCIAhas a remarkable quality of the global convergence reliability and convergencevelocity.
(3) Focus on global function optimization problem, integrating diversitymechanism of immune algorithm with the thought of co-evolutionary and particleswarm neighborhood information sharing, a novel Multi-subpopulation AdaptivePolymorphic Crossbreeding Particle Swarm Optimization immune co-evolutionaryalgorithm(MAPCPSOI) based on two-layer model is raised. Through the bottom layeradaptive polymorphic crossbreeding particle swarm optimization operation of severalsubpopulations, the MAPCPSOI algorithm, firstly, can ameliorate diversity ofsubpopulation distribution and effectively suppress premature and stagnation behaviorof the convergence process. Secondly, the MAPCPSOI algorithm, by the top layerimmune clonal selection operation of several subpopulations, can significantlyimprove the global optimization performance and further enhance convergenceprecision. Compared with other improved particle swarm optimization algorithms,simulation results of function optimization show that the MAPCPSOI algorithm,especially suitable for solving optimization problems of hyper-high dimensionfunction and other complex function, has more rapid convergence speed and highersolution precision.
(4) To address multi-modal function optimization problem, a novel hybridalgorithm(IPSO-P) which combines Improved Particle Swarm Optimization algorithmwith Powell search method and a novel hybrid immune cloud particle swarmoptimization algorithm(PPSO) which integrates Cloud Mutation Particle Swarm Optimization algorithm(CMPSO) with Wavelet Mutation Clonal SelectionAlgorithm(WMCSA) are proposed. The IPSO-P algorithm organically integratesparticle swarm optimization algorithm which has powerful global search capabilitywith Powell search method which has strong local search ability.The IPSO-Palgorithm ensures quick convergent speed and find all extreme points as much aspossible, and solution’s precision is improved. In the PPSO algorithm, cloud mutationoperator based on cloud model is employed to enhance the diversity of population,WMCSA is used to further improve the accuracy of the sub-optimal solutions whichCMPSO has found. The simulation experiments demonstrate the effectiveness of thetwo hybrid algorithms.
(5) The hybrid immune cloud particle swarm optimization algorithm (PPSO) isused to sliding mode optimization control of discrete-time chaotic systems, a neuralnetwork sliding mode equivalent control method based on PPSO algorithm isproposed.When taking the output of BP neural network as coefficient of switch part ofsliding mode equivalent control, the method effectively overcome the chatteringphenomenon of conventional sliding mode equivalent control. The PPSO algorithm isapplied to globally optimize the parameters of neural network sliding mode controllerand then to control discrete-time chaotic systems more effective. Simulation resultsshow that the method requires no knowledge about the precise mathematical model ofdiscrete-time chaotic systems with fast response speed, high control precision andstrong anti-interference ability.
本文借鉴免疫系统的机理并结合其它优化算法开展混合免疫优化理论与算法及其应用的研究。针对组合优化和数值优化问题，本文从机制模型、算法设计、理论分析、性能测试、算法比较等方面进行系统研究，通过仿真实验验证了混合免疫优化算法的有效性；将所研究的混合免疫优化算法应用于复杂离散混沌系统滑模优化控制中，取得了良好的控制效果。论文的主要研究成果与创新如下：
(1)针对组合优化问题，利用免疫克隆选择算法和蚁群算法的各自优势，提出一种基于串联混合方式的优化算法：结合抗体小窗口局部搜索算法的克隆选择和蚁群融合算法(ACLA)。在蚁群算法中引入混沌扰动能在一定程度上避免早熟、停滞；克隆扩增、免疫基因等算子的操作能加快克隆选择算法的收敛速度；局部搜索算法的应用，能有效提高ACLA算法的搜索效率。针对旅行商问题的实验结果表明，该混合算法在收敛速度与求解精度上均取得了较好的效果。
(2)针对组合优化问题，融合协同进化算法、免疫克隆选择算法的各自优势，构造了一种基于多子种群免疫进化的两层框架模型，在此模型的基础上提出一种基于竞争-合作的分层协同进化免疫算法(HCIA)。HCIA算法通过对若干个子种群进行局部最优免疫优势、基于竞争的克隆扩增等低层免疫操作和高层遗传操作，增强优秀抗体实现亲和度成熟的机会，提高了抗体群分布的多样性，使其在深度搜索和广度寻优之间取得了平衡。通过典型组合优化问题——旅行商问题的实验仿真结果表明，HCIA算法具有可靠的全局收敛性及较快的收敛速度。
(3)针对函数全局优化问题，融合免疫算法的多样性机理、粒子群的信息共享及协同进化思想，提出基于两层模型的多子种群粒子群免疫协同进化算法(MAPCPSOI)。MAPCPSOI算法首先通过对若干个子种群进行具有协同合作特征的低层自适应多态杂交粒子群操作，改善了子种群的多样性，有效抑制了收敛过程中的早熟停滞现象；然后通过具有协同竞争特征的高层免疫克隆选择操作，显著地提高了全局寻优能力，进一步提高了收敛精度。函数优化的仿真结果表明：与其他改进微粒群算法相比，MAPCPSOI算法具有更快的收敛速度和更高的求解精度，尤其适合超高维函数及其它复杂函数的优化问题求解。
(4)针对多模态函数优化问题，提出融合Powell法的粒子群优化算法(IPSO-P)及免疫云粒子群优化算法(PPSO)这两种算法。IPSO-P算法将粒子群优化算法的全局搜索能力与Powell法的强局部寻优能力有机地结合起来，在保证求解速度、尽可能找到全部极值点的同时提高了解的精确性。而在PPSO算法中，通过引入基于云模型的云变异算子提高了种群的多样性，利用小波变异克隆选择算法对云变异粒子群优化算法搜索到的较优解进行局部搜索以进一步提高解的精度。仿真实验表明这两种新混合算法的有效性。
(5)将免疫云粒子群优化算法(PPSO)应用于离散混沌系统滑模优化控制中，提出一种基于PPSO算法的神经滑模等效控制方法。该方法通过将BP神经网络的输出作为滑模等效控制的切换部分的系数，有效克服了传统滑模等效控制的抖振现象；利用PPSO算法对神经滑模控制器的参数进行全局优化，提高了离散混沌系统的控制品质。实验仿真表明，该方法无需了解离散混沌系统精确模型，具有响应速度快、控制精度高以及抗干扰能力强的优点。
As optimization problems exist widely in scientific research and engineeringpractice, research on optimization problems is of great theoretical significance andpractical value. With characters of self-organization, good diversity and strongrobustness, immune optimization algorithm simulating intelligent informationprocessing mechanism of biological immune system is suit for solving optimizationproblems. Since optimization problems are becoming more and more complex, it ishard to meet the performance requirements of complex optimization problems withfeatures of strong nonlinearity, uncertainty and time variation only by a singleoptimization method. Hybrid immune optimization algorithm not only can offer newidea and effective way for this kind of problem but also is a direction of thedevelopment of optimization theory and algorithms.
Inspired by the mechamism of immune system, research on Theories andAlgorithms of Hybrid Immune Optimization and its applications is carried through bycombining with other optimization algorithms in this dissertation. Aiming atcombinatorial optimization problem and numerical optimization problem, a systematicstudy of this dissertation is launched on mechanism model, algorithm design, theoryanalysis, performance testing and algorithm comparison. The performance of hybridimmune optimization algorithm is confirmed through the simulation experiments.Hybrid immune optimization algorithm is used to sliding mode optimization control ofcomplex discrete-time chaotic systems, favorable control performance is achieved.The main work can be summarized as follows:
(1) To solve combinatorial optimization problem, utilizing each superiority ofimmune clonal selection algorithm and ant colony algorithm, a serial hybrid algorithm,which combines immune algorithm and ant algorithm with local search algorithmbased on antibody small window (ACLA), is proposed. A mechanism of chaoticdisturbance is introduced into ant colony algorithm to avert precocity and stagnationto a certain extent. In order to improve convergent velocity of clonal selectionalgorithm, the operators of clone expansion and immune gene operation are introducedinto clonal selection algorithm.Through the application of local search algorithm,ACLA can improve searching efficiency. Simulation tests for traveling salesman problem illustrate that ACLA has a remarkable quality of convergent precision and theconvergent velocity.
(2) Aiming at combinatorial optimization problem, combining the respectiveadvantages of co-evolutionary algorithm and immune clonal selection algorithm, atwo-floor model based on multiple-population immune evolution as well asHierarchical Co-evolutionary Immune Algorithm(HCIA) based oncompetition-cooperation is put forward. Multiple subpopulations are operated bybottom floor immune operators such as local optimization immunodominance, clonalexpansion based on competition and top floor genetic operators. Through thoseoperators, excellent antibody affinity maturation and diversity of antibodysubpopulation distribution was enhanced, the balance between in the depth andbreadth of the search-optimizing was acquired. Experimental results for travelingsalesman problem, a typical combinatorial optimization problem, indicate that HCIAhas a remarkable quality of the global convergence reliability and convergencevelocity.
(3) Focus on global function optimization problem, integrating diversitymechanism of immune algorithm with the thought of co-evolutionary and particleswarm neighborhood information sharing, a novel Multi-subpopulation AdaptivePolymorphic Crossbreeding Particle Swarm Optimization immune co-evolutionaryalgorithm(MAPCPSOI) based on two-layer model is raised. Through the bottom layeradaptive polymorphic crossbreeding particle swarm optimization operation of severalsubpopulations, the MAPCPSOI algorithm, firstly, can ameliorate diversity ofsubpopulation distribution and effectively suppress premature and stagnation behaviorof the convergence process. Secondly, the MAPCPSOI algorithm, by the top layerimmune clonal selection operation of several subpopulations, can significantlyimprove the global optimization performance and further enhance convergenceprecision. Compared with other improved particle swarm optimization algorithms,simulation results of function optimization show that the MAPCPSOI algorithm,especially suitable for solving optimization problems of hyper-high dimensionfunction and other complex function, has more rapid convergence speed and highersolution precision.
(4) To address multi-modal function optimization problem, a novel hybridalgorithm(IPSO-P) which combines Improved Particle Swarm Optimization algorithmwith Powell search method and a novel hybrid immune cloud particle swarmoptimization algorithm(PPSO) which integrates Cloud Mutation Particle Swarm Optimization algorithm(CMPSO) with Wavelet Mutation Clonal SelectionAlgorithm(WMCSA) are proposed. The IPSO-P algorithm organically integratesparticle swarm optimization algorithm which has powerful global search capabilitywith Powell search method which has strong local search ability.The IPSO-Palgorithm ensures quick convergent speed and find all extreme points as much aspossible, and solution’s precision is improved. In the PPSO algorithm, cloud mutationoperator based on cloud model is employed to enhance the diversity of population,WMCSA is used to further improve the accuracy of the sub-optimal solutions whichCMPSO has found. The simulation experiments demonstrate the effectiveness of thetwo hybrid algorithms.
(5) The hybrid immune cloud particle swarm optimization algorithm (PPSO) isused to sliding mode optimization control of discrete-time chaotic systems, a neuralnetwork sliding mode equivalent control method based on PPSO algorithm isproposed.When taking the output of BP neural network as coefficient of switch part ofsliding mode equivalent control, the method effectively overcome the chatteringphenomenon of conventional sliding mode equivalent control. The PPSO algorithm isapplied to globally optimize the parameters of neural network sliding mode controllerand then to control discrete-time chaotic systems more effective. Simulation resultsshow that the method requires no knowledge about the precise mathematical model ofdiscrete-time chaotic systems with fast response speed, high control precision andstrong anti-interference ability.
引文
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