族群进化算法及其在全局函数优化和电力经济负荷分配中的应用研究
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摘要
电力经济负荷分配问题(economic load dispatch,简称ELD)是电力系统运营中面临的一类优化问题。由于该问题可归为一类高维、非线性、多约束的函数优化问题,因此寻找一种高效的函数优化算法成为了求解这类问题的关键。进化算法(evolutionary algorithms,简称EAs)是一种模拟自然进化过程的全局优化方法,实践证明EA是一种有效的函数优化算法,但其收敛速度慢,容易早熟等缺点严重影响着EA的实用效果。本文通过引入族群进化的思想和方法,设计了一种新的进化算法-族群进化算法(ethnic group evolution algorithm,简称EGEA)。通过对大量无约束最优化问题和约束最优化问题的优化实验证明EGEA具有较好的搜索效率和抗早熟能力,是一种有效的函数优化算法。在此基础上,本研究成功将EGEA应用到了电力经济负荷分配中。主要工作包括以下内容：
提出了族群进化的基本概念和方法,并首先从二进制编码这个角度来尝试进行族群聚类,实现了一种族群进化算法-EGEA/Binary。该算法使用竞争指数作为评估个体价值的指标,并基于族群组织来控制群体的繁殖过程,同时利用族群的分类能力来筛选典型个体并挖掘蕴含于其中的经验性知识。族群的繁殖和自学习过程形成了一种互补的进化模式,本研究称之为双轨协同进化机制。通过对18个各种类型UCOP的优化实验表明EGEA/Binary不仅是可行的,而且是有效的。
由于EGEA/Binary具有特殊的群体结构,常规的选择方式并不完全适合于EGEA/Binary的迭代过程,因此提出了一种基于竞争指数的模拟退火排序选择算子,通过对12个高维UCOP的优化实验证明该算子是一种适合于EGEA/Binary的选择模式,它不仅易于操作而且能够在保证EGEA/Binary收敛稳定性的同时显著提高该算法的收敛速度。
通过分析交叉点规模对交叉算子空间搜索能力的影响,发现随群体状态的演变交叉算子对交叉点规模的选择是一个需要动态优化的过程。针对此问题提出了使用分阶段调整策略、随机分配策略以及白适应进化策略三种方法来对交叉点规模进行动态调控,并提出利用自适应进化策略来发现交叉点规模控制知识,而将产生的知识应用于随机分配策略中作为实际应用的方法。对多个UCOP的实验也证明了这种交叉模式的优越性能。将这种交叉模式应用于EGEA/Binary的实验结果显示,它能够显著提高EGEA/Binary的搜索效率。
针对二进制编码的缺陷提出将族群进化机制扩展到基于实数编码的进化算法,并设计了一种利用层次聚类过程针对实数编码个体进行的族群聚类方法,同时实现了另一种族群进化算法-EGEA/Hierarchic。使用10个高维UCOP和6个混合函数以及13个标准COP来测试EGEA/Hierarchic的性能,实验结果与权威文献中其它典型算法实验数据的比较显示EGEA/Hierarchic是一种有竞争力的函数优化算法。
提出应用EGEA/Binary与EGEA/Hierarchic两种有效的EGEA来求解ELD问题,并对IEEE的3机6母线系统、3机系统、6机系统、15机系统以及20机系统5个仿真系统进行了测试实验。在对IEEE的3机6母线系统和20机系统的实验中,EGEA/Binary与EGEA/Hierarchic搜索到的结果非常接近于现有文献中的最佳结果,而对IEEE的3机系统、6机系统、15机系统这三个的优化结果则要优于已报道的最佳结果。综合以上实验结果,可以说EGEA是一种对ELD问题非常有效的优化方法。
The economic load dispatch (ELD) problem is one of the important optimization problems in power systems that has the objective of dividing the power demand among the online generators economically while satisfying various constraints. Since ELD problem belongs to a kind of multidimensioned, discrete, nonlinear constrained numerical optimization problem, so the key of solving ELD problem is to find an effective numerical optimization algorithm. The practices prove that evolutionary algorithms (EAs) are good at global numerical optimization, which are simulated by the evolution process of nature. But some defects of EAs, such as premature convergence or converging slowly, have a heavily negative impact on the application of EAs for global numerical optimization. Enlightened by the conception of ethnic group in social science and making use of ethnic group as a view to analyze the structure and evolutionary tendency of population, a novel evolution algorithm, ethnic group evolution algorithm (EGEA), is proposed. The simulation tests prove EGEA is good at global numerical optimization. So we apply EGEA to solve ELD problem and get a good effort. The main achievements are so follows:
Firstly, a kind of ethnic group evolution algorithm (EGEA/Binary), with a dual track co-evolution process and special ethnic group operators, is designed for binary coding. Race exponent, a new evaluation criterion, is designed to measure the competitive capacity of individual, which develops from the idea of keeping population balance between fitness growth and individual diversity. The simulation tests of classical function and challenging composition test function show that the EGEA/Binary can restrain premature convergence phenomenon effectively during the evolutionary process while increasing the search efficiency greatly.
For the evaluation indicator and searching mechanism is different to conventional evolutionary algorithm, so it is necessary to research the selection mechanism of EGEA/Binary. We compare and analyze the performance of EGEA/Binary with several conventional selection operators for high dimensions numerical optimization problem, which make use of population and ethnic group as the selection unit and make use of fitness and race exponent as the selection indicator parameter separately, and find the capabilities of selection operator to adjust ethnic group convergence pressure are influence on the performance of EGEA/Binary heavily. Then, a novel selection operator, race exponent based annealing rank selection, is proposed, and the simulations show this selection operator can improve the search efficiency of EGEA/Binary greatly.
Based on the analysis of relationship between crossover scale and reachable subspace of crossover operator, we find the crossover scale should be dynamically adjusted to population structure. Three control mechanisms, the well-phased control strategy, the random distribution strategy and the adaptation evolution strategy, are built up to adjust the crossover scale. The simulation tests of classical function show these optimization mechanisms are availably, and a kind of valuable control knowledge of crossover scale for multi-dimension functions have been generated by the adaptation evolution strategy.
For binary code has some defects, so we transplant the ethnic group evolution mechanism into real code population and design another kind of ethnic group evolution algorithm--EGEA/Hierarchic. In EGEA/Hierarchic, a kind of ethnic group clusting methond based on hierarchy clustering process is used to create ethnic group organization. The comparisons between EGEA/Hierarchic and other typical algorithm for 10 typical UCOPs,6 composition functions and 13 typical COPs show EGEA/Hierarchic is a competent algorithm for solving global numerical optimization problem.
Finally, we use EGEA/Binary and EGEA/Hierarchic to solve ELD problem. Five IEEE simulation system, including 3 thermal units and 6 buses system,3 thermal units system,6 thermal units system,15 thermal units system,20 thermal units system whose incremental fuel cost function took into account the valve-point effects, transmission loss and other constrains, which have been used to test the performance of EGEA/Binary and EGEA/Hierarchic. The simulation results show that EGEA/Binary and EGEA/Hierarchic have more superior performance when compared with other algorithms in the newest literatures.
提出了族群进化的基本概念和方法,并首先从二进制编码这个角度来尝试进行族群聚类,实现了一种族群进化算法-EGEA/Binary。该算法使用竞争指数作为评估个体价值的指标,并基于族群组织来控制群体的繁殖过程,同时利用族群的分类能力来筛选典型个体并挖掘蕴含于其中的经验性知识。族群的繁殖和自学习过程形成了一种互补的进化模式,本研究称之为双轨协同进化机制。通过对18个各种类型UCOP的优化实验表明EGEA/Binary不仅是可行的,而且是有效的。
由于EGEA/Binary具有特殊的群体结构,常规的选择方式并不完全适合于EGEA/Binary的迭代过程,因此提出了一种基于竞争指数的模拟退火排序选择算子,通过对12个高维UCOP的优化实验证明该算子是一种适合于EGEA/Binary的选择模式,它不仅易于操作而且能够在保证EGEA/Binary收敛稳定性的同时显著提高该算法的收敛速度。
通过分析交叉点规模对交叉算子空间搜索能力的影响,发现随群体状态的演变交叉算子对交叉点规模的选择是一个需要动态优化的过程。针对此问题提出了使用分阶段调整策略、随机分配策略以及白适应进化策略三种方法来对交叉点规模进行动态调控,并提出利用自适应进化策略来发现交叉点规模控制知识,而将产生的知识应用于随机分配策略中作为实际应用的方法。对多个UCOP的实验也证明了这种交叉模式的优越性能。将这种交叉模式应用于EGEA/Binary的实验结果显示,它能够显著提高EGEA/Binary的搜索效率。
针对二进制编码的缺陷提出将族群进化机制扩展到基于实数编码的进化算法,并设计了一种利用层次聚类过程针对实数编码个体进行的族群聚类方法,同时实现了另一种族群进化算法-EGEA/Hierarchic。使用10个高维UCOP和6个混合函数以及13个标准COP来测试EGEA/Hierarchic的性能,实验结果与权威文献中其它典型算法实验数据的比较显示EGEA/Hierarchic是一种有竞争力的函数优化算法。
提出应用EGEA/Binary与EGEA/Hierarchic两种有效的EGEA来求解ELD问题,并对IEEE的3机6母线系统、3机系统、6机系统、15机系统以及20机系统5个仿真系统进行了测试实验。在对IEEE的3机6母线系统和20机系统的实验中,EGEA/Binary与EGEA/Hierarchic搜索到的结果非常接近于现有文献中的最佳结果,而对IEEE的3机系统、6机系统、15机系统这三个的优化结果则要优于已报道的最佳结果。综合以上实验结果,可以说EGEA是一种对ELD问题非常有效的优化方法。
The economic load dispatch (ELD) problem is one of the important optimization problems in power systems that has the objective of dividing the power demand among the online generators economically while satisfying various constraints. Since ELD problem belongs to a kind of multidimensioned, discrete, nonlinear constrained numerical optimization problem, so the key of solving ELD problem is to find an effective numerical optimization algorithm. The practices prove that evolutionary algorithms (EAs) are good at global numerical optimization, which are simulated by the evolution process of nature. But some defects of EAs, such as premature convergence or converging slowly, have a heavily negative impact on the application of EAs for global numerical optimization. Enlightened by the conception of ethnic group in social science and making use of ethnic group as a view to analyze the structure and evolutionary tendency of population, a novel evolution algorithm, ethnic group evolution algorithm (EGEA), is proposed. The simulation tests prove EGEA is good at global numerical optimization. So we apply EGEA to solve ELD problem and get a good effort. The main achievements are so follows:
Firstly, a kind of ethnic group evolution algorithm (EGEA/Binary), with a dual track co-evolution process and special ethnic group operators, is designed for binary coding. Race exponent, a new evaluation criterion, is designed to measure the competitive capacity of individual, which develops from the idea of keeping population balance between fitness growth and individual diversity. The simulation tests of classical function and challenging composition test function show that the EGEA/Binary can restrain premature convergence phenomenon effectively during the evolutionary process while increasing the search efficiency greatly.
For the evaluation indicator and searching mechanism is different to conventional evolutionary algorithm, so it is necessary to research the selection mechanism of EGEA/Binary. We compare and analyze the performance of EGEA/Binary with several conventional selection operators for high dimensions numerical optimization problem, which make use of population and ethnic group as the selection unit and make use of fitness and race exponent as the selection indicator parameter separately, and find the capabilities of selection operator to adjust ethnic group convergence pressure are influence on the performance of EGEA/Binary heavily. Then, a novel selection operator, race exponent based annealing rank selection, is proposed, and the simulations show this selection operator can improve the search efficiency of EGEA/Binary greatly.
Based on the analysis of relationship between crossover scale and reachable subspace of crossover operator, we find the crossover scale should be dynamically adjusted to population structure. Three control mechanisms, the well-phased control strategy, the random distribution strategy and the adaptation evolution strategy, are built up to adjust the crossover scale. The simulation tests of classical function show these optimization mechanisms are availably, and a kind of valuable control knowledge of crossover scale for multi-dimension functions have been generated by the adaptation evolution strategy.
For binary code has some defects, so we transplant the ethnic group evolution mechanism into real code population and design another kind of ethnic group evolution algorithm--EGEA/Hierarchic. In EGEA/Hierarchic, a kind of ethnic group clusting methond based on hierarchy clustering process is used to create ethnic group organization. The comparisons between EGEA/Hierarchic and other typical algorithm for 10 typical UCOPs,6 composition functions and 13 typical COPs show EGEA/Hierarchic is a competent algorithm for solving global numerical optimization problem.
Finally, we use EGEA/Binary and EGEA/Hierarchic to solve ELD problem. Five IEEE simulation system, including 3 thermal units and 6 buses system,3 thermal units system,6 thermal units system,15 thermal units system,20 thermal units system whose incremental fuel cost function took into account the valve-point effects, transmission loss and other constrains, which have been used to test the performance of EGEA/Binary and EGEA/Hierarchic. The simulation results show that EGEA/Binary and EGEA/Hierarchic have more superior performance when compared with other algorithms in the newest literatures.
引文
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