基于knee points的改进多目标人工蜂群算法
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40 2018，54（2）
Computer Engineering and Applications 计算机工程与应用
基于 knee points 的改进多目标人工蜂群算法
刘明辉 1，李 炜 2
LIU Minghui1, LI Wei2
1. 安徽大学 计算智能与信号处理重点实验室，合肥 230039 2. 安徽大学 计算机与科学与技术学院，合肥 230601 1.Key Laboratory of ICSP, Ministry of Education, Anhui University, Hefei 230039, China 2.School of Computer Science and Technology, Anhui ity, Hefei 230601, China
Abstract：There exist some problems that the traditional Artificial Bee Colony algorithm（ABC）and its extension in multi objec（t MOABC）has a slow convergence speed, easily falling into local minima, optimization accuracy lost and other issues under the condition of high dimension, multi peak function. Based on the characteristic of knee points that it can improve convergence and distribution, an algorithm that rapidly identificates the knee points is designed in this paper and applied to the MOABC, it proposes the improved Multi-Objective Artificial Bee Colony algorithm based on the strategy of Knee point（KnMOABC）. In the iterative process, the pareto dominating relation is taken into account firstly, and the knee points are selected as the individuals for next generation, which greatly enhances the convergence speed of the algorithm, at the same time, an adaptive strategy is added into the knee point recognition algorithm to ensure the distributivity of the algorithm. The experimental results show that the performance of KnMOABC is better than that of the three latest multi-objective artificial bee colony algorithm. Key words：multi- objective artificial bee colony algorithm; high- dimensional and multimodal functions; knee points; adaptive identification strategy
LIU Minghui, LI Wei. Improved multi- objective artificial bee colony algorithm based on knee points. Computer Engineering and Applications, 2018, 54（2）：40-47.
摘 要：传统的人工蜂群算法（Artificial Bee Colony algorithm，ABC）及其在多目标上的扩展（Multi Objective Artificial Bee Colony algorithm，MOABC）存在着在高维、多峰函数情况下收敛速度变慢、后期容易陷入局部最优以及 寻优精度丢失等问题。基于 knee points 提高收敛性和分布性的特点，设计了一种快速识别 knee point 的算法并将其 应用到多目标人工蜂群算法中，提出了一种基于 knee points 的改进多目标人工蜂群算法（KnMOABC）。算法在迭 代过程中考虑 pareto 支配关系的同时，优先选择 knee point 作为下一代个体，极大地增强了算法的收敛速度，同时， 在 knee point 识别算法中加入自适应的策略以保持良好的分布性。实验结果表明，KnMOABC 的性能优于三个最新 的多目标人工蜂群对比算法。 关键词：多目标人工蜂群算法 ；高维多峰函数 ；knee points；自适应识别策略 文献标志码：A 中图分类号：TP751 doi：10.3778/j.issn.1002-8331.1711-0020
1 引言
多目标优化（包含多于一个目标函数）已经应用在 生活中的许多领域，如制造流程优化，工程设计，以及化 学工程 。 [1] 通常情况下，多目标优化的各个优化目标之 间是相互矛盾的，不存在一个可使所有目标同时达到最 优的解，而是需要得到一个 Pareto 最优解的集合，这些
解应尽可能逼近理论最优的 pareto 解集[2]。群智能优化 算法可用于找出多目标优化问题的一组非支配解，由于 算法的固有的并行性以及其具有通过重新组合相似的 解来找到较优解的能力，算法在有限循环之后一般能够 找到一组近似较优解[3]。
Computer Engineering and Applications 计算机工程与应用
基于 knee points 的改进多目标人工蜂群算法
刘明辉 1，李 炜 2
LIU Minghui1, LI Wei2
1. 安徽大学 计算智能与信号处理重点实验室，合肥 230039 2. 安徽大学 计算机与科学与技术学院，合肥 230601 1.Key Laboratory of ICSP, Ministry of Education, Anhui University, Hefei 230039, China 2.School of Computer Science and Technology, Anhui ity, Hefei 230601, China
Abstract：There exist some problems that the traditional Artificial Bee Colony algorithm（ABC）and its extension in multi objec（t MOABC）has a slow convergence speed, easily falling into local minima, optimization accuracy lost and other issues under the condition of high dimension, multi peak function. Based on the characteristic of knee points that it can improve convergence and distribution, an algorithm that rapidly identificates the knee points is designed in this paper and applied to the MOABC, it proposes the improved Multi-Objective Artificial Bee Colony algorithm based on the strategy of Knee point（KnMOABC）. In the iterative process, the pareto dominating relation is taken into account firstly, and the knee points are selected as the individuals for next generation, which greatly enhances the convergence speed of the algorithm, at the same time, an adaptive strategy is added into the knee point recognition algorithm to ensure the distributivity of the algorithm. The experimental results show that the performance of KnMOABC is better than that of the three latest multi-objective artificial bee colony algorithm. Key words：multi- objective artificial bee colony algorithm; high- dimensional and multimodal functions; knee points; adaptive identification strategy
LIU Minghui, LI Wei. Improved multi- objective artificial bee colony algorithm based on knee points. Computer Engineering and Applications, 2018, 54（2）：40-47.
摘 要：传统的人工蜂群算法（Artificial Bee Colony algorithm，ABC）及其在多目标上的扩展（Multi Objective Artificial Bee Colony algorithm，MOABC）存在着在高维、多峰函数情况下收敛速度变慢、后期容易陷入局部最优以及 寻优精度丢失等问题。基于 knee points 提高收敛性和分布性的特点，设计了一种快速识别 knee point 的算法并将其 应用到多目标人工蜂群算法中，提出了一种基于 knee points 的改进多目标人工蜂群算法（KnMOABC）。算法在迭 代过程中考虑 pareto 支配关系的同时，优先选择 knee point 作为下一代个体，极大地增强了算法的收敛速度，同时， 在 knee point 识别算法中加入自适应的策略以保持良好的分布性。实验结果表明，KnMOABC 的性能优于三个最新 的多目标人工蜂群对比算法。 关键词：多目标人工蜂群算法 ；高维多峰函数 ；knee points；自适应识别策略 文献标志码：A 中图分类号：TP751 doi：10.3778/j.issn.1002-8331.1711-0020
1 引言
多目标优化（包含多于一个目标函数）已经应用在 生活中的许多领域，如制造流程优化，工程设计，以及化 学工程 。 [1] 通常情况下，多目标优化的各个优化目标之 间是相互矛盾的，不存在一个可使所有目标同时达到最 优的解，而是需要得到一个 Pareto 最优解的集合，这些
解应尽可能逼近理论最优的 pareto 解集[2]。群智能优化 算法可用于找出多目标优化问题的一组非支配解，由于 算法的固有的并行性以及其具有通过重新组合相似的 解来找到较优解的能力，算法在有限循环之后一般能够 找到一组近似较优解[3]。
