第13卷第5期 智能系统学报 Vol.13 No.5 2018年10月 CAAI Transactions on Intelligent Systems Oct.2018 D0:10.11992/tis.201705007 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.TP.20180426.1120.004html 求解离散优化问题的元胞量子狼群演化算法 马龙，卢才武，顾清华 (西安建筑科技大学管理学院，陕西西安710055) 摘要：针对离散空间优化问题，提出了求解离散优化问题的元胞量子狼群演化算法，首先，为了提高算法的全 局收敛速度，采用双策略量子位初始化方法和滑模交叉方法，分别生成量子狼群初始位置和产生头狼，实现种 群多样性：其次，为了描述头狼与猎物间的距离以及增强狼群的遍历范围，采用二进制编码方式和元胞自动机 中的演化规则，分别实现狼群中个体狼与猎物距离的精确描述和量子旋转角的选取调整：然后，为了证明该算 法的收敛性能，采用泛函分析方法，实现了算法全局收敛性能的验证：最后，通过6个标准测试函数的仿真实 验，并与狼群算法以及量子狼群算法的优化结果进行比较。实验结果表明，该算法具有较快的收敛速度和较好 的全局寻优能力。 关键词：离散优化：量子狼群算法：元胞自动机：双策略方法：滑模交叉：二进制编码：泛函分析：狼群算法：量子 旋转角 中图分类号：TP301.6文献标志码：A文章编号：1673-4785(2018)05-0716-12 中文引用格式：马龙，卢才武，顾清华.求解离散优化问题的元胞量子狼群演化算法J川.智能系统学报，2018,13(5)： 716-727. 英文引用格式：MA Long,LUCaiwu,,GU Qinghua..Cellular and quantum-behaved wolf pack evolutionary algorithm for solving discrete optimization problems J.CAAI transactions on intelligent systems,2018,13(5):716-727. Cellular and quantum-behaved wolf pack evolutionary algorithm for solving discrete optimization problems MA Long,LU Caiwu,GU Qinghua (School of Management,Xi'an University of Architecture and Technology,Xi'an 710055,China) Abstract:To solve optimization problems in discrete space,a cellular quantum-inspired wolf pack evolutionary al- gorithm is proposed for solving discrete optimization problems.First,to speed up the global convergence of the al- gorithm,when generating the diversity of population,the method fully utilizes the double strategy quantum bit initializa- tion method and the sliding mode crossover method to help generate the initial position and candidate wolf,respectively. Then,to accurately describe the distance between the wolf and the prey as well as enhance the traverse range of wolf pack,the methods of the binary encoding and evolution rules of the cellular automata are used to realize precise descrip- tion and the selection of the quantum rotation angle,respectively.Then to prove the convergence performance of the al- gorithm,the method fully utilizes the functional analysis to verify the global convergence.Finally,simulation experi- ment on six benchmark functions was carried out,and the comparison between the wolf pack algorithm and quantum-in- spired wolf pack evolutionary algorithm was provided.The results show that the proposed approach has better conver- gence speed and great global convergence optimization ability. Keywords:discrete optimization;quantum-inspired wolf pack algorithm;cellular automata;double strategy method; sliding mode crossover;binary encoding;functional analysis;wolf pack algorithm;quantum rotation angle 在人工智能计算和系统工程等领域中，许多 收稿日期：2017-05-08.网络出版日期：2018-04-26 基金项目：国家自然科学基金项目(51774228,51404182)：陕西 离散空间优化问题常具有解的多样性、动态性以 省自然科学基金项目(2017JM5043):陕西省教育厅 专项科研计划项目(17K0425). 及目标函数收敛速度慢等特点。为了在有限的空 通信作者：顾清华.E-mail:qinghuagu@(126.com. 间环境下快速搜寻到优化问题的最优解，学者们DOI: 10.11992/tis.201705007 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.TP.20180426.1120.004.html 求解离散优化问题的元胞量子狼群演化算法 马龙，卢才武，顾清华 （西安建筑科技大学 管理学院，陕西 西安 710055） 摘 要：针对离散空间优化问题，提出了求解离散优化问题的元胞量子狼群演化算法，首先，为了提高算法的全 局收敛速度，采用双策略量子位初始化方法和滑模交叉方法，分别生成量子狼群初始位置和产生头狼，实现种 群多样性；其次，为了描述头狼与猎物间的距离以及增强狼群的遍历范围，采用二进制编码方式和元胞自动机 中的演化规则，分别实现狼群中个体狼与猎物距离的精确描述和量子旋转角的选取调整；然后，为了证明该算 法的收敛性能，采用泛函分析方法，实现了算法全局收敛性能的验证；最后，通过 6 个标准测试函数的仿真实 验，并与狼群算法以及量子狼群算法的优化结果进行比较。实验结果表明，该算法具有较快的收敛速度和较好 的全局寻优能力。 关键词：离散优化；量子狼群算法；元胞自动机；双策略方法；滑模交叉；二进制编码；泛函分析；狼群算法；量子 旋转角 中图分类号：TP301.6 文献标志码：A 文章编号：1673−4785(2018)05−0716−12 中文引用格式：马龙, 卢才武, 顾清华. 求解离散优化问题的元胞量子狼群演化算法[J]. 智能系统学报, 2018, 13(5): 716–727. 英文引用格式：MA Long, LU Caiwu, GU Qinghua. Cellular and quantum-behaved wolf pack evolutionary algorithm for solving discrete optimization problems[J]. CAAI transactions on intelligent systems, 2018, 13(5): 716–727. Cellular and quantum-behaved wolf pack evolutionary algorithm for solving discrete optimization problems MA Long，LU Caiwu，GU Qinghua (School of Management, Xi’an University of Architecture and Technology, Xi’an 710055, China) Abstract: To solve optimization problems in discrete space, a cellular quantum-inspired wolf pack evolutionary al￾gorithm is proposed for solving discrete optimization problems. First, to speed up the global convergence of the al￾gorithm, when generating the diversity of population, the method fully utilizes the double strategy quantum bit initializa￾tion method and the sliding mode crossover method to help generate the initial position and candidate wolf, respectively. Then, to accurately describe the distance between the wolf and the prey as well as enhance the traverse range of wolf pack, the methods of the binary encoding and evolution rules of the cellular automata are used to realize precise descrip￾tion and the selection of the quantum rotation angle, respectively. Then to prove the convergence performance of the al￾gorithm, the method fully utilizes the functional analysis to verify the global convergence. Finally, simulation experi￾ment on six benchmark functions was carried out, and the comparison between the wolf pack algorithm and quantum-in￾spired wolf pack evolutionary algorithm was provided. The results show that the proposed approach has better conver￾gence speed and great global convergence optimization ability. Keywords: discrete optimization; quantum-inspired wolf pack algorithm; cellular automata; double strategy method; sliding mode crossover; binary encoding; functional analysis; wolf pack algorithm; quantum rotation angle 在人工智能计算和系统工程等领域中，许多 离散空间优化问题常具有解的多样性、动态性以 及目标函数收敛速度慢等特点。为了在有限的空 间环境下快速搜寻到优化问题的最优解，学者们 收稿日期：2017−05−08. 网络出版日期：2018−04−26. 基金项目：国家自然科学基金项目 (51774228，51404182)；陕西 省自然科学基金项目 (2017JM5043)；陕西省教育厅 专项科研计划项目 (17JK0425). 通信作者：顾清华. E-mail：qinghuagu@126.com. 第 13 卷第 5 期 智 能 系 统 学 报 Vol.13 No.5 2018 年 10 月 CAAI Transactions on Intelligent Systems Oct. 2018