基于量子衍生方法的粒子群多目标优化算法
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摘要
常用的多目标优化方法自身的不足及其在实际应用中存在的诸多困难,一直阻碍着多目标优化方法的发展。在20世纪80年代中期,进化算法开始应用于解决多目标优化问题。目前涌现了多种多目标进化算法,其中一些已成功应用到实际应用中,从而形成了一个热门研究领域。量子粒子群算法是将量子计算与粒子群算法相结合的一种崭新的优化方法,具有很强的生命力和极大的研究价值。量子算法中融入了量子力学的许多基本特性,极大地提高了计算的效率,已逐步成为一种崭新的计算模式。
量子粒子群算法大大提高了搜索效率且能弥补粒子群算法容易早熟的不足,具有广泛的研究前景。本文的主要工作和研究成果如下:
1.在分析当前多目标优化算法的优缺点的基础上,针对求解多目标优化中存在的收敛性不够好,分布不均匀的问题,本文将量子理论引入粒子群算法,提出一种基于量子衍生方法的多目标粒子群算法,该算法采用Pareto支配关系来更新粒子的个体最优值和全局最优值,通过定义极大极小距离,并使用该距离方法来裁减非支配解。
2.将该算法应用于多维0-1背包问题,实验结果表明该算法具有较强的搜索能力和寻优效率,与NSGA2算法和SPEA2算法相比在Pareto解集的收敛性指标上有提高,尤其适用于高维复杂函数的优化。
3.将提出的算法应用于军队任务调度和指派的高级逻辑问题。并根据高级逻辑问题中参数多,约束条件加法和为1的特点,提出一种面向和约束的方法,采用三角公式转化约束条件,节约了存储空间的同时也提高了搜索效率。结果表明该方法的可行性和有效性。
The deficiencies of ordinary multi-objective optimization algorithms, together with their implement problems in reality, always prevent the objective optimization methods from development. In the mid-1980s, Evolutionary Algorithm was introduced to solve the Multi-objective Optimization Problem. A variety of Multi-objective Evolutionary Algorithms are proposed at present. Some of them have been successfully applied to practical applications. More and more researchers begin to engage in this field. Quantum Particle Swarm
Optimization algorithm (QPSO) is a new optimum method that combines quantum computation with Particle Swarm Optimization (PSO). It appears strong life-force and be valuable for research. Quantum computation absorbed many essential characters of quantum mechanics, which improved the computation efficiency, and become a brand new model of computation.
QPSO has greatly enhanced the efficiency of search and can prevent premature of PSO and it has a wide research foreground. The following are the major contributions:
1. On the basis of analyzing the advantages and disadvantages of Multi-objective Optimization algorithms, this article presents a Quantum-bit Particle Swarm Optimization (QBPSO) algorithm for Multi-objective Optimization Problems so as to improve the convergence and it is well-distributed. QBPSO adopts the non-dominated storing method for solutions population and use a new population diversity preserving strategy which is based on the Pareto max-min distance.
2. The multidimensional 0-1knapsack problems are tested and the results show that the proposed method can efficiently find Pareto optimal solutions that are closer to Pareto font and better on distribution. Compared with NSGA2 and SPEA2, the value of S increases 11.10% and 11.06% on avenge. Especially, this proposed method is outstanding on more complex high-dimensional optimization problems.
3. Apply our method on Advanced Logistics Problem (ALP) of army’s assignment and scheduling. Generally speaking, there are many parameters in ALP and sum of them is always
1. According to this character, we proposed a new sum constraint oriented method, in which trigonometric formulas are used to transform constraint condition, so as to save storage space and improve the search efficiency. The experimental results indict its feasibility and effectiveness.
量子粒子群算法大大提高了搜索效率且能弥补粒子群算法容易早熟的不足,具有广泛的研究前景。本文的主要工作和研究成果如下:
1.在分析当前多目标优化算法的优缺点的基础上,针对求解多目标优化中存在的收敛性不够好,分布不均匀的问题,本文将量子理论引入粒子群算法,提出一种基于量子衍生方法的多目标粒子群算法,该算法采用Pareto支配关系来更新粒子的个体最优值和全局最优值,通过定义极大极小距离,并使用该距离方法来裁减非支配解。
2.将该算法应用于多维0-1背包问题,实验结果表明该算法具有较强的搜索能力和寻优效率,与NSGA2算法和SPEA2算法相比在Pareto解集的收敛性指标上有提高,尤其适用于高维复杂函数的优化。
3.将提出的算法应用于军队任务调度和指派的高级逻辑问题。并根据高级逻辑问题中参数多,约束条件加法和为1的特点,提出一种面向和约束的方法,采用三角公式转化约束条件,节约了存储空间的同时也提高了搜索效率。结果表明该方法的可行性和有效性。
The deficiencies of ordinary multi-objective optimization algorithms, together with their implement problems in reality, always prevent the objective optimization methods from development. In the mid-1980s, Evolutionary Algorithm was introduced to solve the Multi-objective Optimization Problem. A variety of Multi-objective Evolutionary Algorithms are proposed at present. Some of them have been successfully applied to practical applications. More and more researchers begin to engage in this field. Quantum Particle Swarm
Optimization algorithm (QPSO) is a new optimum method that combines quantum computation with Particle Swarm Optimization (PSO). It appears strong life-force and be valuable for research. Quantum computation absorbed many essential characters of quantum mechanics, which improved the computation efficiency, and become a brand new model of computation.
QPSO has greatly enhanced the efficiency of search and can prevent premature of PSO and it has a wide research foreground. The following are the major contributions:
1. On the basis of analyzing the advantages and disadvantages of Multi-objective Optimization algorithms, this article presents a Quantum-bit Particle Swarm Optimization (QBPSO) algorithm for Multi-objective Optimization Problems so as to improve the convergence and it is well-distributed. QBPSO adopts the non-dominated storing method for solutions population and use a new population diversity preserving strategy which is based on the Pareto max-min distance.
2. The multidimensional 0-1knapsack problems are tested and the results show that the proposed method can efficiently find Pareto optimal solutions that are closer to Pareto font and better on distribution. Compared with NSGA2 and SPEA2, the value of S increases 11.10% and 11.06% on avenge. Especially, this proposed method is outstanding on more complex high-dimensional optimization problems.
3. Apply our method on Advanced Logistics Problem (ALP) of army’s assignment and scheduling. Generally speaking, there are many parameters in ALP and sum of them is always
1. According to this character, we proposed a new sum constraint oriented method, in which trigonometric formulas are used to transform constraint condition, so as to save storage space and improve the search efficiency. The experimental results indict its feasibility and effectiveness.
引文
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[2] 崔逊学,方廷健.多目标进化算法研究.中国科学基金,2002,16:17-19
[3] Eckart Z, K alyanmoy Deb. Comparison of multi-objective evolutionary algorithms: empirical results. evolutionary computation, 2008, (2): 173-195
[4] Carlos A.A Proposal for Multiple Objective Particle Swarm Optimization.In: Proceedings of Congress on Evolutionary computation(CEC'2002).New Jersey: 2002, 1051-1056
[5] Schaffer J D.Multiple objective optimization with vector evaluated genetic algori- thms.In: Proceedings of the first International Conference on Genetic Algorithms.1985: 99-100
[6] Fonseca C M, Fleming P J.Genetic algorithms for Multiobjective optimization: Formulation, discussion and generalization.In: Proceedings of the fifth International Conference on Genetic Algorithms.California: 1993, 62-69
[7] 张勇德. 智能多目标优化方法及其应用研究. 沈阳:中国科学院沈阳自动化研究所,2005
[8] 孟红云,刘三阳.基于自适应领域选择的多目标免疫进化算法.系统工程与电子技术,2004,26(8):1107-1111
[9] K. E. Parsopoulos, M. N. Vrahatis.Particle Swarm Optimization Method in Multi- objective Problems.In: Proceedings of the 2002 ACM symposium on Applied computing.New York: 2002,603-609
[10] Xiaodong Li.A Non-dominated Sorting Particle Swarm Optimizer for Multiobjective Optimization.In Erick Cant et al. (editors), Genetic and Evolutionary Computation -GECCO 2003, Springer, Lecture Notes in Computer Science Vol. 2723,July 2003, 37-48
[11] Gregodo Toscano-Pulido and Carlos A. Coello Coello. Using Clustering Techniques to Improve the Performance of a Multi-Objective Particle Swam Optimizer. In Kalyanmoy Deb et al. (editors), Genetic and Evolutionary Computation--GECCO 2004. Proceedings of the Genetic and Evolutionary Computation Conference. Part I,Springer-Vedag, Lecture Notes in Computer Science Vol. 3102, Seattle, Washington,USA, June 2004,255-237
[12] Fieldsend, J.E., Singh, S. A Mufti-Objective Algorithm Based upon Particle Swarm Opmization, an Efficient Data Stricture and Turbulence. In: Proceedings of the 2002 U.K. Workshop on Computational Intelligence, Birmingham, UK ,2002, 37-44
[13] Thomas Bartz Beielstein, Philipp Limbourg, et al. Particle Swarm Optimizers for Pareto Opmization with Enhanced Archiving Techniques. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC'2003). Canberra: 2003, 1780-1787
[14] Mostaghim, S, Teich, J. Strategies for Finding Good Local Guides in Multi-objective Particle Swarm Optimization (MOPSO). In: Proceedings of 2003 IEEE Swarm Intel- ligence Symposium. Indianapolis: 2003,26-33
[15] Deb K, Agrawal S, Pratap A and Meyarivan T.A fast elitist non-dominated sorting genetic algorithm for multiobjective optimization: NSGA II.In: Proceedings of Parallel Problem Solving from Nature.Berlin: 2000, 849-859
[16] Rudolph G.. On a multi-objective evolutionary algorithm and its convergence to the pareto set. In: Proceedings of IEEE Conf. on Evolutionary Computation, 1998
[17] Kennedy J, Eberhart R C. Particle swarm optimization. In: Proceeding of 1995 IEEE Intenational Conference on Neural Networks. New York: IEEE, 1995, 1942-1948
[18] Eberhart R C, Kennedy J. A new optimizer using particle swarm theory. In: Proceedings of the Sixth Intenational Symposium on Micro Machine and Human Science. New York: IEEE, 1995, 39-43
[19] 曾建潮,介婧,崔志华.微粒群算法.北京:科学出版社,2004,13-47
[20] Yoshida H, Kawata K, Fukuyama Y, et al. A Particle Swarm Optimization for Reactive Power and Voltage Control Considering Voltage Stability. In: Proceedings of Torres G L, Alves da Silva A P. Eds. Brazil, 1999, 117-121
[21] Y. Shi, R. C. Eberhart. A Modified Particle Swarm Optimizer. In: Proceedings of the IEEE of Evolutionary Computation. Piscataway: IEEE Press, 1998. 69-73
[22] Shi Y, Eberhart R C.Empirical Study of Particle Swarm Optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation. Piscataway, NJ: IEEE Service Center, 1999, 1945-1950
[23] Shi Y, Eberhart R C.Fuzzy Adaptive Particle Swarm Optimization.In: Proc. Congress on Evolutionary Computation 2001. Seoul, Korea: IEEE Service Center, 2001
[24] Clerc M.The Swarm and the Queen: Towards a Deterministic and Adaptive Particle Swarm Optimization.In: Proc.CEC 1999. 1999, 1951-1957
[25] Angeline P J. Using Selection to Improve Particle Swarm Optimization. 1998. Anchorage, Alaska, USA. IEEE International Conference on Evolutionary Computation. 84- 89
[26] Angeline P J. Evolutionary Oprimization Versus Particle Swarm Optimization: Philosophy and Performance Differenves. In: The Seventh Annual Conf. on Evolutionary Programming. 1998
[27] Kennedy J, Eberhart R C. A Discrete Binary Version of the Particle Swarm Algorithm. In: Proceedings of the 1997 Conferenve on Systems, Man, and Cybernetics. Piscataway, NJ: IEEE Service Center, 1997, 4104-4109
[28] V. Cours Pareto. D' Economies Politique, volume I and II. Rouge, Lausanne, 1896
[29] 郑向伟, 刘弘. 多目标进化算法研究进展. 计算机科学, 2007, 34(7): 187-191
[30] 石川, 李清勇, 史忠植. 一种快速的基于占优树的多目标进化算法. 软件学报, 2007, 18(3): 505-516
[31] 闫震宇, 康立山, 付朋辉等. 基于演化算法实现多目标优化的岛屿迁徙模型. 小型微型计算机系统, 2004, 25(2): 237-241
[32] 杨善学, 王宇平. 基于 Pareto 最优和限制精英的多目标进化算法. 计算机工程与应用, 2007, 43(2): 108-110
[33] 侯中喜, 陈小庆, 郭良民. 基于排挤机制改进的多目标进化算法. 国防科技大学学报, 2007, 28(4): 18-21
[34] 王小平, 曹立明.遗传算法——理论?应用与软件实现.西安: 西安交通大学出版社, 2002, 115-122
[35] Fonseca, C, P. Fleming. An overview of evolutionary algorithms in multiobjective optimization, Evolutionary Computation, vol. 3, no.1. 1995, 1-16
[36] Hron J. Multicrterion decision making. Handbook of Evolutionary Computation, New York: 1997
[37] Tamaki H, Kita and S. Kobayashi. Multiobjective optimization by genetic algorithms: a review, 517-522
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