改进自适应差分进化算法及其应用研究
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摘要
近年来,进化计算作为计算智能领域中的新兴学科发展迅速。进化计算所涉及的算法称为进化算法,主要包括遗传算法、遗传编程、进化策略、进化规划等。进化算法具有自适应、自搜索、并行性等特点,已广泛地应用于解决各种科学和工程问题。
差分进化算法属于进化算法的新兴分支,是一种基于种群的并行迭代优化算法,其性能主要由变异尺度因子,交叉概率因子和种群规模等控制参数决定,具有结构简单、收敛迅速、鲁棒性强等优点而受到了广泛的关注和研究,并已应用于数据挖掘、模式识别、数字滤波器设计、人工神经网络、组合优化、多目标优化等问题。但是,标准的差分进化算法存在着早熟收敛和搜索停滞等缺陷,限制了其优化能力和应用范围,因而迫切需要加以研究和改进。
本文对差分进化算法及其应用进行了研究。首先分析了控制参数对差分进化算法的影响,设计了种群自适应调节差分进化算法；其次针对离散空间优化问题,设计了改进的二进制差分进化算法；再次,为解决多目标优化问题,提出了多目标自适应差分进化算法；然后,研究了基于差分进化算法的基因调控网络未知参数识别问题；最后,研究了三维衣身原型曲面的智能分割问题。本文的主要研究内容和创新点具体如下：
(1)提出基于种群自适应调节的差分进化算法。种群自适应调节差分进化算法结合两种差分进化策略,使得算法在初期具有较强的全局搜索能力,而在后期具有较强的局部搜索能力；采用两种不同的种群调节方案,使得算法有效的提高了运行效率。利用多种经典测试函数对该算法进行实验检验,并与其它常用差分进化算法进行比较,结果表明该算法能够实现种群的自适应调节,全局搜索能力强,精度高,鲁棒性好,收敛速度较快。
(2)提出改进的二进制差分进化算法。种群自适应调节二进制差分进化算法改进了DE/current-to-best/1策略中的变异方法,使得算法适应离散空间优化。该算法可在运行过程中根据搜索状态自适应调整种群规模,提高了算法的效率和优化精度。与其他二进制差分进化算法的实验对比结果表明,该算法优化精度较高,收敛性能良好。
(3)提出多目标自适应差分进化算法。为求解多目标优化问题,提出多目标自适应差分进化算法,该算法将多种差分进化策略进行集成,通过多策略选择机制增强算法的优化能力。通过实验表明,多目标自适应差分进化算法所得的最终解集更加逼近真实的Pareto最优边界且在目标空间分布的更加均匀,具有良好的分布性和收敛性。
(4)基于差分进化算法的基因调控网络未知参数识别。对带有随机时滞和噪声扰动的基因调控网络进行了稳定性分析,并基于差分进化算法提出一种基因调控网络未知参数的识别方法,以达到准确获取参数的目的。通过理论分析和仿真证明,该识别算法具有良好的鲁棒性和准确性,对分析、解决实际问题有一定的指导意义。
(5)基于差分进化的三维衣身原型曲面智能分割算法。针对三维衣身原型曲面的特点,研究了三维曲面的展平及分割问题,提出了基于差分进化的三维衣身原型曲面智能分割算法,实现了对衣身曲面的智能分割,得到将衣身曲面划分为可展区域和非可展区域的准确分界线。通过实验证明了该智能分割算法的有效性和鲁棒性。
In recent years, as a new subject of computational intelligence, evolutionary com-putation has developed rapidly. Evolutionary algorithm contains some branches, such as Genetic Algorithm, Genetic Programming, Evolution strategics, Evolutionary Pro-gramming, Differential Evolution; and these algorithms have not only some different features but also some common properties. Since Evolutionary algorithms are self-adaptive, auto-optimizing, parallel, it is reasonable and available to solve the problems in the science and engineering by using evolutionary algorithms.
Differential Evolution (DE) is a kind of evolutionary algorithms. It has received wide attention for its simple structure, fast convergence, and robustness. In particular, the differential evolution algorithm is an efficient population-based search algorithm for global optimization. There are three main control parameters of the DE algorithm: the mutation scale factor, the crossover constant, and the population size. These pa-rameters are of great importance to the efficiency of a DE algorithm. DE algorithm has been successfully applied in diverse fields such as data mining, pattern recognition, digital filters, artificial neural network, combinatorial optimization, multi-objective op-timization, etc. However, the original DE algorithm has some shortages, so it is urgent to improve the original DE algorithm.
In this thesis, the differential evolution algorithm and its application are investi-gated. To begin with, the importance of the control parameters for differential evolution algorithm is given, and the population adaptive parameter strategy is proposed. Then for discrete space optimization, we introduce the adaptive parameter of binary differ-ential evolution algorithm. Furthermore, the multi-objective self-adaptive differential evolution algorithm is designed to solve numerical optimization problems with mul-tiple conflicting objectives. In addition, the SAPA algorithm is used to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs) with random delays and stochastic perturba-tions. Finally, the intelligent partition for3-D basic body surface is studied by the DE algorithm. The main contents and the innovative points can be listed as follows:
(1) A self-adaptive DE with population adjustment scheme. A self-adaptive DE with population adjustment scheme (SAPA) is proposed to tune the size of offspring population. The novel algorithm involves two self-adaptive DE strategies and two population adjustment schemes. The performance of the SAPA algorithm is evaluated by a set of benchmark functions. Simulation results show that the proposed algorithm is better than, or at least comparable to, other classic or adaptive DE algorithms. Performance comparisons with some other well-known evolutionary algorithms from literatures are also presented.
(2)Population Adaptive Binary Differential Evolution Algorithm. By improving the mutation of the DE/current-to-best/1strategy, we propose a new pop-ulation adaptive binary differential Evolution, which can be applied to the discrete optimization space. The proposed algorithm adaptive adjusts in accordance with the solution-searching status, which improves the efficiency of the algorithm and optimized accuracy. The experimental comparison with other binary DE algorithm indicates that the population adaptive binary differential evolution algorithm have better convergence and higher accuracy.
(3)Multi-objective Self-adaptive Differential Evolution Algorithm. Multi-objective Self-adaptive Differential Evolution (MOSDE) algorithm is proposed to solve numerical optimization problems with multiple conflicting objectives. The Multi-objective Self-adaptive Differential Evolution algorithm involves three self-adaptive DE strategies. The usefulness of the MOSDE algorithm is demonstrated with extensive nu-merical experiments showing improvements in performance compared with the previous state of the art.
(4)Parameter identification of stochastic genetic regulatory networks with random delays. Based on the differential evolution algorithm, the parameter identification of stochastic genetic regulatory networks with random delays is studied. The simulation results show that SAPA algorithm is superior or comparable to the other algorithms and can be efficiently used for identifying the unknown parameters of stochastic genetic, regulatory networks with random delays.
(5)The Intelligent Partition for3-D Basic Body Surface Based on Dif-ferential Evolution. Through analyzing the characteristics of the3-D Basic Body Surface, the3-D surface flattening and segmentation problem are studied. Then the intelligent partition algorithm based on differential evolution is designed, which solves the problem of partition of basic body surface. Simulation results show that the pro-posed algorithm is better than, or at least comparable to, other Evolutionary algorithm and can effectively search the optimum route which segments the basic body surface.
差分进化算法属于进化算法的新兴分支,是一种基于种群的并行迭代优化算法,其性能主要由变异尺度因子,交叉概率因子和种群规模等控制参数决定,具有结构简单、收敛迅速、鲁棒性强等优点而受到了广泛的关注和研究,并已应用于数据挖掘、模式识别、数字滤波器设计、人工神经网络、组合优化、多目标优化等问题。但是,标准的差分进化算法存在着早熟收敛和搜索停滞等缺陷,限制了其优化能力和应用范围,因而迫切需要加以研究和改进。
本文对差分进化算法及其应用进行了研究。首先分析了控制参数对差分进化算法的影响,设计了种群自适应调节差分进化算法；其次针对离散空间优化问题,设计了改进的二进制差分进化算法；再次,为解决多目标优化问题,提出了多目标自适应差分进化算法；然后,研究了基于差分进化算法的基因调控网络未知参数识别问题；最后,研究了三维衣身原型曲面的智能分割问题。本文的主要研究内容和创新点具体如下：
(1)提出基于种群自适应调节的差分进化算法。种群自适应调节差分进化算法结合两种差分进化策略,使得算法在初期具有较强的全局搜索能力,而在后期具有较强的局部搜索能力；采用两种不同的种群调节方案,使得算法有效的提高了运行效率。利用多种经典测试函数对该算法进行实验检验,并与其它常用差分进化算法进行比较,结果表明该算法能够实现种群的自适应调节,全局搜索能力强,精度高,鲁棒性好,收敛速度较快。
(2)提出改进的二进制差分进化算法。种群自适应调节二进制差分进化算法改进了DE/current-to-best/1策略中的变异方法,使得算法适应离散空间优化。该算法可在运行过程中根据搜索状态自适应调整种群规模,提高了算法的效率和优化精度。与其他二进制差分进化算法的实验对比结果表明,该算法优化精度较高,收敛性能良好。
(3)提出多目标自适应差分进化算法。为求解多目标优化问题,提出多目标自适应差分进化算法,该算法将多种差分进化策略进行集成,通过多策略选择机制增强算法的优化能力。通过实验表明,多目标自适应差分进化算法所得的最终解集更加逼近真实的Pareto最优边界且在目标空间分布的更加均匀,具有良好的分布性和收敛性。
(4)基于差分进化算法的基因调控网络未知参数识别。对带有随机时滞和噪声扰动的基因调控网络进行了稳定性分析,并基于差分进化算法提出一种基因调控网络未知参数的识别方法,以达到准确获取参数的目的。通过理论分析和仿真证明,该识别算法具有良好的鲁棒性和准确性,对分析、解决实际问题有一定的指导意义。
(5)基于差分进化的三维衣身原型曲面智能分割算法。针对三维衣身原型曲面的特点,研究了三维曲面的展平及分割问题,提出了基于差分进化的三维衣身原型曲面智能分割算法,实现了对衣身曲面的智能分割,得到将衣身曲面划分为可展区域和非可展区域的准确分界线。通过实验证明了该智能分割算法的有效性和鲁棒性。
In recent years, as a new subject of computational intelligence, evolutionary com-putation has developed rapidly. Evolutionary algorithm contains some branches, such as Genetic Algorithm, Genetic Programming, Evolution strategics, Evolutionary Pro-gramming, Differential Evolution; and these algorithms have not only some different features but also some common properties. Since Evolutionary algorithms are self-adaptive, auto-optimizing, parallel, it is reasonable and available to solve the problems in the science and engineering by using evolutionary algorithms.
Differential Evolution (DE) is a kind of evolutionary algorithms. It has received wide attention for its simple structure, fast convergence, and robustness. In particular, the differential evolution algorithm is an efficient population-based search algorithm for global optimization. There are three main control parameters of the DE algorithm: the mutation scale factor, the crossover constant, and the population size. These pa-rameters are of great importance to the efficiency of a DE algorithm. DE algorithm has been successfully applied in diverse fields such as data mining, pattern recognition, digital filters, artificial neural network, combinatorial optimization, multi-objective op-timization, etc. However, the original DE algorithm has some shortages, so it is urgent to improve the original DE algorithm.
In this thesis, the differential evolution algorithm and its application are investi-gated. To begin with, the importance of the control parameters for differential evolution algorithm is given, and the population adaptive parameter strategy is proposed. Then for discrete space optimization, we introduce the adaptive parameter of binary differ-ential evolution algorithm. Furthermore, the multi-objective self-adaptive differential evolution algorithm is designed to solve numerical optimization problems with mul-tiple conflicting objectives. In addition, the SAPA algorithm is used to solve global optimization problems with applications in identifying unknown parameters of a class of genetic regulatory networks (GRNs) with random delays and stochastic perturba-tions. Finally, the intelligent partition for3-D basic body surface is studied by the DE algorithm. The main contents and the innovative points can be listed as follows:
(1) A self-adaptive DE with population adjustment scheme. A self-adaptive DE with population adjustment scheme (SAPA) is proposed to tune the size of offspring population. The novel algorithm involves two self-adaptive DE strategies and two population adjustment schemes. The performance of the SAPA algorithm is evaluated by a set of benchmark functions. Simulation results show that the proposed algorithm is better than, or at least comparable to, other classic or adaptive DE algorithms. Performance comparisons with some other well-known evolutionary algorithms from literatures are also presented.
(2)Population Adaptive Binary Differential Evolution Algorithm. By improving the mutation of the DE/current-to-best/1strategy, we propose a new pop-ulation adaptive binary differential Evolution, which can be applied to the discrete optimization space. The proposed algorithm adaptive adjusts in accordance with the solution-searching status, which improves the efficiency of the algorithm and optimized accuracy. The experimental comparison with other binary DE algorithm indicates that the population adaptive binary differential evolution algorithm have better convergence and higher accuracy.
(3)Multi-objective Self-adaptive Differential Evolution Algorithm. Multi-objective Self-adaptive Differential Evolution (MOSDE) algorithm is proposed to solve numerical optimization problems with multiple conflicting objectives. The Multi-objective Self-adaptive Differential Evolution algorithm involves three self-adaptive DE strategies. The usefulness of the MOSDE algorithm is demonstrated with extensive nu-merical experiments showing improvements in performance compared with the previous state of the art.
(4)Parameter identification of stochastic genetic regulatory networks with random delays. Based on the differential evolution algorithm, the parameter identification of stochastic genetic regulatory networks with random delays is studied. The simulation results show that SAPA algorithm is superior or comparable to the other algorithms and can be efficiently used for identifying the unknown parameters of stochastic genetic, regulatory networks with random delays.
(5)The Intelligent Partition for3-D Basic Body Surface Based on Dif-ferential Evolution. Through analyzing the characteristics of the3-D Basic Body Surface, the3-D surface flattening and segmentation problem are studied. Then the intelligent partition algorithm based on differential evolution is designed, which solves the problem of partition of basic body surface. Simulation results show that the pro-posed algorithm is better than, or at least comparable to, other Evolutionary algorithm and can effectively search the optimum route which segments the basic body surface.
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