基于进化计算的单目标优化问题研究
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摘要
随着科学技术的发展，在工程应用中经常遇到有关优化方面的问题。由于维数高、局部极值点多、约束条件限制等困难，传统算法在解决优化问题时存在很大的困难，而进化算法则表现出良好优化能力。
本文致力于研究基于进化计算的单目标优化问题。所获主要结果如下：
（1）在解决单目标无约束优化问题时，已有的差异进化算法尽管具有较强的全局搜索能力，但其局部搜索能力具有较大局限性，有可能导致较差的搜索精细度。为了克服该算法的上述缺陷，本文构造了一类建立在搜索个体邻域基础上的新的差异进化算法（简记为LiNDE）。新算法在保持较强的全局搜索能力的基础上，增加了对邻域的搜索，从而大幅度提高了算法的局部搜索能力和搜索精细度。第二章中的数值试验结果表明LiNDE算法比已有的SANSDE算法、SaDE算法和NSDE算法的实际计算效果更好。该算法有创新性，其实用性和可靠性得到验证。
（2）为了使智能算法在进化过程中具有更好的适应性，设计了基于生命周期的新算法（简记为LIO）。LIO算法能较好地模拟高级智能生物在其生命过程中生长、成熟直至凋亡的全过程。新算法将优化过程分成三个阶段，即前期的学习阶段、空间探测阶段与结构重组阶段。第三章中的数值试验结果表明LIO算法比已有的CSA/FC算法、CSA/RC算法和CSA/SC算法的实际计算效果更好。该算法有创新性和较好的实际计算效果。
（3）结合优化技术以及佳点集理论，改进了已有的交叉算子，构造了一类建立在佳点集交叉算子算法(简记为COAGPN)，该算法能更为有效地搜索有界闭区域中的佳点集合，这个点集是闭区域中最能代表该有界闭区域特征的点集。第四章中的数值试验结果表明COAGPN算法比已有的SAFF算法和SMES算法实际计算效果更好。
Many optimization problems exist widely in scientific research and engineeringapplication. With the increasing of dimension, the number of local optima andconstrained condition, the classical optimization algorithms are difficult to obtainqualified solution. However the evolutionary algorithms perform well.
To solve single-objective unconstrained single-objective optimization problemand single-objective multiple constrained optimization problems, the evolutionaryalgorithms are employed. The qualities of optimization problem solutions areimproved by modifying the exploring and exploiting ability of evolutionaryalgorithms. The research results are profound and systematic. The Main resultsinclude the followings:
(1) In order to improve the ability of neighborhood search of differentialevolutionary (DE) algorithm, we propose a new variant of DE with linearneighborhood search, called LiNDE, for global optimization problems (GOPs).LiNDE employs a linear combination of triple vectors taken randomly fromevolutionary population. The main characteristics of LiNDE are less parameters andpowerful neighborhood search ability. Experimental studies are carried out on abenchmark set, and the results show that LiNDE significantly improved theperformance of DE. A ccording to experimental results of LiNDE, we can learn thatLiNDE is better than SANSDE, SaDE and NSDE. LiNDE has innovation.
(2) In order to exploit and preserve the diversity of immune optimizationalgorithm when solving high dimensional global optimization problems, a novelevolutionary optimization algorithm based lifespan (LIO) model is proposed. LIOincorporates a lifespan model, local and global search procedure to improve theoverall performance in solving global optimization instance. The experimental resultsof the LIO are significantly better than that of the conventional clonal selectionalgorithm (CSA) in terms of the performance evaluation criterion proposed.According to experimental results of LIO, we can learn that LIO is better thanCSA/FC, CSA/RC and CSA/SC. LIO has innovation.
(3) A new hybrid Good Point set algorithm is applied to solve the constrainedproblems. Good Points Set, can make the local search achieve the same sound results just as the state-of-the-art methods do, such as orthogonal method. But the precisionof the algorithm is not confined by the dimension of the space. An integratedmechanism is used to enrich the exploration and exploitation abilities of the approachproposed. Experiment results on a set of benchmark problems show the efficiency ofthe algorithm. According to experimental results of COAGPN, we can learn thatCOAGPN is better than SAFFand SMES.
本文致力于研究基于进化计算的单目标优化问题。所获主要结果如下：
（1）在解决单目标无约束优化问题时，已有的差异进化算法尽管具有较强的全局搜索能力，但其局部搜索能力具有较大局限性，有可能导致较差的搜索精细度。为了克服该算法的上述缺陷，本文构造了一类建立在搜索个体邻域基础上的新的差异进化算法（简记为LiNDE）。新算法在保持较强的全局搜索能力的基础上，增加了对邻域的搜索，从而大幅度提高了算法的局部搜索能力和搜索精细度。第二章中的数值试验结果表明LiNDE算法比已有的SANSDE算法、SaDE算法和NSDE算法的实际计算效果更好。该算法有创新性，其实用性和可靠性得到验证。
（2）为了使智能算法在进化过程中具有更好的适应性，设计了基于生命周期的新算法（简记为LIO）。LIO算法能较好地模拟高级智能生物在其生命过程中生长、成熟直至凋亡的全过程。新算法将优化过程分成三个阶段，即前期的学习阶段、空间探测阶段与结构重组阶段。第三章中的数值试验结果表明LIO算法比已有的CSA/FC算法、CSA/RC算法和CSA/SC算法的实际计算效果更好。该算法有创新性和较好的实际计算效果。
（3）结合优化技术以及佳点集理论，改进了已有的交叉算子，构造了一类建立在佳点集交叉算子算法(简记为COAGPN)，该算法能更为有效地搜索有界闭区域中的佳点集合，这个点集是闭区域中最能代表该有界闭区域特征的点集。第四章中的数值试验结果表明COAGPN算法比已有的SAFF算法和SMES算法实际计算效果更好。
Many optimization problems exist widely in scientific research and engineeringapplication. With the increasing of dimension, the number of local optima andconstrained condition, the classical optimization algorithms are difficult to obtainqualified solution. However the evolutionary algorithms perform well.
To solve single-objective unconstrained single-objective optimization problemand single-objective multiple constrained optimization problems, the evolutionaryalgorithms are employed. The qualities of optimization problem solutions areimproved by modifying the exploring and exploiting ability of evolutionaryalgorithms. The research results are profound and systematic. The Main resultsinclude the followings:
(1) In order to improve the ability of neighborhood search of differentialevolutionary (DE) algorithm, we propose a new variant of DE with linearneighborhood search, called LiNDE, for global optimization problems (GOPs).LiNDE employs a linear combination of triple vectors taken randomly fromevolutionary population. The main characteristics of LiNDE are less parameters andpowerful neighborhood search ability. Experimental studies are carried out on abenchmark set, and the results show that LiNDE significantly improved theperformance of DE. A ccording to experimental results of LiNDE, we can learn thatLiNDE is better than SANSDE, SaDE and NSDE. LiNDE has innovation.
(2) In order to exploit and preserve the diversity of immune optimizationalgorithm when solving high dimensional global optimization problems, a novelevolutionary optimization algorithm based lifespan (LIO) model is proposed. LIOincorporates a lifespan model, local and global search procedure to improve theoverall performance in solving global optimization instance. The experimental resultsof the LIO are significantly better than that of the conventional clonal selectionalgorithm (CSA) in terms of the performance evaluation criterion proposed.According to experimental results of LIO, we can learn that LIO is better thanCSA/FC, CSA/RC and CSA/SC. LIO has innovation.
(3) A new hybrid Good Point set algorithm is applied to solve the constrainedproblems. Good Points Set, can make the local search achieve the same sound results just as the state-of-the-art methods do, such as orthogonal method. But the precisionof the algorithm is not confined by the dimension of the space. An integratedmechanism is used to enrich the exploration and exploitation abilities of the approachproposed. Experiment results on a set of benchmark problems show the efficiency ofthe algorithm. According to experimental results of COAGPN, we can learn thatCOAGPN is better than SAFFand SMES.
引文
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